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Science and Math For Adults?
Peter Trepan writes "Like most Americans, I made it through high-school and college without a thorough understanding of major scientific and mathematical concepts. I'm trying to remedy this situation both for personal betterment and so I can supplement my *own* kids' education. The problem is, most textbooks are not designed to convey an understanding of the subject, but to squeeze in all the 'facts' required by state law. I'm looking for books that don't just tell me an equation or a concept works, but also explain *why*. Would you please list books that have helped you gain a greater understanding of the basic concepts of algebra, chemistry, calculus, physics, and other core areas of science?" This is similar to an earlier question, but with a broader focus.
0 + 1 = 1 = First Post !
Feynman has 6 easy/not so easy peices on physics... I enjoyed those. On A whole I will recomend any of his books... Math I'm not sure... I'd like to try and find a math book (that teaches you as much as a text book) thats not as dry as one... For calculus for the easy stuff Learn Calculus the easy way is a interesting concept, its taught through a story.
Too Obvious?
zero, the biography of a dangerous idea by charles seife (sp?)
the god particle, by leon lederman
the particle garden, by someone whose name i can't remember.
good math and good physics. enjoy!
-Leigh
Try enrolling in some night classes at your local Community College if you have the time. It's pretty cheap, and you may be able to get your employer to pay for it.
I wish I had something to offer you, but unfortunately, as a product of the California State Public School System in the 80's and 90's, I'm in much the same boat. I got taught a lot of rules and dates, not a lot of theory or application.
Since this thread may well have people who can be helpful responding in it, though, I'd like to ask quickly: can anyone suggest any good books on calculus as it applies to the physical world (i.e. astronomy, music, etc.)? I've been told by many geeks that calculus is the math that's most applicable in the real world (besides arithmetic, of course), but I've never been able to see how that works.
Thanks in advance!
How To Get Humans To Mars
Stephen Hawking's "Universe in a Nutshell" is a good start on physics and relativity. I've never taken any physics and was able to understand it fairly well.
No, the correct logic is: 1 + 1 = 2 2 * 2 = 4
Calculus Made Easy by Silvanus P. Thompson and Martin Gardner. This is exactly the sort of book you're looking for, in the subject of Calculus. To quote from the preface, on the subject of modern math textbooks: Their exercises have, as one mathematician recently put it, "the dignity of solving crossword puzzles." The purpose of this book is to explain the philosophy of Calculus, and teach you how to differentiate and integrate simple functions. I recommend reading the Preface in a bookstore, skimming the first few chapters. I think you'll like it.
I'm as mimsy as the next borogove but your mome raths are completely outgrabe.
One article that I found interesting A Guide to Infinity
Rus
Cheap UK and US VPS
Any of his non-fiction books, and there's a ton. All subjects, from algebra to the brain to chemistry. (He even wrote about the Bible...)
They say the first thing to go is your penis. Well, it's either that or your brain. I forget which...
You might check out some of the materials on display at ArsDigita University, they have lectures online and a critique of each course, together with a list of texts...personally, Sispser's text for Theory of Computation was very helpful in explaining a lot of the higher-level CS Math.
The solution that most math texts take then is to give you *lots* of problems/drills so that the mechanics get ingrained, allowing the insight to come later.
When I screwed up my second year calculus course *really* badly (like 6% on the midterm...) I used a Schaum's Outline to get back on track (and eventually ace the final). It's main benefit is *heaps* of problems to work through. That made me a convert to the problems approach to math teaching.
The key is to do all the problems, in order.
That said, I can't really recommend one math text over another, just so long as there are lots of problems, and hopefully a solution key in the back for at least half the excercises.
Unfortunately I have no first hand experience, but on Public Radio "Science Friday" this subject came up and there were quite a few hearty endorsements for 'Hurricane Calculus'
http://en.wikipedia.org/wiki/Signature_bloc
I seem to get by in math, but as far as understanding it goes, I just get over. I'm I really going to have to apply these advanced principals that I don't understand in the real world? If so I'm DOOMED!
"Foudations of Mathematics" by Denbow and Goedicke (old, but an amazing book for the understanding of most math concepts) "Mathematical Sorcery" by Clawson (More of a "evolution of modern math concepts")
They really are.
One option is to ask someone who knows better, in HS my math teacher was always looking for books that explained it better.
Find a topic, and pursue it, the local public/college/university library should have some decent books available for details.
Also check the used bookstores, read the book a bit, many professors try to find the best book to explain the concepts. Used outdated books a revision behind tend to have the same quality, and the same information, just new page numbers and diagrams.
you know, come to think about it. this could very well be the reason why I absolutely sucked at math but did exceptionally well in other subjects in school and today? I've allways been the type to understand something as long as it was easily explained to me. With math I always understood it in class but an hour later trying to do the homework completely a noob again. Been accused of being a slacker and all, and spend days totally studying math and still cannot get it.
I've always found it easier to learn something when I know the history of how/ it was developed.
For math, I can definitely recommend "A History of Mathematics" by Carl Boyer
For Physics I would recommend the Feynman lectures highly. In these, he mixes theoretical development with modern application.
Not sure what to tell you about chemistry or other sciences!
KRL
...teach some form of 'Math 002' or Science 101 of some kind. Find your local university and see if they have a weekend/evening program (if you're working) and then go to it, work hard. reading books for betterment is a good thing too, but sometimes it helps to have someone to talk to about it.
As a rock-in-roll Physicist once said, No matter where you go, there you are.
I just got a copy of this and it seems really good so far. It also got good reviews on Amazon.
This post was generated by a Cadre of Uber Monkeys for Monkey-Man2000 (603495).
There are "for Dummies" books that cover many of the topics you've listed. I was never fond of them, but you may want to take a look at them.
The biggest problem when you're undertaking a self-study endeavour is that most books that are available are either
- Very specialized topics (What does pi mean?)
- Refresher-course books (Lots of problems, few explanations)
The specialized topics books - commonly reviewed in magazines such as Scientific American - are fun to read, but I'm not sure if they serve the purpose of what you're seeking.
How much of algebra do you know? If you can look through the table of contents of a textbook for Algebra I and II and are confident in all the topics, then I'd move on to geometry/trigonometry before calculus.
Also, keep in mind that conceptual physics texts are divided between algebra-based and calculus-based reasoning. Take whichever you're more comfortable with.
Some 'refresher-course' books that will come in handy with the conceptual books that others may suggest:
Schaum's Outlines
Research & Education Association's Problem Solvers series
CliffsNotes and SparkNotes
The problem is, most textbooks are designed to be companion references, with all the 'facts' squeezed in so the teacher can spend time helping everyone understand the concepts etc. The two work together.
Simple answer is, you need to take adult education classes. I left college barely half-way through, and ended up taking night classes- intro to calculus was one; another was an intensive Economics class. I found them worthwhile; I probably would have enjoyed the class more if I wasn't young enough to be most of the other student's kid(you would fit in FAR better, from the sounds of it.)
Without the classes, you don't get the benefits of peer learning, in-class interaction("Did everybody get that?" [blank stares] "Heh, ok, let me explain it a different way...") the discipline that testing creates, nor the resource of having a Really Smart Person(professor) to go to when you need help. There are also other benefits- making friends(you're probably all in similar 'boats' so to speak, so people socialize pretty readily), and networking. My old boss decided to do part-time classes for an MBA, and got a lot of networking out of it(granted, those were business classes, more prone to networking activities, but you get the idea).
Please help metamoderate.
The Mathematical Universe:
by William Dunham
It was the first math book I read in high school and I loved it. It is available for $19.95 at www.bn.com It covers a broad area of mathematics with 26 chapters from Arithmatic to Z(The complex plane). Along the way it talks about Riemann, Newton, Euler, Gauss, and many others. Also, it talks about some of the famous problems. Great book.
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bash-2.04$yes "Don't you hate dialup connections?"| write USERNAME
"Mathematics for the Million" by Hogben, Lancelot.
Note that it is not ".. for the Million s "
The real "Libtards" are the Libertarians!
Nothing better for easy reading but comprehensive coverage.
Volume 1 - Motion, Sound, and Heat
Volume 2 - Light, Magnetism, and Electricity
Volume 3 - The Electron, Proton, and Neutron
You need the check out The Teaching Company. I've gone through a a number of their courses on CD, and they've all been superb. I just recently finished their World War II course, and I'm currently doing the Foundations of Western Civilization. Given you're question, you'd probably want to look at their Science & Math offerings. I did the Joy of Science course last year as a refresher for all that stuff I'd forgotten since high school and college, which sounds kind of like what you're looking for. (I've no affiliation with The Teaching Company other than being a satisfied customer.)
Go to the nearest university book store, or even just find the web page for a universities math department and find the text book for the subjects you want and order it online.
I don't think very many text books just give you a equation and say use this. My HS was a poor ass sucky redneck school and didn't do that, we just didn't have much of a variety in subjects. Also I think saying books just do what the states require only applies to states with said systems. Many, maybe most, just say you need to have a class in this that and the other thing.
Also once you get into learning the hows and whys of lots of math you will see why people tend to just want the equation, far less frustrating and confusing for learning. Learning how to do it and then going back for the why is often better for subjects like math. Same for say engineer, it seams a whole lot more fun till your actualy doing it and find out 99% of it sucks big time and is not what you think engineers do.
One book to stay away from if calc. is you game is Thomas Finny, that book sucks beyond belief.
It's certainly not about the "fundamentals" of math and science, but I have to say that the book that did the best at explaining physics and cosmology to a humanities geek like me was *A Brief History of Time*. Hawking filled it with simple explanations and allegory, and in the tradition of *Flatland* managed to explain hard-to-grasp concepts to everyone.
It won't help you learn "the basics" in terms of math and science, but if you want to understand the theory behind complicated cosmological principles, I highly recommend *A Brief History of Time*. It would even be a good introductory read before you delve into the math-filled complexities of textbooks and such, because it might open your mind a bit toward understanding the math better if you understand the principles behind the math first.
Chasing Amy
(We all chase Amy...)
"The more corrupt the state, the more numerous the laws"-Tacitus
go and brows their math and science section. while it will be hard to find books on the basics, they do exist.
I am the Alpha and the Omega-3
If you're still concerned with algebra, this won't come in handy until later in your studies.
Keep in mind that during the 80s-90s (I think), there was a revolution of sorts in the way calculus was taught in colleges. Professors supporting this reform movement wanted students to understand the concepts instead of memorizing the formulas.
Sounds good, right? Only in concept (no pun intended).
To truly appreciate this reform, you'd need to take classes where this curriculum is being used. Just picking up a textbook using this method will probably confuse you, as it's not suppemented by the teacher's explanations and other methods of instruction.
That said, here are some common textbooks used in calculus courses today. While I know you'll probably be doing a lot of self-study, just having a regular textbook is helpful for obtaining practice problems and clarification.
James Stewart, "Calculus"
Finney, Weir, Giordano, "Thomas' Calculus"
Hughes-Hallett, "Calculus" (Don't buy this - it's full of horrible explanations, imho)
Larson, "Calculus with Analytic Geometry"
I couldn't get the hang of trig when it was presented to me from dull books by a public servant but when I was learning how to be a machinist and actually doing things with, say, sine bars, it made a lot of sense.
Calculus with a lot of real-world examples would be great.
That's more like physics. Force equals mass times acceleration (F=MA).
Relativity Visualized
by Lewis Carroll Epstein.
(ISBN 0-935218-05-X)
This guy explains relativity concepts and the ideas behind those concepts without making you understand eight yards of derivative calculus. The theories are presented in a visual style so that even a novice, unitiated reader can get them. He then goes on to explain the consequences of those theories and details how they effect the universe, again with the unitiated reader in mind.
The next Slashdot story will be ready soon, but subscribers can beat the rush and slashdot the links early!
Try "The Number Devil: A Mathematical Adventure". It's a cute book suitable for both children and adults that gets into various math concepts and patterns (fractals, Fibonacci sequence, irrational numbers, etc..) by explaining them in the context of a story.
This book breaks all subjects down, and starts explaining each of them in terms of a single point, or single atom. Then it expands each topic out to the real world, ending with real, practical examples of how the topic affects the physical world.
This may be the best book on physics I ever read.
The author's full name is Hans C. Ohanian. Enjoy!
This space for rent.
Feynman introduced his sister to astronomy by giving her a college text and telling her to read from the begining till she couldn't understand what was going on, then start from the begining again. (I think this was in his "What do you care..." book.)
I ran across a number of softcover books in the mid 80s that were basically stories where the protaganist was dropped on an island with amnisia, and he had to help the islanders (or countryman) solve various problems that ultimately involved most of the major areas of mathematics including basic algebra, trig and calculus. Some plane geometry and I would not be surprised if there was some Boolean algebra as well. You were expected to follow along and do some of the work as well. These were in fairly large format softcover, similar to college text workbooks. (8.5"x11")
Good luck.
-Rusty
You never know...
As an engineering student in the U.S., I have found that most foreign students seem more adept with the basic foundations of mathematics, especially algebra. I attribute this to the fact that that most American students are not introduced to the basics of sets and mappings until far too late. For me, I found one book in particular to be very useful in helping me to get a firmer grasp on algebra and functions which are indispensible for fully grasping calculus, differential equations, and systems later on. The book is called "Applied Algebra and Functional Analysis", by Anthony N Michel and Charles Hergert. As for Calculus, I found "Calculus Made Easy", by Martin Gardner to be very helpful as a supplement to most of my texts in college.
A Tour of the Calculus
Calculus Made Easy
The Universe in a Nutshell
Physics for Poets
I highly recommend Godel, Escher, Bach -- An Eternal Golden Braid by Douglas Hofstadter. I've only read it coming from a math-saturated background, but as it gives the background on how all of basic number theory works, it might actually be a good place to start.
Error 404 - Sig Not Found
None as far as I know in Calculus (it is usually too engineering oriented), not even think of algebra. Numerical methods - ROFL. So on so forth. If there are any readable ones they are by physicists..
Still, one exemption comes to mind. It is the finest textbook of all in probability theory. Feller. Note - it is probability theory and applications. No fscking statistics. Amazon has it .
In btw, when reading the rant in the introduction keep in mind the emphasis which in the US (and some other countries) is put on statistics without proper knowledge of probability (and how many stupid things people do as a result).
Baker's Law: Misery no longer loves company. Nowadays it insists on it
http://www.sigsegv.cx/
You need the check out The Teaching Company. I've gone through a a number of their courses on CD, and they've all been superb. I just recently finished their World War II course, and I'm currently doing the Foundations of Western Civilization. Given you're question, you'd probably want to look at their Science & Math offerings. I did the Joy of Science course last year as a refresher for all that stuff I'd forgotten since high school and college, which sounds kind of like what you're looking for. (I've no affiliation with The Teaching Company other than being a satisfied customer.)
When it comes down to it we don't know everything.
The base upon which most science is built, save for math which is pretty much a mental exercise, has a bit of uncertainty.
We observe the real world. Then we try to describe it, preferably mathematically. It says nothing about why it works, nor does it ensure that our current description is correct. Just that as far we know that's how the world is.
And strangely, I still find more comfort in this than god.
A list of his books
Since what you're looking for is about as broad as the universe, I figured I'd point you to the man who set me straight back in 8th grade. Godel, Escher, Bach not only taught me much about the arts, sciences, and mathematics, but it rekindled a passion for learning that the education system had done it's best to beat to a pulp. And that's a passion I still have today thanks to him.
No Zen is good zen
...and very little from the books.
I suppose it depends on the type of learner you are, but frankly, I imagine seeing and using the information being delivered to me. Rather than simply "knowing" the things I learned, I understood them and used what I learned to add more peices to the puzzle I call "reality."
In more simple terms, everything you (should have) learned should be assimilated into the way you operate within your environment. Ever heard "you use it or you lose it"? There's a lot of truth to that.
Rather than try to get what you missed from books, perhaps it's time to make a much more grand display by going back to school. It doesn't have to be thought of as "remedial" but rather as a "brush-up" or simply continuing education. If you show your children that learning only ends when you die, their minds will be open for life with the expectation that they can grow and improve themselves at any point in their lives... not just during the beginning phases. By the time they reach it, "middle aged" will be 50-something anyway.
Best advice? Go back to school and pay attention this time.
Mastering Technical mathematics, by Norman Crowhurst A Tour of the Calculus, by David Berlinski The Calculus Tutoring Book, IEEE The Feynman Lectures in Physics (3 vols), Richard P. Feynman Asimov on Chemistry, Asimov on Physics, by Isaac Asimov e - The Story of a Number, by Eli Maor I didn't get much education in high school, and ended up supplementing many college textbooks with the books above, among others. For Calculus, there is a book called "The Concept of Limits" that is an excellent guide to the first hurdle encountered by students of calculus, but I can't remember the author. Good Luck!
A Tour of the Calculus is a particularly comendable book. It only covers the more basic tenants and theorems of Calculus, but gives you an immense sense of the power behind such theorems and of the near-glacial process which has formed them and the calculus as a whole. Reading it gave me a much deeper understanding of the particular topics it covered, as well as the Calculus and math in general.
~metal_llama out.
---
move every sig!
I need something like this as well, my math sucks.
Why dont some of you open source programmer geniuses write some math E-Software?
If you use Linux, please help development of Autopac
Not only a good book, but so useful that you'll be applying it the next time you open a newspaper: How To Lie With Statistics by by Darrell Huff. Please, do yourself a favor and at least read the reviews on Amazon.
For chemistry, I recommend 'Uncle Tungsten" by Oliver Sacks- not too heavy on chemistry, but great to read. His other books are fantastic as well.
I'm in community college, let me tell you that this wont help, the reason why it wont help is because the goal will still be to get a good grade, pass your tests, and learn the knowledge you need to do this.
Now, if you can find a class which ISNT graded, then yes its a good idea, and I'll take math as long as it doesnt ruin my GPA if I do bad.
Otherwise I'm just going to avoid calculus, and all that crap so I can have a GPA over 3.0.
If you use Linux, please help development of Autopac
These might seem ridiculously old, specialized, or classical, but I remember liking them a lot and really getting a lot out of them.
Math-
Geometry: Euclid - The Elements. You probably don't need to learn geometry again, but your kids might, and the proofs are very well done and worth reading if you've never seen them. You don't have to read all of the books (there are 12 (or 13? I don't remember)). You could probably find a suggested course of study on the web site of the University of Chicago, Harvard, or St. John's College.
Probability: William Feller - An Introduction to Probability Theory and it's Applications (2 volumes). It's a bit expensive since it's nearly out of print, but very well done. You could probably find it used on abebooks. There aren't enough problems per chapter, but if you search the web you can find plenty of problems (Harvard teaches a class on this text and they have problems on line).
Number Theory: I remember that in college we read an essay on "Continuity and Irrational Numbers" by Richard Dedekind (found in Essays on the Theory of Numbers) that was very good. I have never taken a class on number theory or anything like that, but I found the essay very interesting and not too much work (a few days of reading, maybe a week tops).
I can recommend that you DON'T waste your time with Calculus by James Stewart. It won't kill you, but there must be better text books out there.
Science:
Physiscs:
Relativity The Special and General Theory - Einstein. Not too hard, actually, and you could almost certainly find a class, lecture, or study group that's working on it if you didn't want to tackle it by yourself. There are also all sorts of books that help explain it (Amazon lists tons) if you just want a study guide.
Eight Lectures on Theoretical Physics - Max Plank. Lectures 1, 3, 5 & 6 work together to explain quantum theory and Plank's constant. They aren't all that hard, mathematically. There are a few equations per lecture, but not too many, and their generally pretty well explained in the text. You might need a friend who knows math to explain a few of them.
Genetics is probably not a field that you're interested in, but The Selfish Gene by Richard Dawkins and The Red Queen by Matt Ridley are both very good. If you're not sure if you are interested, read The Selfish Gene first. Then, if you find you like that kind of stuff, you can move on to The Red Queen.
Here is a amazon link.
I have found this book to be very helpful. It covers a very broad array of topics: linear algebra, trigonometry, calculus, complex analysis, differential equations, statistics ....
There are numerous engineering related examples and problems so that you can get an idea of the applicable domain of each subject. I think there would be something in this book for readers from high school level through graduate school.
word.
I hope I spelled his name correctly - read his books Innumeracy and Beyond Numeracy, excellent introductions to practical mathematics and advanced mathematics, respectively. I tutored math in college, and by *far* the best way I have found to explain calculus to students who "just don't get it" is using Paulos's "driving on the turnpike" analogy.
I just remembered another.
Proofs from the Book
by Martin Aigner, Gunter Ziegler, Gunter M. Ziegler, and Paul Erdos(In spirit)
The book goes through artistic proofs in many areas of mathematics. Proofs from the Book shows that math is beautiful if we take the time to find simple explainations with ingenius arguments.
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Interestingly enough, there's a remaindered book by Berlinski called, 'the advent of the algorhythm' which I found very helpful.
Although its main concern is mathematical logic, Berlinski's explanations of the thought behind the numbers is a nice thing to have. His book makes you think about numbers--about what a numbers really are and how they work.
The book's actual math is broken up by sections of very well-written prose that offer relief when the mathematical ideas leave you feeling hollowed-out and brain-fried.
The advent of the algorhythm is not an easy read without a big math background, but it did a lot to bring me a new understanding and appreciation of what is there in math.
I don't like Berlinski's conclusions, the main point of his book, but the what he teaches along the way is great stuff.
I hope this helps.
To mail me, remove the 'mailno' from my email addy.
"Yeah. It smells, too..."
If you're looking to answers to the question "why?" it shouldn't suprise you that you're not alone. Since the beginning of time and throughout the ages, the human mind has confronted the same questions. My best advice is to read the original thinkers, the ones who first came to an understanding of whatever subject matter you pursue, as this is closer to the natural course of human understanding (in opposition to the textbook fact-collection approach which you mention.) The Thomas Aquinas College curriculum includes four years of mathematics, from Euclid to Dedekind and Lobachevsky, and for physics, you cannot outdo Netwon's Principia Mathematica and original treatises by Maxwell and Einstein. So if you really want answers, consider chatting with the instructors there, and/or the purchase of a Great Books set.
http://tinyurl.com/4ny52
Physics:
Motion Mountain Physics free text-900 page pdf which seems pretty damn good, I found it about a month ago.
Feynman Lectures On Physics
Basic Physics: A self teaching guide
Algebra:
Practical Algebra: Algebra from the beginning
Linear Algebra free text-I'm going through this book right now to supplement the god-awful text we're using in my linear algebra class at college.
History of Math/Fun
Zero: The Biography of a Dangerous Idea- I really liked it. It's a short, fast moving, entertaining account all about zero and the history of mathematics.
hooray! it's a sex wiki
What a wonderful price too, I can really use this book.
Now I must admit my algebra skills on the upper level (linear algebra and upper level algebra) is kinda weak.
Hopefully this book will teach me calculus without forcing me to memorize hundreds of formulas.
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For math I recommend "Calculus" by Michael Spivak. It is seriously misnamed, it should be "Introduction to Real Analysis". It clear, well written, though dense. It assumes nothing, starting with the definition of numbers. Some 600 pages later you'll have covered about half of a math degeree from a non-technical university.
If you liked that you should do the other half of standard mathematics. I recommend "Algebra" by Bartel Leendert van der Waerden. After Spivak you'll have enough background. If you can make it through van der Waerden you'll know more math than most professional physicists.
I can heartly concur with the posters who recommended "The Feynman Lectures" they are brilliant.
For a more complete study I recommend "The Berkeley Physics Course" in 5 volumes.
Most Dover publications are available directly through Barnes & Noble and Amazon.
The Elegant Universe by Brian Green
It's a great physics book that mainly focuses on String Theory but starts at a pretty basic level from Newtonian physics to quantum mechanics. Good for someone that is just curious about physics and for the person that considers themselves fairly savvy in the area.
There is an academic discipline known as "History of Science". The writing is often entertaining and accessible.
In each book, there is a bibliography of the sources that it used, in case you want to do additional research on the subject.
As an added bonus, each book is less than $15, and they can be picked up at any Barnes & Noble. So its worth picking up to see if you are interested in a certain subject.
Hope it helps, I've enjoyed them.
010_digital_100
I went to a small private school where I more or less studied advanced subjects (like calculus) on my own. I went through the Saxon Wang Calculus and Trigonometry With Analytic Geometry my senior year. With that knowledge, I was able to test out of Calculus 1 and 2 when I got to college. I was recently able to get another copy of it off ebay for about 28 bucks. Great beginning calculus book that's full of examples.
honestly, if you do end up buying a text book, i'd buy a college text book, because with the exception of the text books i used in my ap classes (which were all college text books), my high school text books universally sucked hairy goat testicles.
;-)
better yet, if there's a college nearby, why not see about taking a "101" class or two as an extended studies student... many employers have plans set up for continuing education, so it may even be cheap for you
just my $1/50
There are two books for Calculus that I particularly recommend. The first has been mentioned above several times already:
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t ail/-/0486 404536/qid=1059865826/sr=8-1/ref=sr_8_1/104-943995 5-4464720?v=glance&s=books&n=507846
Calculus Made Easy
http://www.amazon.com/exec/obidos/tg/detail
and the second, which I haven't seen mentioned yet, but which I consider much more important:
Calculus: An Intuitive and Physical Approach
http://www.amazon.com/exec/obidos/tg/de
The "intuitive and physical approach" really means exactly that. Calculus is developed in the book as the necessity arises to solve certain problems, just as it was developed (mostly) in the first place. Not only that, but the math is continually related back to actual problems, which keeps the concepts from floating off into the academic fairy land where math and logic become nothing more than manipulating scribbles on paper by arbitrary rules.
One man's religion is another man's belly-laugh. - LL
Mathematics: A Human Endeavor, Harold R. Jacobs
... and at over 3 inches thick, this wonderful book also makes an excellent doorstop ;)
If you want an easy introduction to some scientific priciples and want to read a funny story at the same time read the "Science of the Discword" books by Terry Prattchett... very funny and very informative. You get alteranting chapters of story and science.. they ecplain the formation of the world and all kinds of stuff in an pretty easy to understand way... A definate read!!!
Larry Gonicks "Cartoon Guide to *" are good. I particularly like the one on physics.
I am a mathematician, but I don't know any good textbooks to recommend. "A mathematician reads the newspaper" is a good read though.
is a fun book. It explains the basic physics of electricity and electrical devices in a very entertaining way. Check it out here:l /-/0962 781592/qid=1059866050/sr=8-1/ref=sr_8_1/002-366266 4-1016845?v=glance&s=books&n=507846
http://www.amazon.com/exec/obidos/tg/detai
"Ignorance is not innocence, but sin." --Robert Browning
Alas, "differential equations for dummies" found no titles. (I always liked the "why" of double integration - "say you are in a room filling with poisonous gas, which is heavier than air, coming from a pipe in the center of the ceiling... Where is the best place to stand to live the longest." Heh, my answer is "outside the room!")
Ask Slashdot, and you'll likely get the same information, just sorted on a different "key", but I guess that's what you wanted...
This issue is a bit more complicated than you think.
The quality of public education (altough this isn't the case everywhere, I suspect its the case in most places) needs to be addressed.
I am a student in high school, I have found the burden of education being shifted from the school system to the student. I don't mean the studying part, thats always the student's responsibility.
What I mean is that to get a good education, you really can't depend on the school system at all to get a good education. The textbooks are not at all good enough for really learning the subject, so students have to spend their precious time getting tutoring, reading other books, or asking other people.
The textbooks don't explain the concepts well, examples that don't help, and too much off-topic content that has nothing to do with the subject (mostly politically correct garbage to appease state and local textbook review boards).
Teachers are problematic too. All it takes to get a teaching job in Texas is a degree in education (there are other ways, but this is by far the most common) and pass some teaching "certification".
We have teachers who are teaching but know very little about the subject, or only know what the book says. For basic/intro classes, this usually isn't an issue, but higher level classes (AP science classes, Physics, Calculus, Statistics, etc.), you really want a teacher who knows the stuff.
Does a teacher nessicarily need a physics degree to teach AP Physics? Not nessicarily, in my opinion. I just think that the teacher should have a good college background in science. The same applies with Math. Someone who has background in Math, Engineering, or CompSci would be much better than someone with an 'education' degree because that person will have gotten a decent math background and the ability to think and apply it in a way that students will be able to learn better.
I'm looking for books that don't just tell me an equation or a concept works, but also explain *why*. Would you please list books that have helped you gain a greater understanding of the basic concepts of algebra, chemistry, calculus, physics, and other core areas of science.
This is broad. My own list that you might find useful (or not):
algebra -- a good introduction is Earl Swokowski's "Fundamentals of Algebra and Trigonometry". It's often available in used book stores, campus book sales, etc.. It is a text book, though, and you may or may not enjoy this method of learning. If you want more of an overview of math, take a look at Paulos' "Innumeracy". If you want some lighter reading, try stuff by Martin Gardner.
calculus -- builds upon algebra so you need to know your algebra, especially limits, before you tackle calc. Know the limits well because it will help in many ways. I often refer to Elliot Gootmans' "Calculus" from Barron. For fun, also try "A Tour of the Calculus". Many chapters in "A History of Pi" are interesting (and approachable) also. Stay away from the Dover books until you have a pretty good grasp. They're cheap, but their approach is sometimes a little heavy-handed.
physics -- Feynman's "Six Easy Pieces".
For general reading, also try:
Godel, Escher, Bach (Douglas Hofstadter)
Islands of Truth (??Ivars Peterson??)
BTW, I'm a big proponent of using mathematics software as an addition to traditional study. There are programs such as MuPAD, GnuPLOT, Octave and Maxima that are available for free that can really help in the understanding of concepts. Many people are more visual so a graph is eminently useful.
If you want a general and very accessible introduction to relativity, time, etc. in terms of physics, you might want to check out Stephen Hawking's excellent books A Brief History of Time and The Universe in a Nutshell. He explains the basic history and principles in various areas of physics, and goes into theoretical stuff like why time is pear-shaped, etc. Some of it is pretty out there, but the style of writing is very enjoyable and you can get a lot out of both books. They're a lot of fun to read, and really get your mind going on the possibilities.
"Wow, you're like some kind of superhero able to ward off happiness and success at every turn."
-- Ryan Stiles
What a great topic. Almost 20 years ago I did everything I could to just get through calculus. Now, I have no idea what it even is at all. Nothing. I might as well have never taken it. But, as I grow older and wiser, or just older, I feel the need to learn this as well as some basic chem and physics. I think I will take a look at some of these books. Thanks, Lou Sir
The Cambridge Guide to the Material Universe is a wonderful book describing what is the Physics and Chemistry of matter.
Unfortunately what is covered in far too many popularizations of phyics is the high energy stuff that either very abstract or does not really pertain to common experience. Not so the material covered in this book.
--_Calculus Made Easy_ might be a good book for a beginner. Understanding what differentiation and integration are is absolutely crucial (more so than being able to calculate the "derivative of ...", imo). The only way to accomplish this understanding is reading through a ton of examples and applications as well as explanations which will offer several points of view (grahical, analytical, geometrical, algebraic, etc.) on how to conceptualize these important concepts. After that, I would get a book explaining how calculus is applied to physics in particular to see some of the mathematical constructs "in action."
--If you're rusty on algeba, brush up on it first, because you really can't do calculus without algebra.
--For physics, I would recommend Feynman's _Six Easy Pieces_. After than, you might try reading some of the Feynman lectures or _Six Not-So-Easy Pieces_...basically anything by Feynman is good.
The math program I was a part of in high school, at Whitney Young Magnet School in Chicago, was called IMP, or Integrated Mathematics program but it could have just as easily stood for Interactive Mathematics Program.
Basically the way it was structured was that instead of the traditional math program where one learns algebra the first year, geometry the second, trig the third and then moves onto precal, we learned a litte bit of each every year.
Furthermore, instead of them just shoving facts down our throat and saying here, memorize these (such as all the proofs from traditional geometry) we were actually guided along in discovering them for ourselves.
Every problem was given to us in word problem format. Each unit, which represented a major concept such as the quadratic equation or some of that other stuff, was presented as one big word problemm and it was broken up into smaller pieces which slowly led up to the solution of the actual problem.
So instead of coming out of it with simply memorizing the quadratic equation, pythagorean theorem, pi, geometric proofs and the like, we were actually able to discover these on our own.
It's just too bad the teachers weren't all that great and the program didn't much fit into the "flash/bang" you need to know this information right now that most high school classes are based around. God forbid students actually understand and can apply the information they are learning.
I also can't seem to recall who published the books we used but I'm sure a bit of googling can solve that.
Douglas Hofstadter won a pulitzer for this little gem. This is a fantastic book to read for anyone remotely interested in the mathematical principles behind some of the more glamorous aspects of computing. Hofstadter's "Achilles & the Tortoise" dialogues are a frequently hilarious tribute to Lewis Carol that remain some of my most favorite things in print.
If you're lacking a basic understanding of algebra then this book may be a tad over your head, but if you can get into it you will find it immensely rewarding.
P.S. Algebra? ALGEBRA?!!?? You made it through college without algebra?
This man could make any subject accessible. Good stuff.
There are a series of books that have titles beginning 'The cartoon guide to...'. More really well written books.
Best of luck - enjoy.
There's also another text of the same name by C. Ray Wylie and Louis C. Barrett covering differentila equations, numerical methods, oed, fourier series and intergrals, laplace transforms, etc. (I never took the second part of the class :D).
Anyway, I'd suggest using an Inquiry Physics texts - Here The Physics Education Group at University of Washington presents Physics/Physical Science/Math from a purely hands-on/experimental method. The Physics by Inquiry texts are designed to teach teachers who are not traditional science teachers (elementary and high school) and are written in a very clear and precise manner.
They are broad in material (traditional physics/physical science/astronomy all using applied math) and every experiment relies mostly on things you can get around the house.
--Tim
Check out How Stuff Works
-jc
I found this book by William Dunham to be (inexpensive and) a readable account of some of the greatest discoveries in mathematics throughout history. I'm a math guy by training so I've been used to the circuit of class-homework-test for learning math but I found that a story format was very entertaining. For instance, the proof of the pythagorean theorem which is discussed in chapter 2 of the book was state-of-the-art back in Pythagoras' day, so even though it's something taught early in high school, at one time it was something the world's top intellectuals had to unravel. And the later chapters of the book are not inaccessible either. I think none of the book even goes into calculus. So overall it's an easy way to become involved in some of the historical gems of mathematics.
1 + 1 = 2 * 2 = 4, therefore 1 + 1 = 4. I'm a genius!
Mathematics for the nonmathematician by Morris Kline is a great intro. It covers the basics up to integral calculus, with nice peices on probability and set theory. Kline takes a historical aproach,showing how and why each topic was developed, also each chapter is fairly independent, so you can pick and choose the parts that are of interest. I've got the dover edition, and it's ISBN is: 0-486-24823-2
Especially if you are looking to -suppliment- an education system that is based on "here is a TYPE X problem ... you solve it this way with this algorithm ..."
... simply put "connect-the-dots". "Combinatorics", well that's just "counting things".
I suggest books such as Proofs from THE BOOK. Firstly it deals with topics outside the -regular curriculum- but whose problems are easily explained to (and understood by) just about anyone. "Graph Theory"
This book is particularly good as it offers, in many cases, more than one proof for a given problem, looking at problems in different creative ways to find elegant solutions. Feynman was a huge advocate of this (see the "Cargo Cult Science" chapter in his book Surely you're joking Mr. Feynman!
"Calculus - An intuitive and physical approach", Morris Kline.
Very useful self-teaching intro to calculus. Gives some great notes on different notations.
"Introduction to mathematical philosophy", Bertrand Russel.
Gives you some very good tools for how to think about mathematics.
"Mathematical logic", W.V. Quine.
"The pleasures of counting", T.W. Korner.
Gives natural applications of math and how to decide what tools to use to solve those problems.
"Math toolkit for real-time programming", Jack W. Crenshaw.
How-to recipes for math primitives and how to use them to build up to advanced applications.
[Set Cain on fire and steal his lute.]
Given that you, yourself, are not very math/physics savvy, text books alone may not be enough. You might easily end up in a situation of the blind leading the blind when trying to help your kids. Understanding math/physics will often go beyond what any textbook can tell you. You might do a lot better from a person you can interact with who can see how well you are grasping a concept.
:)
If you literally want to go to the trouble of hiring a tutor, then you'd get him/her for your kids obviously, but I don't know what to recommend for adult education. Given the current economy I'm sure the tutor might be willing to help you out as well in a package deal.
I heard something on NPR the other afternoon about a new series of books (ie: seomthing like 50 so far & counting) that are none longer than about 50+ pages. The main point is that each concept is covered on one page, so the math book is 50 concepts on 50 pages. This does not exactly answer the question answered, but it is a very nice tangent and, from the sounds of it, very nice books. I'm going to go buy some for myself now. Jason
They publish a large selection of math and science books. Most are reprints of some of the best works on their subject ever published. Because they are reprints, they are relativly cheap. I am currently extending my math background to include graduatle level stuff. I have spent less the $70 (US). That is less then just one current textbook.
Grade A Original, Fantastic & Highly Edifying Calculus Primer
. ht ml
http://www.profemc2.com/flash/profMcSquaredV1.0
It's a hoot, and you'll actually learn calculus.
Read "A tour of the Calculus," by David Berlinski concurently. I brilliant and superbly written English exploration of the subject. You'll never look at math the same way again after reading this book.
For Physics, start with Nick Herbert's "Quantum Reality" for Quantum theory and Steven Weinberg's "Dreams of a Final Theory" for the quest for the Theory of Everything.
These two books are the only popular books that that get their respective subjects right. Accept no substitutes. After you read these you can read the other popular titles without being led astray.
Throw in Leon Lederman's "The God Particle" for good measure. It won't teach you physics but it's a good look at the life of an experimentalist, a sadly parched literary field.
As for Algebra, well, as my Psychology professor used to protest, it's a motor skill. You have to sit down and work problems with a paper and pencil. Work enough of them and think about what it is that you're doing at the time and you'll figure it out on your own.
Schaum's Outline Series title " Modern Elementary Algebra" should do it for you. But you have to put in the work.
For other stuff I'll agree with things others have posted. Feynman's "Six Easy Pieces" and his classic "Lecture" books. Damnably expesive. Worth every penny. You'll treasure them forever. You won't hand them down to your kids because you won't be able to bear to part with them. This makes them even more expensive because you'll have to buy a copy for each of them.
And finally, every nonfiction work Isaac Asimov every wrote. They're priceless. They're also cheap in paperback. Especially if you pick them up used. They're all over the place. Hunt around and you can get them for something like a dime apiece. Try the Salvation Army. Honest. I've found some there.
KFG
Real math involves proofs. In fact, for mathematicians that is the definition of mathematics. The rest is "just" application. Since the original poster is complaining about the lack of explanation why, I suggest that he look into proofs and other creative aspects of real mathmatics. If you haven't learned that math is a creative art you haven't learned jack. Ok, so I'm opinionated, but this is slashdot and what else is new.
Anyway I suggest that anybody of any age interested in math check out equations and wff-n-proof from the wff-n-proof people.
Regarding books, he had a vague request so I'll make some vague suggestions. Springer Verlag publishes lots of great mathbooks, as well as quite a few not so great. Some of them I can even read, and they do have a some series and books advertised for undergraduates. Look for yellow in any self respecting University library or technical bookstore.
Actually, going through a university library or bookstore is probably the best advice I can give under the teach a man to fish philosophy. Learning to go through a stack and pick out books that are readable but challenging is basically the secret to scholarhood. That and faith in the fact that once you've ground through one the rest will be a smidgen easier.
Oh, and you can also check out the math section of Cononical Tomes I made a few contributions when it first started, and would assume that it has only grown.
For what you do, it might be useless, but for people in Engineering and other fields, calculus is a VERY important subject. As a current CS major, I agree with what you say about descrete math and linear algebra, but I think you are discounting the need for Calculus.
RonB
It is human nature to take shortcuts in thinking.
I guess not, if it was, this question would have never been posed.
It is human nature to take shortcuts in thinking.
Speaking of slackers, what's with this question? Right, everybody wants to be Ptolemy, 'cause It Is Good To Be King. Except when the revolution is coming for you, dragging a frehly greased Guillotine to enliven the show. But most of you probably don't have clue number one what this bit is all about either, do you? Of course you don't! You're Slack-dotties, you can't be expected to have learned anything in school. You spent all your time trying to pretend you weren't in school, fuckheaded idiots that you were. I was like that too, but back in my day they'd tie you to the desk and keep you after school until... well, no, they didn't really do that. And that cliche about the rulers and your knuckles? Hardly ever. Really. Of course they didn't HAVE to rap most kids across the knuckles to get their attention back then. No one with that million-miles-away glazed look that says hey yeah, I like school so much better when I stuff the earbuds in and crank the mindless, mind-shredding noise up. Anything to avoid having to use the mind you've spent half your life trying to lose, right Slackies?
You young pukes make me sick!
But that's not what I came here to sing about. No, I came to sing the praises of some Good Books. I did see a few nods to Feynman, and a few of his essays are simple enough for even Slackdots to get the feeling that they sort of understood, or at least appreciated, whatever exactly he was going on about. But mostly you gotta have math, and to get math you gotta WORK AT IT.
'cause there still ain't no bloody god-be-damned royal road to mathematics. No Easy Street slide for slackers, neither.
You want to learn calculus? I mean learn it well enough to be able to start to learn about how it (and some harder maths as well, but calc will get you in the door of understanding; arithmetic and its yuppie cousin algebra just let you turn the cranks that were designed by people who had the chops) truly is the language of science, which ain't just a cute turn of a phrase, though it is that, but it's like a real, no false analogies here, metaphor for the way our understanding of the entire fucking universe has developed over the last few centuries. As oppposed to how you slackwits have closed your minds to any deeper understanding than the ability to catch a fly ball, and that, though you haven't the understanding to know it, has more to do with a few eons of evolutionary development of your central nervous system than it does with your brain, so called.
So You Want To Learn Math And Science?
Get thee to your community college; odds are damned good that they'll have the courses you need to fill in those gaps in your mental toolkit. Of course it's harder now - old brains are less flexible than young, but if you've reached the point that you can see the utter stupidity of your younger self who squandered those golden years, learning to be a twit instead of something worthwhile, something that might be useful for more than impressing your half-drunken friends that you're a wit - it's half true, after all - why, at that point you might be about to find that maturity does bring some compensation for the things you have to give up getting to it. If you haven't blanched and run away yet, back to your comfortable, mindless, slacking drift through life, you may be able to find the gumption to exert yourself and go to school in order to learn what you missed the first time around.
I mean, the odds aren't very good - if you're reading this, you're probably in the slacker half of the population, more inclined to rant and rail on the
There are many different areas of maths and a range of books to cater for all levels.
You need to understand which topics you want to get a feel for. The options range from very pure maths ie Logic and Set Theory, through Algebra, Geometry and Calculus and on into Applied Maths, Mechanics, Dynamics, Numerical Analysis, Statistics.
There are many common features in understanding each area.
First off, the motivation for the material in each subject is to solve problems. The questions mathematicians address tend to come from the real world, and then later people come along and rationalise / rigorise the area. This leads to the second common point:
Maths is about abstraction. Solve a set of problems then step up a level and work out what is going on at a more general level. In fact this is why all the text books use a ton of practice problems. Until you understand the examples you can't see the common thread.
Thirdly the topic you are looking at has been chewed over for decades. People have worked out the ways to explain the topic so as to hide the rough edges and at the same time point up the links to other areas of maths. This can leave new readers puzzled as to why something is emphasised, or even worse to give the impression that you have to master every damn topic before you can move forward.
I'll mention a couple of books that I used way back when, others will doubtless have their own views:
Mathematics for the Million: Lancelot Hogben Lots of stuff about numbers and series here.
Statistical Inference: Silvey still one of the cleanest texts on stats I know.
Anything by Feinman on Physics
>> books that have helped you gain a greater understanding of the basic concepts of algebra, chemistry, calculus, physics, and other core areas of science?" . However, I had $20 to plunk into an account at nearlyFreeSpeech.net( worth checking out ), and so, I wonder, can this post to SlashDot manage to exhaust my entire bandwidth account in one swoop ? I was unable to make the fancy frames-page-index at www.xmemes.com work well outside of MSIE, sorry.
Karukstis, Kerry and Van Heck, Gerald. Chemistry Connections: The chemical basis of everyday phenomena. (ISBN: 0124008607)
Anything in the Commentaries on the Fascinating Chemistry of Everyday Life series by Dr. Joe Schwarcz:
how many babies does it cost to troll around in the humvee all weakend? figure it out yourself.
if you consider the #'s at all, we've gotten ourselves in a dangerous quandry.
lookout bullow. the daze of the evile greed/fear based misinformers is definitely #ed.
consult with/trust in yOUR creator. vote with yOUR wallet. that's the spirit.
pay attention. add up the cost of that, & you'll be way ahead right away. tell 'em robbIE.
30 kids in a highschool classroom, 100 kids in college.
The book is a refrence, but the only way to learn the garbage in the book is to practice.
I find the results of that practice absolutely useless in the real world so I cannot motivate myself to practice.
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Example: A lot is riding on what people in the US think about the administration policy in Iraq. Exactly what does the average American know about Iraq? Does he know what the difference between a Shia and Sunni muslim is? Or the distinctions between religious conservatism and fundamentalism?
Example: You can't get ahead without being persuasive. What makes a piece of writing convincing and credible?
I know there's apt to be a geek bias against social sciences and liberal arts; but aren't most people's education in these areas just as defective? Is any form of ignorance good?
Post may contain irony: discontinue use if experiencing mood swings, nausea or elevated blood pressure.
My mind does not like to remember information which is utterly useless, but some people are better at that than others.
all the formulas and steps are useless information that you memorize so that you can do calculus so that you can know math which you'll never use a day in your life and most likely wont remember 5 years later.
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I'm looking for books that don't just tell me an equation or a concept works, but also explain *why*. Would you please list books that have helped you gain a greater understanding of the basic concepts of algebra, chemistry, calculus, physics, and other core areas of science?"
/. journal entry, I list a bunch of math and science related stuff I just bought. In particular, I just bought several "lower level / refresher" type math books, to use for some self-study before tackling calculus (which I will be taking at a college, not teaching myself... although I may try and get a headstart if I have time).
In my last
Anyway, if you look over that list, you might find a few things that you would also be interested in.
// TODO: Insert Cool Sig
Did you know, that Winston Churchill once said "Science should be on tap, not on top" ? As with many 50-year-old Americans who experienced Vietnam as teenagers, I have always been obsessed with "on tap, not on top". I have written this up at: http://www.xmemes.com/cssg/ToolPeople_000.htm An eminently readable book which is a great start on game-theory issues is Poundstone's "Prisoner's Dilemma", which I briefly recommend at: http://www.xmemes.com/cessno/PrisonersDilemma_000. htm
( The above text was clipped from the middle of my original post, although I previewed it ? )
On the topic of calculus, don't learn anything past calculus I (well, bits of calculus II are useful). The rest is completely useless and you'll forget about it all in a couple of years anyway because of its uselessness. If you want something that's useful go for discrete math and/or the good bits of linear algebra. Your comment is completely offbase. Actually, Linear Algebra is about as important as Calculus in many scientific/engineering disciplines.
More importantly, you claim that anything more advanced will be forgotten, but the later courses often serve to reinforce earlier material. For example a course on Fourrier theory reinforces both Linear Algebra and Calculus.
Most math departments have a course somewhere after the introductory sequence which teaches basic proof techniques often by studying the definition of numerical systems from logical axioms.
These basic proof techniques are the very basis of mathematics. The reason so many people get through high school with little understanding of math is that they are never forced to do any proofs outside of Geometry.
In short, if you cannot prove anything, you know practically nothing about mathematics.
http://yetanotherpoliticalrant.blogspot.com
No, the correct logic is: 1 + 1 = 2 2 * 2 = 4
That kind of conclusion has nothing to do with logic. It has to do with your assumption that the formal system used by the original poster assigned to + and * the meanings of integer addition and multiplication, and the symbols 1 and 2 as natural numbers. In fact there is no such requirement, they can mean whatever they like, or have no meaning at all. Consider for example if both + and * were used to represent string concatenation. Then the original expressions would be correct, and yours false. Or if they did represent normal integer arithmetic, but the strings "11" and "22" represented 2 and 4 respectively. Neither has any inconsistencies or is at all invalid, though the second, having two different ways to represent the number 2, is rather silly, as is the first for having two different symbols for string concatenation.
I always enjoyed Halliday, Resnick and Walker's introductory physics text. It's calculus-based and designed for freshmen-level students. Not only does it provide a good, broad understanding of physics basics, but it also utilizes physical intuition to explain many of the concepts. As a graduate physics student, I still keep it around as an excellent reference book. Finally, the problems at the ends of the Chapters are among some of the classics of physics.
what can anyone say about the bible that is objective?
Try Wikipedia, it's information written by the poeple, so I'm sure the information would be more geared to explanations and more knowledge based approache than pure fact based approaches. You could also try Wikimedia-textbooks, but I'd wait till its ismore mature.
For a pedagogical treatment of the fundamental particles and forces considered in physics I can highly recommend:
http://particleadventure.org
Full of nice illustrations, and even has little multiple choice questions along the way to keep the reader on track.
You won't be able to do calculations in field theory afterwards, but it is a great start - especially as a motivator.
PrisonersDilemma_000.htm - will not work with the "space" in it. Let's try the full URL one more time: http://www.xmemes.com/cessno/PrisonersDilemma_000. htm
( Sorry about these fumbles, dare I accuse the preview of not being 100% WYSIWYG ? )
Algebra requires you memorize hundreds of formulas, steps, rules, conditions, etc and thats exactly why I cant remember it no matter how many times I learn it.
Its also useless, all the stuff you memorize never applies to anything in the real world.
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PrisonersDilemma_000.htm - when I dragged my mouse across the full URL in the preview window, and copy/paste it into the address bar, it works. However, after "submit", doing the same thing puts that "space" in front of the ".htm". Oh, well !
Concepts of Modern Mathematics - Ian Stewart
Mathematical Mysteries -- The Beauty and Magic of Numbers
He proceeds in explaining the interesting connections numbers play in our world similar in which Paul Hoffman portrays in his book, Archimedes' Revenge, except without so much of the story-telling. Semi formula book but can be read without the slightest clue of understanding them.
[rant]
I believe Stephen Hawking to be extremely overrated. I picked up one of his books at a bookstore and threw it done in utter disgust. I personally have a bitter dislike of dumbing everything down for the layman and glitzing all the empty space with fancy graphics...okok, that is a bit harsh as I think his books are great for children.
[/rant]
Anyways for the highschool/college folk crowd I definitely ever so highly recommend
It uses very simple math to explain the various heuristics that can be used in Math solutions. The book is right up there for Math what Feynman's lecture is for Physics.
40 Years later is it still required reading for first year MIT students.
Help fight continental drift.
People go to community college to transfer into a good university and get cheap credits, not get an education.
If they wanted me to focus on an education perhaps they wouldnt make the GPA so damn important.
What is the point of avoiding difficult but important classes simply to preserve your GPA? Are you in school to get an education or to simply achieve some arbitrary GPA? I've been in the position of hiring people for technical positions and I've always been far more impressed by a mediocre GPA in a substantial curriculum then a high GPA in an easy curriculum.
Ok say I do take a few math classes and get a few Cs, well then my GPA goes under 3.0 and I can forget about transfering into a good 4 year university, I can also forget about scholarships and grants which also require a high GPA of above 3.0 or 3.5, I really cannot afford any Cs and I know for a fact that its simply impossible for me to get an A or B in math. I take classes which I know I can/will get an A or B in.
This isnt about the jobs, this is about getting a degree from an elite private university.
I recently returned to school myself, so I do have sympathy with amount of work required to do really well in a course, and I do understand that those planning to continue to a four year school or go on to graduate school need to match minimum requirements, but in my opinion you'll be better served by reducing the number of classes you take in a given term then by trying to ditch the challenging courses.
I never take more than 4 classes per semester, and I never get anything below a B in grades, those are the rules I follow.
Maybe if universities werent so strict and competitive on the GPA issue I could actually focus on learning but right now I have a goal, that goal is to get into Harvard, Tufts, Boston College,Boston University or North Eastern, all which are ELITE private universities which will NOT let you in with a sub 3.0 GPA, you most likely wont get in with a sub 3.5 GPA, so no its not about "learning" right now, its about moving up the ladder, it will be about learning once I get into university, thats when I'll take math clases, get a C or two, and learn something.
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I confess that I made it through 3 semesters of college calculus and an engineering degree pretty much not understanding the underlying concepts of calculus. It's surprising what you can accomplish by rote. This book was a real forehead-slapper for me, and I can't recommend it highly enough. Many years after graduating, I've finally learned what I should have back then. If it were up to me, this would be the first book anyone learning calculus ever read. I wish Sylvanus Thompson were still alive (I think Calculus Made Easy was published in 1919) so I could give him a big smooch.
Most colleges and universities will let those from the community "audit" a class for a very reduced rate, my college charged like 60 bucks a class, you didn't get a grade, but you could attend all the classes, and tests were optional, at the discression of the professor. If you can spare the time, it's probably going to be much more useful to hear the lectures than just reading a text.
Degaussing scares the bad magnetism out of the monitor and fills it with good karma.
I strongly despise everything new age, but I have to say that I liked the tao of physics. It's written by a trained research physicist, and its basic point is: there are some similarities between quantum physics and some oriental religions. It's not an introductory textbook, but I think if you already have some background in physics, it forces you to think about the fact that physics isn't as different from the rest of human thought as physicists would have you believe.
It won't make you a new age convert.... relax.
While I'm sure that the people recommending GEB and Hawking have your best interests at heart, they're answering the wrong question. If you want to learn math, you're going to have to start at the beginning and work your way up. "Popular" math and science books won't help you with the basics.
What you'll want to do instead is what they do in school. Start with some basic number theory(nothing fancy, maybe just enough to know the difference between integer/real/rational/etc). After that, assuming you understand how to add, subtract, multiply, and divide, you're going to want to get into some basic algebra, then calculus, then geometry or whatever else you want. Unfortunately, I learned algebra way back in middle school so I don't have a textbook to name, but I do have some advice that applies at all levels:
* Do the problems in the book. Then do some more. Then do even more, just for good measure. Some of the other posters have complained about doing problems. Ignore them. Nothing will give you a better feel for how algebra and calculus work than actualy *doing* them.
* Understand each piece of information before you move on and how it relates to the whole. Any decent textbook should offer problems that use both new and previously gained knowledge. Make sure your textbook of choice has lots of examples and that those examples are worked out well. Never underestimate the value of a fully worked out problem. It may be worth it to get multiple textbooks, look them over, and then return the ones you don't want.
* Be persistant. Children learn math by doing it every(other) day for years. You're an adult. You can learn faster and better, but that doesn't mean you get to be lazy. Do a bit every day, even if it's just working one or two problems. Daily practice will ingrain concepts in your brain and also make it easier to pick up a book and start on something new.
* Don't get too formal. Wanting to know "why" is great, but "why" must often take a backseat to what is being learned. Often, the reason for doing something may not be obvious until you already know how to do it.
* Have I mentioned doing problems?
Now I do have one actual book to name, and that's:
Calculus by Larson, Hostetler, and Edwards
This book has tons of examples and illustrations, as well as excellent problems. It even features a two chapter algebra/pre-calc review!
Some people have mentioned the calc book by Stewart. We use that book at my college, and given the number of people who seem to have problems with it I cannot recommend it for self-teaching.
Good luck!
Visit the
Alan Turing - On the Computable Numbers:s p
http://www.abelard.org/turpap2/tp2-ie.a
Did you know, that Winston Churchill once said "Science should be on tap, not on top" ? If science ends up just making weapons and non-scientists or even VOTERS get to pull the trigger, then social science, being "controlling", is clearly worth study ! To get to the bottom of things I wonder why Zahavi's book "The Handicap Principle" is not more frequently praised. I rant - http://www.xmemes.com/ciss/Handicap_000.htm I was unable to make the fancy frames-page-index at www.xmemes.com work well outside of MSIE, sorry.
For great math books that will bring out the kid in you (by means of an entertaining fantasy story as a pedagogical approach), I recommend Algebra the Easy Way (Barron's Educational Series) (ISBN 0764119729, $13.95US) and Calculus the Easy Way (also Barron's Educational Series) (ISBN 0812091418, $13.95US), both by Douglas A. Downing. I wouldn't necessarily recommend other titles in the series (not having read them), but these two follow the exploits of people from the Kingdom of some-name-I-forget-how-to-spell. I read them as a child interested in learning more mathematics, and they definitely focus on a solid conceptual understanding. Share them with your kids as a good bedtime story! I used to beg my mom to read the Algebra book to me.
Clouds in a Glass of Beer: Simple Experiments in Atmospheric Physics by Craig F. Bohren and Jearl Walker is enjoyable to read, and helps look at physics from the point of view of the home rather than the laboratory. It is an attempt to avoid the "overfat physics volume" syndrome.
which might interest you is:
Mathematics for the Million by Lancelot Hogben.
A down to earth treatise for the ordinary person.
Mathematics for the Million - Lancelot Hogben
ISBN: 0-393-31071-X
(This ISBN is from a 1993 printing of the 4th (last I believe) edition, originally published in 1895. The first edition was circa 1862).
This book is hands down one of the best adult math texts around, as shown by how it has endured over time. It covers all the practical branches of math one should know including calculus, and starts out at a very basic level. Throughout it explains the real meaning of the math, this is not a fact memorization book at all.
Also, if you're further interested in calculus, I'd recommend:
Calculus Made Easy - Silvanus P. Thompson and Martin Gardner
ISBN: 0-312-18548-0
(Original by Thompson was from 1851, the ISBN here is an updated version (by Martin Gardner) published in 1998).
Covers (again, with real explanations, not memorization of facts) the real meaning and understanding of calculus, both differential and integral.
11*43+456^2
Calculus is INCREDIBLY important, and from a philosopical point of view it might even be dangerous. :)
Imagine a field of mathematics that explicitly has at it's underpinnings the hypothesis that as you break up a line into smaller segments, eventually if you make each segment have no length, they still all add up to a lenght.
Philosopy aside, it's an INCREDIBLE tool for particular applications. Need the area of a sphere, no problem. A cone, still no problem. An oddly shaped object that looks like a art-deco running shoe? BIG problem, that is unless you use calculus.
Did you know that the eminent John Von Neumann, being thoroughly familiar with the principle of defense needing to be eternally vigilant while offense needs only a single opportunity, was resolutely supportive of preemptive war ? Or so it says on page 142 of my copy of Poundstone's "Prisoner's Dilemma". Did you know, Winston Churchill once said "Science should be on tap, not on top" ? I have written this up at: http://www.xmemes.com/cssg/ToolPeople_000.htm If science ends up just making weapons and non-scientists or even VOTERS get to pull the trigger, then social science, being "controlling", is clearly worth study ! I was unable to make the fancy frames-page-index at www.xmemes.com work well outside of MSIE, sorry. I well know that when one starts talking soft-science like game-theory it's easy to sound lame, while tool-science produces such powerful, well, *tools*. To shy back from such controlling topics for fear of sounding lame, well, that would make one a "tool person" !
I read Isaac Asimov's Realm of Algebra when I was in grade 6, and didn't learn anything beyond it until around grade 10. Actually, I didn't even finish reading Realm of Algebra -- if I did, who knows how many grades worth of math I would have learned in one sitting!
Unfortunately, it is out of print, and has been for some time. I have seen people asking outrageous sums of money for it used, upwards of $300 U.S. This is truly a book that is crying out to be open-sourced/pirated. Maybe someone who owns one would scan it into a tidy little pdf or something. Do the same to Realm of Numbers too.
Mike van Lammeren
It will challenge your head, your brain, and your mind.
I have found Larry Gonick's "Cartoon Guides" charming, accurate (if sometimes kinda understandibly rushed), and very compelling. Gonick is most famous for his "Cartoon History of the Universe," but he also has a "Cartoon Guide to Physics" and a "Cartoon Guide to Statistics" among other science titles. It's perfect for the adult novice and the young student as well. The cartoons illustrate abstract concepts visually, while maintaining a great sense of humor and fun.
Five Golden Rules: Great Theories Of 20th-Century Mathematics -- And Why
They Matter (John L. Casti)
It Must Be Beautiful: Great Equations Of Modern Science
(collection of essays, edited by Graham Farmelo)
Mathematics: The Science Of Patterns
(Keith Devlin)
Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions
(Thomas F. Banchoff)
The parent poster points to one of the few well-developed Mathematics textbook series that offer students a braod understanding of mathematics. If you are looking for a textbook series that actually let's you understand why the math works the way it does instead of just accepting it as truth, then I have one of two suggestions. Both of these series were actually rated as exemplary by the Untied States Department of Education.
IMP: Integrated Mathematics Program. IMP (as the parent poster said) takes all the mathematics taught in high school and blends it together in a format which is VERY GOOD at showing how mathematics develops logically. Subjects are not isolated lessons which involve repeated "practice of skills." Each lesson involves only two or three (at most) complex math problems which are set up specifically for students to do so that they can learn why math works. The only thing you may want to consider though is that this textbook series does not specifically say how the math works; only by actually doing the lessons does one gain an understanding of the math involved. If you're looking for a more direct detailing of the math, I would suggest this next series.
CPM: College Prep. Math. This textbook series is divivided into the traditional "Alg. I, Alg. II, Geom/Trig, Calc" classes, though it too does a very good job of making each lesson a logical progression of the last two or three (in fact, it actually gives a "guide bar" at the end of each chapter showing how much each "portion" of Alg / Trig / whatever has been conceptually developed). The biggest difference compared to IMP however is that it explains what the mathematics is doing as it develops in the textbook. Also, there are a lot more practice problems. One drawback is that the book is not the most reader-friendly...many of the text pages are rather cluttered, plus the book is only printed in black & white.
By the way, avoid the Saxon series like the plague. If you want to know why, or if you want to discuss anything else about what I've mentioned, just drop me an email.
(And if you're wondering, I am a Math teacher...this isn't just another geeks advice that you're getting.)
Forget the numbers and take 20 minutes to contemplate something along the lines of why the geometry of a tree is useful to trees (as plants). If you find any thoughts or ideas during this endevour interesting then you've discovered what math is truly about. Now you have motivation to understand the tools that math provides. This will take you further in your desire to learn and certainly in the need to understand.
Enjoy.
Isaac Asimov books are great, especially about quantum physics, always have been always will be. He doesn't talk down to you and his insights are always brilliant. They are a bit dated but still relevant, and always interesting. Sometimes the best thing to do when you do not understand something like the quadradic formula is to back track and use simple tools then when you start to see with algebra things start to make sense. It is always true that visualisation of the effects of variables is important and until one starts to see in math it is about the same as reading music until you start to see with your ears. For some it comes easy others not. If interest is not there then it is almost impossible. What would be great is if patterns in math became more of a teaching tool. Some of the best math insights come from thinking about how to write an equation to create a pattern. Thats is how great discoveries have come.
OH THE SHAME I fell off the wagon and use sigs again!
In my own experience (from grade school math through grad school math), I have almost always found that the texts aren't terribly helpful until *after* you've learned (at least to some basic level) the mathematics. In one of the posts above, SuperBanana notes this problem, and suggests that you try adult ed courses. I agree that the human interaction with a professor and fellow students can be invaluable. In fact, some of the biggest mathematical ah-ha moments I've had have been when I've been trying to work through an idea with friends. Only then did the stuff in the textbook really make sense.
... and how to find them before the teacher does
Now, that's not to say that there aren't good books out there to help you learn about mathematics. It's just that the ones that are written as textbooks (particularly in the traditional theorem-proof style) don't seem to be written with a learner in mind. By presenting all of the mathematics in a *mathematically* logical progression, many of them end up hiding the kinds of thinking that has to happen in order for someone who doesn't already know the math to learn it. After all, mathematicians don't do their work by smoothly going from stating fixed definitions to giving a theorem with proof- there's a lot of work going on there that we don't see in the formal presentation. I should be careful, though, not to exaggerate. Most textbooks try to give some exposition to help the reader along. However, this usually doesn't do enough to change the fundamental problem of structure that comes with using the mathematically logical sequence to guide the organization of a book intended for learners.
You may find that some of the newer so-called "reform" materials may be closer to what you are looking for. Many of them do make an explicit effort to focus on the ideas and concepts underlying the mathematics (though some complain that they don't focus enough on developing fluency with procedures). The trick with these is that, when used in schools, they generally work best with teachers who themselves have this kind of deep understanding and thus know where the materials are pointing. There has been quite a bit of venom circulating around these newer materials. My suggestion is to try a few different kinds of materials in both the "traditional" and "reform" styles, and see what works for you.
So, here are a few suggestions of books that I found useful in making sense of mathematics, its ways of thinking, and how it can relate to the world. The first several aren't really textbooks, but rather books about mathematics.
Philip J. Davis & Reuben Hersh - The Mathematical Experience
George Polya - How to Solve It
John Allen Paulos - A Mathematician Reads the Newspaper
John H. Conway & Richard K. Guy - The Book of Numbers
Barry Cipra - Misteaks
The Calculus Consortium at Harvard has developed several textbooks, including Functions Modeling Change: A Preparation for Calculus (Eric Connally, Deborah Hughes-Hallett, Andrew Gleason) and Calculus, Single and Multivariable (Deborah Hughes-Hallett, Andrew M. Gleason, William G. McCallum)
I have used the tapes (they now have DVD) from the Teaching Company [ http://www.teach12.com ] very successfully with my middle-school and high-school aged children. They have high-school specific courses as well as more general science and math offerings (as well as others). They go on sale once or twice a year for 50%-75% off. Highly recommended.
And the woman (Monica Neagoy [ http://www.monicaneagoy.com/math.html ] ) who teaches Algebra 1 is HOT! (well, from a geek's POV)
A few other useful web sites for Math and Physics learning (there are tons more):
Drexel Math forum. Lots of explanations, hints, resources, etc. Homework help!
http://www.mathforum.org/
On-line Graphing Calculator (helps to understand interaction of algebra and graphs, etc.). Nice.
http://www.coolmath.com/graphit/
NYS regents exam prep center has some decent tutorials and links to other resources. Some "teaching to the test" but still a useful review, especially when combined with the Teaching Company tapes or other resources.
http://regentsprep.org/
Mathematics Encyclopedia
http://mathworld.wolfram.com/
Math books online (many fairly advanced):
http://www.math.fsu.edu/Science/Books.html
One thing I have not found is a good on-line basic math textbook, but then again textbooks are rarely very good anyway.
I am going to have to revisit math after running from it for over 25 years. I'm 39 now and will hit the big Four-Oh in November. I intend to get my teaching credential, and to do it, I have to return to school. And I'm going to have to basically take up where I left off regarding math. In California Community Colleges, you have to have at least Intermediate Algebra on your transcript with a C or better, or test out at that level or beyond.
So starting September 2nd, I have to revisit Pre-Algebra. Yes, folks, she's a geek, but she sucks at math. Luckily I have a very nice circle of friends who are absolute wizards on the subject, and my husband would have been a math major had the music bug not bit him.
It's either that or go through life without a degree. And that, my friend, sucks even worse than that C in math will. I was looking at McJobs for the rest of my life. Sure, K-12 teachers aren't paid much, but the perqs are golden. And it pays way better than the CA minimum wage. And most importantly, you are hopefully helping to turn kids onto lifelong learning.
Knowledge is power. Knowledge shared is power multiplied.
No (Score : 5, Funny) ?
blah, useless thread.
Bleh !
This is going to ruffle a few feathers, but really I do mean well...
--- Begin Education Rant ---
If your only goal is to pass tests and get a good grade, and gather up some knowledge, then you would make a fine apprentice.
Unfortunately, if you desire the "really know" the stuff, and no amount of schooling is going to get you there, unless the schooling is directed toward education.
Education is what you were supposed to go to school to get, but all of the pressures placed on schools to get you ready for the workforce weakens the cirricula to the point where many educational programs are just "white-collar" apprenticeships. If you want education, you will have to challenge yourself to get one. Nobody can give you "insight" in a field as that's the gift you give yourself after you have had enough exposure to that field's challenged.
For some it's very little exposure to gain insight, for others it's a whole lot, and for many, they claim they have it far too early (and dangerously may have a very flawed understanding). Education is a work in progress, and by protecting your GPA, you make make yourself more "marketable" (only for that first job), but you won't necessairly make yourself any more educated.
If you're worried about the GPA, then take the class. You will put much more work into the subject than 80% to 90% of your classmates, and you will learn FAR more than they will. But if you only take the classes you know you can pass, you will leave with 4 years of your life wasted because you are only marginally better than when you entered.
--- End Education Rant ---
For an extremely accessible and entertaining overview of "what it's all about", the "Introducing ..." books come highly recommended. They won't teach you any formulae, but they will give you an excellent picture of what mathematics/physics/quantum theory/et cetera are all about and the history of the big questions that have driven these fields. Don't be put off by the cartoonish style of the books - they're written by people who know and love their subject.
- /1840 460571/qid=1059872794/sr=8-1/ref=sr_8_1/104-380183 5-2881520?v=glance&s=books&n=507846m azon.com/exec/obidos/tg/detail/-/1840 460113/qid=1059872822/sr=5-1/ref=cm_lm_asin/104-38 01835-2881520?v=glancec /obidos/tg/detail/-/1840 461586/qid=1059872822/sr=5-2/ref=cm_lm_asin/104-38 01835-2881520?v=glance
1 153/ qid=1059873620/sr=2-3/ref=sr_2_3/104-3801835-28815 20
Check out
http://www.amazon.com/exec/obidos/tg/detail/
http://www.a
http://www.amazon.com/exe
(Don't pay too much attention to the odd poor review: they're from people who were expecting textbooks where these books simply try to show you the big picture.)
For physics and mathematics, I cannot recommend volume I of Richard Feynman's "Lectures on Physics" highly enough. Feynman is the clearest scientific writer I've ever come across. Within a few pages he can take you from basic addition all the way to an understanding of calculus that my entire schooling in the fast stream for mathematics never managed to convey.
Look at
http://www.amazon.com/exec/obidos/ASIN/020102
Cheers.
I'm heading back to school and have forgotten way too much math. The best single book I've come across is "All the Mathematics You Missed But Need to Know for Graduate School" [Thomas Garrity, Cambridge University Press 0-521-79285-1].
It's weak in that it lacks practice problems, but it gives good familiarity with the major topics in about 340 pages. No mean feat.
Also good, of course, are "Div, Grad, Curl and all That" and "How to Solve It"
The man who never alters his opinion is like the stagnant water and breeds Reptiles of the Mind -- William Blake
Although I didn't actually formally use any of these math books, my sister and several of my friends used "Integrated Math" published by Houghton Mifflin Co. The idea with this book is that they teach you math by showing you how to use it and not do like "Saxon" and merely drill you to death. I would recommend at least taking a good look at this series for high school level mathematics.
If you would like something a little bit more advanced (college freshman level), Integrated Physics and Calculus by my undergraduate advisor and math professor is a very nice text that integrates the learning of calculus with uses in physics. I would recommend something like this over the Feynman series that people talk about.
A couple of avenues to consider...
Die Menschen verhoehnen was sie nicht verstehen. -- Goethe.
A very good general physics textbook is Ohanian's Physics. For something even easier and maybe more fun to start off with, there's "the cartoon guide to physics". :)
As for chemistry, you may want to have a copy of Linux Pauling's, err.. Linus Pauling's General Chemistry (a Dover paperback). He was truly a giant in the field.
Eli Maor's book e: The Story of a Number is an interesting read, and you can pick up a lot of calculus from it (I read it in high school before I had calculus, and learned a lot). It's may not be meant to convey understanding of the math so much as to explore the history (which is actually pretty interesting--did you know the inventor of the logarithm was excommunicated?), but there's still a lot of math to be learned from it (like the difference between Newton's and Leibniz's Calculus, and why we use Leibniz's, but still consider Newton to be the father/inventor of the Calculus [and why Calculus gets capitalized and a definite article]).
This side up.
Euclid's Window
The Story of Geometry from Parallel Lines to Hyperspace
Leonard Mlodinow
I've always considered myself a math retard (cant do anything more complicated than algebra) and I try to avoid math stuff because I never felt I 'got it'.
However, while reading this book, I kept finding myself saying "Why didn't they tell me this stuff in high school and college? It would have made things so much easier to understand."
And while you might think that any book about mathmatics/geometry must be pretty boring, I actually found this book hard to put down - its under 300 pages and I had read most of it in three days.
Being a biologist by profession, I find that the non-technical/textbook books tend to be very helpful and a nice change of pace for me. Some books that I recommend are (sorry for no authors, but I'm doing this off the top of my head): A Tour of the Calculus: A nice history of calculus and *why* it is so useful. Relativity: an intro into his theory in simple terms. Also see, a brief history of time by Hawking. The Beak of the Finch: Pultizer prize book and a fascinating read about the study of the evolutiuonarry relationships in Darwin's finches in the Galapogos Islands. Fermats Enigma: nice story of one of the most famous math problems ever. These books might not make you more proficient in actually doing any problems, but they are good insights into why and how math/science thinking is done.
Why is it that whenever you say something against the Slashdot orthodoxy, you get modded as a troll. Little twat geeks cannot seem to handle different opinions.
You might want to try a lab in the subject you are interested in. They usually offer good insight into how things work, once you know what is going on it is usually easier to see where you need to start. As a Physics Grad Student I have taught labs and recitations. The students seem to understand the more challenging problems better if they do a lab and Pay Attention to what is going on.
Drawing pictures of what is happening is also very useful when working problems.
Find this book somewhere and read some of it: "Calculus: One-Variable Calculus with an Introduction to Linear Algebra," by Tom Apostol. It is unlike any other calculus book I've seen and I found it to be far more fascinating for its difference. It is not a "dummies" book--probably a polar opposite, in fact. I wish it could have been my calculus book when I was learning. There's two volumes, but they are fat, dense books, so you may not ever need (or reach) the second volume... (Oh, and try to find it in a library, because you'll never see it in a store and it has a serious price tag.)
Some of the more scholarly archeological periodicals and researchers do a good job. That isn't to say that they are always right, but many of them are good informational sources.
Mr Tompkins in Wonderland and Mr. Tompkins Explores the Atom are both fictional narratives that demonstrate relativity through greatly exaggerated examples-- apparently Mr. George Gamow has written an umber of other physics books as well.
They're fun to read, and definitely helped me in high school AP physics.
I would recommend Mas-Colell, Whinston, and Green's "Microeconomic Theory" and Obstfeld and Rogoff's "Foundations of International Macroeconomics" Both presume only a limited background in mathematics (and economics) and have generous explanations of the mathematical tools being used.
Sig (appended to the end of comments you post, 120 chars)
Danny.
I have written over 900 book reviews
Try Thinking Physics for general physics and Relativity Visualized for special relativity. These books are elementary but very clear and fun to read.
I don't know how old your children are, but everyone deserves to read Hans Magnus Enzensberger's The Number Devil: A Mathematical Adventure .
True, it only explains basic mathematical concepts, but does so in such a charming way you and your children might end up hooked on mathematics forever.
Who wouldn't want a Number Devil anyway?
The liver is evil and must be punished.
Not everyone by birth is a genius at math, some people must work for YEARS to get the B in math.
"If you can't even get a B in a community college undergraduate math class,"
I'm not a Math person.
"you're not going to make it at Harvard or any truly "ELITE" university, private or not. Sorry."
Thats exactly why I wont major in math or science at Harvard.
"Getting a real education takes work on your part, not simply gaming the system for least effort per credit or slapping the right label on a bogus degree. It's not something other people do to you, it's something you do for yourself."
I am working, but I also know the system is not a very fair system, and the system does not reward hard work, it rewards those who "game" the system. So yeah I could learn math, get a C in math, have a bad GPA and never get into an elite private university, or I can get a good GPA, find some way into an elite university, and then take the math classes when I'm there.
I see no reason why I should take them now and get bad grades now when my grades actually matter when I can get bad grades later. And what you said doesnt make any sense, you act like a person must get a B in every single class they ever took in college, we all know that this is very unlikely as most people are humans who have strengths and weaknesses. I might get a C in Algebra and Calculus, but I'll never have to take those two classes again once I actually go ahead and do it, so for you to tell me that because I cant get a B in calculus that I'll never be able to handle university is pretty ignorant, I mean sure if I were majoring in math and science you'd be right, but I suppose you didnt do a good job looking at the list of possible majors which do not require you take tons of math classes.
If you use Linux, please help development of Autopac
I'm sorry, but you seem to be arguing a point here and - while I understand the point - I'm not sure how it orginated to anything in my previous post (i.e. the parent post).
In any case, to answer your questions:
A) Yes, I was aware that von Neumann was suportive of preemptive war.
B) No I did not know about the Churchill quote.
C) I have read Poundstone's "Prisoner's Dillema" and found it to be quite an interesting read, as well as a nice overview of some of the ideas in game theory.
If what you are taking exception to is the phrase "Atrocious new age speculation", I assure you that game theory and social sciences were not what I meant by that phrase. It was a criticism of Capra's amd Zukav's attempts to imbue physics with a layer of spiritualism that cannot be accommodated within the scientific method. Zukav, in particular, seems to have done way too much acid.
In other words, please don't take the statement as a criticism of the so-called "soft sciences" for which I have a healthy respect. The statement was a criticism of non-science and it's popularization through books claiming to be about science.
Ah, mumbo-jumbo. 1st-and-only rule of economics - get either a monopoly or a niche, with niche being merely a diminutive form of monopoly. Then you use the divide-and-conquer ratchet - visit your many suppliers and pick the cheapest one, iterate. "Niche" has some subtlety when there are complementary functions to be performed, like the complementary proteins in rice and beans. This is well discussed by Brandenburger and Nalebuff in Co-opetition. I rant - http://www.xmemes.com/cess/CoOpetition_000.htm To thus oversimplify, I invite a scathing response from PoiBoy. I mean, you have invested years in studying details which I have obviously never touched on. So the question remains - are there some underlying fundamentals beneath all of that mumbo-jumbo, which I have missed out on ? If so, someone must have made an attempt to simplify them for the non-specialist, and I'm always interested in knowing about such distillations. I was unable to make the fancy frames-page-index at www.xmemes.com work well outside of MSIE, sorry
http://www.math.com/
http://homeschooling.about.com/cs/math/index.htm?t erms=math
http://homeschooling.about.com/cs/science/
http://physics.about.com/
What is Science?
Even on the off chance that the About network doesn't have all the information you need, they have a large number of links to sites with relevant information across the Web, so there's a very good chance that you will be able to use them to find what you are looking for.
Also...although these are not strictly an answer to your question, I would still heartily encourage you to follow the links to these (listed in a suggested order of reading...my probably misguided opinion only) text files, web pages, and books, as I think they could be of enormous benefit to both your children and yourself...indeed, anyone who wishes to read them. Although I understand that several of these could possibly only be understood at tertiary level, they also as far as I know are not normally included in *general* curriculums, and IMHO they should be.
It used to be in the past that the education systems of most nations didn't want us to know the why (philosophy, religion, history, political theory) of life, but were content enough to let us know the how. (Science without analysis, numeracy and literacy skills, etc) Now however we are seeing that primarily in America, but also in other places, government education departments no longer even want to allow people to know the how.
Mathematics is part of the how - a means to an end, a way of solving problems - but it is not a destination in itself. The material I've given you links to in my second section is concerned with finding out *why* - "Why am I here? Who am I? How do I know what reality is? What do I want to do with my life? What moral values do I believe in?"
The answers to these questions are far more important than becoming merely literate or mathematically capable for their own sake. Figure out what your purpose is first, and the rest, although still requiring work, will be relatively easy. That is what the links in the second list will help you do, and it's not something you'll be taught to do in any contemporary public school, either...Governments consider people with purpose to be highly dangerous.
If I face up to it now it could RUIN me and make it so I cannot afford to go to college at all, It can also keep me from getting into an elite school if I screw up now, I mean sure after you've got 10 As and Bs, the occassional C wont mess up your GPA, but when you have only around a dozen As and Bs, that C will totally destroy your GPA.
The GPA is everything when it comes to transfering out of community college, and shouldnt my goal be to get into university first, and then worry about learning once I've established my abilities to the world?
If you use Linux, please help development of Autopac
I took a diff eq class that finished with 6 people. I then took a complex class that had about the same amout before I dropped out because of real world commitments (9/11). I don't think it's because of room, other than schools that are specifically for the engineering studies. There is just not the interest.
There are exactly two books that have ever got me interested in science, and after reading each, I've said the same thing - "Why the hell didn't I have books like this in school?"
Bill Bryson's "A Short History of Nearly Everything" and Terry Pratchett's "The Science of Discworld"
Both gave me an incredible overview of the issues and concepts in science, and serve as a great jumping off point for further reading, once you've spotted areas that really interest you. The Discworld book is probably a lot better if you've read some of Pratchett's other books (don't be fooled by the title - it's actually an overview of our science, not the Discworld's), but the Bryson book is readable by anyone.
Wasting your time since 1997.
The best place to understands the concepts behind (for example) Algebra is to go to your local University and find out what the first year Honors Math texts are. (at the U of Alberta, at least), Honors math was intended for people going into PhDs, and so they tended to explain why something is being done, rather than just how. You might find the same sort of attitude in honors physics and Chemistry texts, as well.
OS Software is like love: The best way to make it grow is to give it away.
Against the Gods:The Remarkable story of Risk. Read it for a finance class, and while it is suppose to be on risk management, its the story of the development of statisitcs, which means it is also a story on the development of math. Its an easy read, an give a good borad view on statistical concepts and how they are used (and abused).
Barbara Lee Bleau Ph.D. are excellent books. I was in a similar situation in that I decided to go back to college at age 32. Being that I was educated in Louisiana (worst in the nation) I never was properly taught many math principles. I was very fortunate when friend pointed me to these books. Both book start under the assumption that your math understanding is at an elementary level (basic addition, subtraction, multiplication, and division.) It is a truly great teaching guide and workbook which was so successful for me that I passed the math placement test at The Univ. of North Texas and will be taking Pre-Calc this semester. As for physics, I have seen several great books recommended so far. I'm reading Dr. Hawking's book right now.
There is nothing inherently safe about liberty. That's why so many people died protecting it.
Particle Garden is written by Gordon Kane. I was lucky enough to go to one of his lectures. I can tell by how well he did his lecture that his book will probably be pretty readable.
E=mc^2 by David Bodanis is an easy to read book and explains that equation we all "know" so that even cameron diaz can understand it. www.davidbodanis.com has got lots of physics related stuff for the interested too.
Physics: The Human Adventure, Gerald Holton and Stephen Brush
Nice, historical look at how well known physical concepts of today were discovered.
Physics for Scientists and Engineers, Paul Fishbane and Stephen Gasiorowicz
First few chapters good if you have a basic knowledge of calculus. For the later chapters (ie, Electricity and Magnetism, basic quantum mechanics) good idea to have a calculus book handy, I reccomend
Calculus: Early Transcendentals, James Stewart
First chapter is a good review of algebra, precalculus, and analytical geometry. Through chapter 7, fairly straightforward. Chapter on sequences and series is kind of fuzzy, though it mostly makes sense.
Hope this helps!
#define CLUE 0
I am writing this post in case you read the parent's wise comments and decide that to know mathematics you must know proofs. Proof theory is part of logic, a discipline that is sometimes slotted under math, sometimes philosophy, and sometimes by itself. Unfortunately, the proofs of logicians are nothing at all like the proofs of mathematicians.
Logical proofs are rigorous -- they can be checked mechanically for accuracy and even generated through largely automatic means. Mathematical proofs are known by the technical term "hand-waving" and are actually an informal argument for other mathematicians (just as legal arguments are intended for other lawyers and judges). If the "proofs" of mathematics were as rigorous as the proofs of logic, then how could we ever run into problems where proofs are later found to be incorrect? Some nutcase who thinks he's proved Goldbach's Conjecture would be turned away by the journal's oracle (to borrow an idea from programming competitions) if they were too lazy to check the proof on their own computer.
And don't go smoke a bunch of Hofstadter and think that mathematics is too undecidable for automated proof tools: if mathematicians were serious about producing rigorous proofs they'd simply have to assist their theorem provers at choice moments with the necessary insight. As a result, every mathematics paper would be a long serious of simple, incremental steps which can be examined by a layman or even a computer. Instead, they perpetuate their own job security by writing in tongues.
If you ever hope to do mathematics, don't make the mistake I did: avoid learning symbolic logic at all costs.
Try A Tour of the Calculus by David Berlinksi. This book reads like a novel, though at times a dry one. The author does a nice job of assuming that we know next to nothing about math, and lays the foundation of the calculus accordingly
I really hate to say this but you should take a proof course and always study the proofs for the theorems and try to proove some things yourself. In math you'll definently start out with courses where solving problems is enough but later on it becomes all proofs. I for one really hate doing proofs and find it all very trivial but it gives me a better understanding of the mathematics involved.
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Go canucks, habs, and sens!
All of Feynman's books rock.
My favorite textbook for all time is a physics book, Halliday, Resnick et al's Fundamental's of Physics. (Some of the problems are mediocre, but the text is wonderful) If I hadn't had it in my university physics classes I would've gotten an F instead of an A.
Also, as some other posters have said, Calculus is extremely important. It is a different way of thinking, better in many cases.
Ben
Looking for freelance Actionscript (Flash/Flex) or ColdFusion work and/or freelance developers. Email me, put Slashdot
One thing I noticed about studying math since I got out of school is that I learned stuff I didn't realize in school. Like PI. I learned what PI is: you take the diameter of a circle and wrap it around the outside of the circle. It will go 3.14 times. I don't think I ever realized that when I was in school.
Ah - a layer of spiritualism that cannot be accommodated within the scientific method. I like your crisp response - so to stick the neck out, that it may be crisply chopped off... Let me plead guilty in-advance to being obsessed with big ideas, while my ability to cope with detail is suspect. I got a 4-year-degree in Physics but was not top-of-class. What do you think of the "root of all control-cascades" concept ? http://www.xmemes.com/cwhisper/WigIcon_000.htm http://www.xmemes.com/cwhisper/GravityIsWeakToo_00 0.htm
It seems likely that posting will stick spaces in these long url's, I have found.
OK, "God must be at the root of all control-cascades, duh, so that it non-falsifiable, therefore it is beyond science, end-of-subject."
However I still dream that some rich person might wonder about closing-the-loop with the stare-angle-trainer concept. http://www.xmemes.com/cstare/StareAngleTrainer_000 .htm
Supposing that on quiet days one might be on the edge of being able to filter through to the nano-whispers, another human presence ought to be an extremely strong signal. So I wonder, if the Stare-Angle-Trainer were built, THAT would be at least falsifiable. If from legions of promising test subjects, none could be trained into tracking a human stare, then listening for whispergods would seem less likely, that's a kind of falsifiability, at least.
The very best book that I encountered during my undergraduate days was Frank Shu's The Physical Universe. It is classic. Although it was published in 1982, Shu's book is still something that I would recommend to anyone who really wants to understand physics and astronomy.
The material on the solar system is dated, but that's not the point. The real value is the historical approach, in which the reader is invited to work out key problems himself. The problems are integrated in-line with the text, and the more difficult problems (those requiring calculus) are identified as such. Despite the book's being billed as an introduction to astronomy, it really grounds the reader in the fundamentals of mechanics and thermodynamics. The material from basic physics is given excellent motivation by its immediate application to certain astrophysical problems. The reader is not left to wonder, "Why do I need to learn this?" Shu presents the physics, and then immediately shows why it's interesting and valuable.
I don't have a copy myself, but spent more than an hour one day reading "Who was Fourier?" in a bookstore and trying to figure out how I could use it in a class. Certainly worth looking at.
I learned intergration from a text book, audio software and a calculator. A friend needed a program written to aproximate definite integrals to an arbitrary amount of percision. Integration by Parts I think it was called, but I'm not sure, it was 5 years ago. At any rate the idea was that the program would allow you to plug in the equation, the range, and the number of points to use.
Well I didn't know how to integrate, I mean I knew what it was supposed to be but not how to do it. So I mulled over the information in the book and relasied that this was a process analogus to upsampling in digital audio. You get a step square wave when you digitise audio. Now if you want to move from a low sample rate to a higher one you can get a more accurate representation of the analogue curve. However if you have low sample data, the information has already been lost. YOu can, however, reconstruct it to an extent. What you do is use a variety of methods, the simple ones being like the midpoint or trapezoid rule, to estimate where the intemediary datapoints were.
Well, with integration, you have a smooth curve, and you are taking discreet samples of it to calculate the area, so it is much like digitisation. This particular method was to pick the detail to an arbitrary level. I then wrote a program and got it to workright. At the end of all that, I understood how it worked and could do integrals of the type described without the help of my program.
No one taught it to me, I just took the information in the book and worked it out. Now this isn't to say that real teachers are worthless, far from it, however it is possable to learn on your own just from a book and doing some kind of hands on practise.
OK, there IS a second law of economics - use your monopoly power to build
. ht m
a huge war chest, from which you can undercut the prices of startup-wannabes so
that they go out of business, being unable to outlast your price-wars.
Searching the net, to this day I see things like the-Myth-of-Predatory-Pricing,
from which derives much of my contempt for mumbo-jumbo-economics.
Predatory pricing is straightforward and intuitively obvious and we see it every
day, e.g. the Circuit-City-Commercials, so for folks steeped in mysterious
equations to deny this obvious technique, well, that's mumbo-jumbo !
http://www.xmemes.com/cess/PredatoryPricing_000
I cannot figure out how to stop the posting process from putting spaces in my URLS !
This oldie-but-goodie was an intelectual break through for me. It consists of three 1966 Asimov texts in one volume. The three books, "Motion, Sound and Heat", "Light, Magnatism and Electricity", and "The Electron, Proton and Neutron", were put into one volume as "Understanding Physics" in 1993 by Barnes and Nobel. I read it myself about 1995 because it showed up on the bargain rack at about $5 for the hardback. It is still only $9.98 from their web site (see link above).
The book reads chronologicaly from ancient Greece through the sixties and show how we came to believe and/or prove what we know of these subjects. In a chapter on the "Ether" and the Michalson-Morely experiment, I had in my mid-thirties the "Aha!" moment I never had in school about General Relativity. Also particularly valuable to me was the description of exactly how Mendelev arrived at the periodic table, and how that lead us to predict the properties of elements we hadn't even discovered yet! This book was specifically written for non-scientists who wanted to know some of the big ideas that were driving the discussion of the day, and it has Asimov's quality writing and historical perspective to make it very readable.
I say "we" and "us" because Asmimov wrote of how the human race, not just and individual, devised ways of thinking and investigating that lead to thing no one individual could have dreamed of. Anyway, its my favorite "science" book, and I highly recommend it.
Any technology distinguishable from magic is insufficiently advanced. - Geek's corollary to Clarke's law
One of the best way to learn mathematics is by following its history and see how new ideas were formed/discovered. It makes the concepts less abstract (less seemed pulled out of thin air by ur dull prof) and A WHOLE LOT more interesting. One book that offers such a perspective is: http://www.amazon.com/exec/obidos/tg/detail/-/0393 04002X/ref=cm_wl_vvu-pg.1-pos.1/104-4995310-126551 5?v=glance&coliid=I13AVPIN0XVDBH&me=ATVPDKIKX0DER# product-details
I've always found the Schaum series to be a great and very fast introductory books. I've sampled their Stats, Chem and maybe Math.
The thing I'd like to stress about Math is the importance of graphs. If you don't understand the graphs, there's no point battling with differential equations and multi-variate calculus. Thomas&Finney is a kick ass book on calculus, which will serve you right from high school through college. Too bad I got hold of it only in my final year at college.
I don't mean to discourage you here, but the only way to really understand things like math and physics, especially math, is to sit down with one of those text books with all the "facts" and go through it till you understand everything. If you don't understand the basic stuff in that text, you need to get a text from a previous topic in the same subject, like if you don't understand trig, you need to go back and learn algebra better. It's not that the texts are flawed, it's that your understanding of basic concepts is flawed and you need to review.
This is all assuming you really want to understand the subjects. If all you want to do is fool the average person who has no idea what you are talking about anyway then by all means, get a "physics for dummies" book, but there really is no shortcut to math and physics besides putting in the time.
It's not like there is a new and different way to learn math and science once you are an adult. It's the same way you learn it when you are younger, study really hard.
"The problem is, most textbooks are not
designed to convey an understanding of the
subject, but to squeeze in all the 'facts'
required by state law. "
If text books are no good, then where do all the college students around the world get all their understanding? Is there some secret they know that you don't?
I wouldn't have had a problem if the post had just asked for a source of information to help their children with homework and such, but everyone trying to find a shortcut to understanding math and physics are just insulting those who put in the time to study it.
Feynman explains the "why" and in such a natural way that you're much more likely to remember it later, especially if the original poster is learning it by himself. (BTW, the exercises reprints accompanying the lectures are available -- look for scsi-guy's ebay store, for one.) The lectures wouldn't work that well to teach yourself during a semester; you can't juggle four or five real classes, all the homework, and still internalize Feyman's lectures, which were supposed to be presented over two years.
It raises the costs a lot (too much unless you are treating yourself or better yet, can get them from the library), but I found that listening to the audio tapes while reading the lectures to be a very powerful experience. There's no substitute for the subtlety, emphasis, and cadence that a great teacher brings to a subject he has mastered.
The beauty of the Feynman lectures is that they are very accessible. You don't have to "get deep" to get understand the main points.
As far as the depth goes--either Feynman himself or the foreword mentioned that they were a bit much for many of the students, but that as the course progressed, many of the seats vacated by the students were taken over by the other Caltech faculty.
One extremely well-written textbook is Calculus in Context. It is modestly below the level of my high school and college math texts, but years later, when I want to remind myself how to do something and why it's the right thing to do, it's a great reference.
If anyone reads this and can give a lead on where to buy copies of the calculus text that Feynman himself mentioned in "Surely You're Joking..." I'd really appreciate it.
--
It isn't likely that you will be able to find such a book. In order to gain even a rudimentary understanding of math or physics requires several years of undergraduate work and a few years of graduate, at which point you might have a decent grasp of the subject you studied. Certainly these are broad areas, and you will still barely be scratching the surface.
Euclid was once employed as a tutor of mathematics in the royal household of King Ptolemy I, who complained about the difficulty of the theorems which Euclid expected him to learn.
When the king asked whether there might be an easier way to approach the subject, Euclid gently reproached him: "Sire," he said, "there is no royal road to geometry."
Guidelines:
1. If you really want to understand mathematics, stay away from suggestions made my engineers; in particular, eschew books that dumb down mathematical theory in favor of the 'this is how you compute the solution' approach. Silvanus Thompson I find to be especially egrigious in this regard (those who try to learn calculus from Thompson will never understand the rigorous notion of a Limit, which is hardly pedantic since the derivative is itself a limit and the Riemann integral is the limit of a Riemann sum).
2. Be patiant with yourself. Geometry, Analysis (which includes what is called calculus) and Algebra have required centuries of constant effort to develop. If you go for the 'fast and cheap' approach to learning it, you will aquire nothing more than skills, when what you really want is knowledge.
Books:
Preliminary topics: Before you can think, you must memorize certain things and learn other things by rote. This will be hard and painful, but these fundamental topics are to mathematics as the alphabet and grammar is to Shakespeare, Milton, and Joyce. They are: the notion of a function, the laws of exponents, elementary trigonometry (sine, cosine, tangent, and their inverses), the binomial theorem, the definition of a polynomial, factoring polynomials, setting up applied problems in algebra, linear equations and their graphs, simple nonlinear equations and their graphs, slope and area, the Pythagorean Theorem. Most of these basic noitions are covered in Forgotten Algebra (which is published by Barrons for people just like us, and College Algebra, by Michael Sullivan.
Fundamental Notions:
By fundamental notions I mean ideas that form the basis for other ideas. Mathematics is all about definitions, and definitions are all about ideas; you cannot learn complicated ideas without understanding basic ideas (if you don't believe me, try explaining why every vector space has a basis to someone who doesn't understand what linear independence is). Unlike preliminary topics, fundamental notions are actually fun to learn--you get to think instead of just memorize and drill! I know of one wonderful book for this sort of thing, for someone in your position:
1. A Tour of the Calculus, by David Berlinski. This will make you think about what 'continuity' is. Good preparation for calculus, which is all about continuous functions, and good because it presents mathematics as a branch of philosophy (which it is).
Single Variable Calculus
Single variable calculus is where you will find most of the major concepts in the subject; the next time you will think this much is in linear algebra, when you study why the derivative for a n-dimensional vector space is actually representable in terms of matrix multiplication (the derivative is a linear map.) Here are some good books on calculus:
1. Calculus, Thomas and Finney. This text features a superb fusion of theory and application. The exercises are challenging, but doable for an independent student, and solution guides are available (these are indispensable as you search, at 2AM, for the mistake in your integration by partial fractions problem that required nine pages and is off by a constant).
2. Calculus, by Michael Spivak. My favorite calculus book. A brilliant synthesis of upper division real analysis and run-of-the-mill calculus. Reading it is like feeling awestruck by the beauty of someone you have known for years and years. This also has a solution manual (which you will need, because here there are proofs).
Advanced Mathematics
Don't stop learning math just because you
"Oh, the tragedy of math gone wrong. I can't even talk about it." -Wil Wheaton http://www.wilwheaton.net
Many of the books published by Dover are written for readers who are not specialists in the field in question. As a result, they are quite easy to read at a fair pace and provide a good picture of the core ideas behind fairly developed subject matter.
Though they are relatively inexpensive, they can be quite addicting. Pace yourself.
A much better book is Riordan's, The Hunting of The Quark.
I'm glad that you have taken an interest in learning/relearning many general scientific and mathematical principles, as well as not-so-general for the sake of your own children (at least partially). Although not a parent, and really not old enough to be a parent, in my opinion, I still remember the huge impact that my father had on my life with his awesome, well-rounded education. Being a pharmacist, he helped spark my curiousity in biology and science in general (although I've strayed away and am majoring in computer and electrical engineering, ehh heh... but that passion is still there!), and being great with the handy work in the house and under the car, he gave me a very wide knowledge base at a young age, which has a priceless impact on children.
Now that I am older and can appreciate the importance of that fully, it hurts me in a way to see parents struggling in coming to their childs aid with homework, projects, or just guidance in general...
The importance of knowledge is often overlooked in today's fast-paced, pay-someone-else-to-do-it kind of world (at least the US is getting that way, I'm seeing), but gaining it at a young age, and keeping the fire strong throughout the years is one of the most important aspects of life.
"If God gave us curiosity and intelligence, we would be ungrateful if we supressed our passion to explore the universe." -Unknown
George Gamow's One, Two, Three... Infinity is an irreplaceable classic combining the author's deep understanding with jokes and whimsical stories about numbers and physics. An absolute joy, one of my favorite books since age twelve.
Sigmund
I'm not sure about over there in the US, but all my books (I'm in year 12 in .au) are quite good. None of them are focussed toward rote learning concepts (although chem has tendency to bombard me with formulae), to the point where our curriculum explicitly states that we should be "consolidating a conceptual understanding" rather than cramming.
It seems strange to me that you could get through high school and college without knowing "the basic concepts of algebra, chemistry, calculus, physics", because all of these are taught from the (compulsory) start of secondary school here, and in years 11 and 12 if you choose them as electives. If you're looking to be able to "supplement [your] own kids' education," just grab their textbooks (starting from year 8 if you're not even familiar with basic albebra).
For a literate and entertaining look at the concepts of calculus, I highly recommend David Berlinski's A Tour of the Calculus. It won't teach you how to solve problems, but it will teach you the concepts behind limits, differentiation, and integration along with the important theorems and their proofs.
I've always enjoyed books on recreational mathematics. You get a little bit of everything including number theory, game theory, geometry, etc. And most of it presented in fun contexts you wouldn't see in normal math books. I highly recommend the Martin Gardner series of books on the topic, collected from his old columns in Scientific American. You might also look for books by A. K. Dewdney who took over the column after Gardner left.
See http://www.seanet.com/~hgg9140/math/index.html.
I've long had a simple, surprisingly effective method of evaluating whether or not a particular book is going to be easily comprehended...
I pick up the book, open it somewheres around 1/2 way in, and start reading. If I haven't more or less figured out what's going on in 2 pages or so, I pick up another book and do the same.
You'd think that since subjects like math are typically studied linearly, building on previous concepts, that this would certainly not work.
But I've found this to NOT be the case at all!
Barnes and Nobles, the local Tower bookstore, or even the local thriftstore are goldmines of incredibly valuable information, and I've had great luck with the above method.
If the subject of study is fairly static (english, mathematics) your local thriftstore will often have used school textbooks for $0.50.
I have no problem with your religion until you decide it's reason to deprive others of the truth.
It is or is not accurate.
;)
That's an old indian trick; a statement of totalogy
--Joey
Richard P Feynman was a wonderful man and teacher. I highly recommend his other writtings and ruminations as well. (Physics)
- Isaac Asimov is your friend. Realm of {Numbers, Algebra}, the Understanding Physics series, collections of his F&SF essays sorted by subject matter.
- Lancelot Hogben's Mathematics for the Million is a classic work of mathematics for nonspecialists; it will take you up through the calculus and into probability theory.
- An Indian mathematician named Jagjit Singh wrote various books on aspects of math and science; I remember best one that dealt with error-correcting codes. Alas, checking the Dover Publications web site shows only Great Ideas of Modern Mathematics still in print, but evidently one can find used copies of others (e.g. Great Ideas in Information Theory, Language and Cybernetics) online.
- Dover also prints The Strange Story of the Quantum, which does a nice job of taking you from the whole brouhaha over black body radiation and the "violet catastrophe" through Planck, Schrodinger, and Heisenberg.
- While we're talking about quanta, check out Richard Feynmann's QED, and his other works for the general public.
Those are getting on a bit in years; I'm not aware of a good introduction to topology or algebra (in the sense of monoids, groups, rings, etc.) or category theory for the general public, but with luck others will.I was also bit by the GEB bug as a young'un, I went so far as to write a "critique" of his ficticious alter-ego Egbert B. Gebstadter in the form of a dialogue (in imitation of one of the many that appear in GEB.) I sent this to Hofstadter himself, and was delighted to receive a very personal response. That was in 1986, and I'm happy to report that we've actually enjoyed sporadic (including occasional f2f) contact throughout the intervening years.
Wonderful human being, awesome writer, and absolutely and forever an idol for me. Thanks Doug.
-- Alan Canon (Louisville KY)
He covers the whole range of science and technology in a clear, well-organized presentation. There's even a short appendix on math.
It's a few years old and so it doesn't cover the most recent discoveries, but it should be perfect for your needs.
Morris
Get an understanding of evolution. Read Richard Dawkins' The Selfish Gene.
David J. Griffiths has written three introductory physics books and all are outstanding. Highly readable and engaging, the books are great as introductions and are very useful as references and refreshers. He leaves in the equations and tells you how to solve problems, but also adds a great detail of physical insight into any derivation. Griffiths seems to recognize that physics is (at least) two things: Knowing things, and being able to do things. (Many time people claim that these also form two categories, Theorists and Engineers, and Researchers are said to be a combination of the two, but I don't buy that.)
But, again, what makes Griffiths great is his readability. Discussing the variance and standard deviation of a wave function--or, rather, a probablitiy distribution--at the beginning of his Intro to QM book, Griffiths write "This quantity [sigma_squared = ] is known as the variance of the distribution; sigma itself (the square root of the average of the square of the deviation from the average--gulp!) is called the standard deviation."
The "gulp!" tells you to go back and read that again to make sure you understand it! He also adds occasional (funny) puns, and don't skip the footnotes! Definitely three highly readable and very helpful intro volumes!
(And as a bonus, he also provides very nice math primers--in fact, I used his EM book to help me with a vector calculus math class!)
is 'Mathematics for the Millions -- How to Master the Magic of Numbers' by Lancelot Hogben. ISBN 0-393-30035-8.
If you are looking for a book that explains why the various matematical properties and axioms are what they are, only a text for a graduate degree course would explain that stuff. However if you are looking for a "why'd they do that" then this book is for you.
Originally written in 1937 this is an awesome book. I found this book a godsend while I was in college. It is basically a history of mathematics. By giving a historical perspective, most of those mathematical "WHY" questions get answered because you can see how the mathematics evolved step by step.
It covers the basics: how numbers developed and why, how geometry developed and was used, how trigonmetry sprang from geometry, how spherical geometry/astronomy came from applying trig to navigation problems, how improvements in technology linked motion to geometrical figures that could be described by algebra, and how problems in describing motion lead to the developement of calculus. Throw in statistics being developed to try to predict games of chance for good measure.
The material is layed out with quite a bit of detail and has plenty of examples and diagrams.
With this book under your belt, much of the reading suggested by others will be far more understandable.
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All the texts I've seen aimed at school students have no relation to the physical world at all - mainly I suspect because many high school teachers don't know how the mathematics they teach can have any possible application. If an engineer or a mathematition chooses a text for a course they are less likely to pick something that is there just to tick a box labelled "student knows calculus", and are more likely to pick something that leads to understanding.
Then again - I was a lazy student that never bothered to learn my times table - I couldn't see any point in learning more than the prime numbers.
Surreal Numbers by Conway. Not exactly what the original question asked. Here is an excellent text which shows how math is actually done. I.e. how proofs come into existence. More correctly, ONE of the ways how math is done. This is a delightful short book, written in story form. Not only is the subject very interesting, the insight into how math is done is lovely. I highly recommend this. WARNING: Reading the book requires a certain level of mathematical sophistication. Definitely NOT a light read.
SR Book List. Many of the books in this list are what you are looking for, and you can easily try them out before purchasing them.
Where the Music Matters
He's certainly opinionated:
It's pocket-sized, short on formulae and long on clear, elegant explanation of the concepts.
The topics, per the table of contents, are:
- Models
- Numbers and abstraction
- Proofs
- Limits and infinity
- Dimension
- Geometry
- Estimations and approximations
Gowers covers quite a range of ground within those topics, and manages to make sense of concepts like hyperbolic geometry.The book is not intended to replace a full-sized textbook, just a helpful explanation of the ideas behind the theorems.
It's published by the Oxford University Press, and the ISBN is 0-19-285361-9.
It teaches the theory behind the mathematics - it actually starts you out on the "why" of more basic mathematics (algebra, trig., etc.) and moves on from there, building theorem upon theorem until you get to calculus and beyond.
!!go to the library!!
1-Read anything about science and math by Isaac Asimov.
2-Read anything about biology (I'm Joe's Liver) in past issues of Reader's Digest.
3-Forget calculus. Master algebra forward and backward.
4-The history of science , math and human endevor is what makes it all make sense so try to learn it in historical contexts. This also human-izes the whole thing and makes it easier to remember cause its not just facts and figures but STORIES.
The key to really mastering these subjects is to have a good teacher.
By all means, get some of the books recommended by fellow Slashdot readers. I'm familiar with many of them and a lot of them are great.
But at some point, no matter how good the books are, you'll get stuck on some point - and that's where you need to find a good teacher you can turn to. It doesn't have to be someone you see in person - someone you correspond with via email or over the phone would be fine.
It doesn't have to be someone with any sort of credential - but ideally it should be someone who is either currently a student (studying math/science at a much higher level than you) or someone who uses these subjects in their work. The main key, though, is to find someone who really loves math/science, and someone who's really patient.
I love helping people who really want to understand math or science. It gets old fast if the person just wants to know how to get the right answer and doesn't care why. If they really care, and they're really patient enough to take the time to learn it really well, then I'm always more than happy to take the time to help. It's fun! I really love it when the light bulb comes on in somebody's head! (Feel free to email me - I'm great with Trig, Calc, & Discrete Math.)
How to tell a good student: The bad student asks, "how do you solve this problem?", but the good student asks, "I tried to solve it this way, but it didn't work...why?"
How to tell a good teacher: The bad teacher, in response to the good student's question above, responds, "that's the wrong way to solve it; here's the right way". The good teacher responds, "interesting approach - let's figure out why it didn't work".
Mathematics is not a science. It's not a set of facts.
Rather, it's an artificial construction which was build
from some axiomatic bases by logical means.
School math is a super-lite version of what math really is.
Real math is "source", while many non-math
(non-physics) students
usually study "binaries" - compilations of popular facts.
So, if you want to study mathematics, look into the sources.
I've found that usual western math books are not
aimed to give understanding: just like binary programs,
they are for "users", not "hackers".
Yes! I highly recommend Dawkins, especially The Blind Watchmaker and Climbing Mount Improbable.
It's interesting that one of the authors recommended by so many on this thread, David Berlinski, is as famous for writing The Deniable Darwin as he is for A Tour of the Calculus.
You can also read replies to his article in Commentary (including one from Dawkins).
I would have been mad about all the bullshit in college like what you bring up, but the biggest bullshit is teaching science majors crap that is useless for getting a job, useless on a job other than re-teaching this useless crap, and sheds no insight into reality. E.G. Calculus tricks belong in computer programs not the heads of 20 year olds - they serve no good purpose. EVERY physics major I graduated with and kept in touch with wound up writing computer programs for a living. A little reality heads up would have been nice; but then fewer physics majors means fewer instructors in physics are needed; so career couseling BY the department I was majoring was filled with LIES.
I didn't see this posted, but if you want a wonderful little book that'll really open up the world of math (without you having to understand a lot of math in the process) I highly recommend the book "Fermat's Enigma" It's a nice, light read, and will take you through the history of math from the Pythagorean Brotherhood, to the solving of the world's greatest math problem.
I concur with others above, books are no substitute for teachers.
Once you get past single-variable calculus, particularly a firm grip on integration, I highly recommend H.M. Schey's book, "div, grad, curl, and all that" which clearly explains multivariable vector calculus, along with some physics for concreteness and good measure.
Physics by Giancoli
Introducing Pure Mathematics by Robert Smedley and Garry Wiseman
Further Pure Mathematics by Brian Gaulter and Mark Gaulter
In addition, I would recommend several maths books:
Discrete Mathemathics for New Technology by R.Garnier and J. Taylor
A First Course in Abstract Algebra by John B. Fraleigh
Of course also the asimov books others have mentioned. The Introducing and Further books are very interesting since they start from zero and go to quite advanced calculus concepts, yet attemp to cover all important mathematical concepts in existence. They take a while to read, but it's worth it.
Instant Physics - Rothman
This is exactly what you ask for. It covers basics mechanics and electrodynamics, but does it so you understand why things work.
The Illustrated History of Time - Hawking
This book is the reason I became a physics major. But do yourself a favor and make sure you pick up the illustrated version.
Calculus Made Easy - Thompson
I hated calc until I read this. Within the first two chapters it all made sense, and I understood the amazing utility of the method.
Fermat's Last Theorem - Singh
This book covers a whole lot of the 'why' of math. I highly recommend anything by Singh; he is a great science writer. The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth - Hoffman. It's the biography of Erdos, but it goes over a lot advanced math concepts in an easy to understand manner. Erdos's life is also fascinating. He was a bit of a math gypsy.
Posting here because I can't find an appropriate thread and I want to be near the top.
Look at any of the penguin classics. They are very cheap, and many of them are quite good. I have physics, math, and computer science texts that cost around 10 bucks each that are worth their weight in gold. They generally aren't state of the art (hence "classics"), but many provide both an introduction to the material and enough depth to be worthy of an upper division class on the subject.
The best piece of advice I can give anyone trying to learn from a textbook is to tell them to work through the problems. Anyone should be able to pick up many of the textbooks listed below and work though as many of the problems as time allows (limited either by patience or by real life events). Most textbooks provide answers to selected problems, so you can check your progress.
I should also probably qualify the above by saying that I have both been a professional scientist and a lecturer at a university in the past (Ok, so I am still a scientist).
The man's subject was "math books" and so on, and most of you weirdos can't read very well, immediately launching into a lot of useless books and off topic. Go back to school to learn English composition and how to think clearly despite having a high I.Q. So, I immediately am off topic, myself....
I would recommend going to "The Learning Company" and purchasing their various recorded programs to view at your leisure. Also, check out the listings for your local community college for video, or telecourses, on math and science. You will find them quite useful, videotape them in a series yourself, use TiVo, and so on, to collect them. I did it this way, needing a few math courses for another degree in a different state, which required Algebra, and was able to CLEP test out of the math after a refresher course or two for free. Also, go to Amazon and simply do a search on Math books and you will books on what you are looking for, with better advice than you are getting here in the reviews....
Lewis Epstein wrote two very good physics books that are enjoyable and easy to read while remaining scientifically sound. One is "Thinking Physics", and the other is "Relativity Visualized". I used examples from Thinking Physics in a college physics lab I taught, and the students responded well.
It's priced as a textbook, and isn't as sexy as some of the popular science books, but if you want a taste of how physics is done (rather than a list of what physics has done), it's hard to beat. The basic physics chapters rival any intro physics text I've seen.
Also, I note that many people have recommended th Feynman Lectures. While I have a great fondness for them, they may be something of a shock to anyone new to the field. By all means, take a look, but don't despair if you find them hard to follow. (Most people don't really fall in love with them until after they've spent several years learning the material from more traditional textbooks.)
I can only speak about mathematics but I have always hated the complaint that mathematics never teaches "why things work". First many do not realize that many of the true ideas behind school mathematics are very profound and need quite a lot of work to even approach a "proof" that demonstrates a true meaning of the subject.(also some proofs obscure the true meaning) For many this would not explain "why" and was largely the complaint against the "old school" system of mathematics instruction.
Accepting that many ideas cannot be proved in the limited time that a teacher has with a student; then what would be an acceptable explanantion of "why" something works? (for some people basic physics is enough, for some it is pretty pictures, etc...)
For math anyway...
Here's some books I found to be very good..
Practical Algebra: A self teaching guide, by Peter Selby and Steve Slavin(second edition). One of the best math books I've found. Covers both concepts and details, has good excercises to do..
How to ace Calculus, The streetwise guide, by Colin Adams, Abigail Thompson, and Joel Hass. Not hugely detailed, mostly conceptual, but good. No excercises, made to be used in conjunction with a real text book.
Blessed are the pessimists, for they have made backups.
When I attended BYU for a while it was the same sort of thing.
Physics tests were 'multiple choice' -- 0-9, fill in the dot. Do a normal 'word problem', figure out all of the math, get your answer -- say 1.0992, then fill in the least significant digit on the test form.
Did you keep your significant values straight? Did you round correctly? If it should have been 1.099 or 1.09921 you're wrong, even if you did 90%+ of the problem correctly.
Curve was typically 29+ A, 28 B, 27 C, 25-26, D, 24 and under an F.
I'm still very bitter about this. Glad I got to pay a lot of money to get screwed over by a broken system. I ended up going to an other school which worked out a lot better. Smaller classes with teachers interested in teaching.
"But actually trying to use m4 as a general-purpose langage would be deeply perverse" --ESR
I highly recommend it, you my also be intrested
in QED an excellent book on
Quantom Electro Dynamics designed for the masses
and is a non technicall aproach to technical
material.
DRYICE
The best piece of advice I can give anyone trying to learn from a textbook is to tell them to work through the problems. Anyone should be able to pick up many of the textbooks listed below and work though as many of the problems as time allows (limited either by patience or by real life events). Most textbooks provide answers to selected problems, so you can check your progress.
Absolutely, 100%. Nobody is born with the ability to take a triple scalar product or multiply two matrices (both happening in your video card when you're playing Doom!). As a great Calculus teacher once announced to his class through a thick French Canadian accent, "Math is not a spectator sport." (Actually, it came out as "Matt ees not a spectator sport.")
Having said that, Calculus is my favorite kind of math. It's incredibly elegant and probably the most useful advanced math, as it touches everything you do. Consider your car. If you calculate your speed using a watch and the odometer, you have an idea how fast you were going, but your speedometer is actually showing you the value of the derivative at any instantaneous time. Your speedometer shows the rate of change of position (distance travelled) at any instantaneous time. That's calculus.
Don't be afraid. "Calculus" (besides being a formal term for tartar the dentist scrapes off your teeth) means small stones in Latin... small stones as used for counting.
Two *great* books on the subject:
Remember: Do the problems, succeed. Don't do the problems, fail. It's that simple.
Fire and Meat. Yummy.
try www.teach12.com. they have a bunch of courses taught by well respected professors. i've only bought the humanites stuff but a friend has some of the sciences courses and says they're great too. also make sure you ask them if there's a sale on the phone. usually the web rates are the lowest, but occasionally there's an partially advertised sale they'll let you in on.
Feynman Lectures (again)- no competition if you are looking for that much depth. Physics for the Inquiring Mind - as good as Feynman but MUCH simpler- written for Liberal Arts students at Princeton many moons ago. Out of print but worth the hunt. I teach physics at a state university...all textbooks I have seen written in the last 15 years are SHIT. No editorial control, lots of pretty pictures and not much else. I have made thousands of dollars from publishers correcting these books for errors after calling them up and berating them for low quality. Halliday and Resnick (old editions, like 1970's) is widely available in used bookstores and is very good, if very dry. Compared to today's texts one of its most notable features is that it contains NO errors.
Math is a very important thing in High School... But not in the way that a lot of you think... There are two uses for math in High School...
1) To teach the concepts of basic math and calculus.
2) *The most important* To exercise the students
brain and to keep them mentally alert.
When a student graduates from school it is a huge shock to them because the world is a lot slower then it is in school (at least it should be if they were working hard). Suddenly you don't have home work every day... You don't have tests every week and there are no such things as exams... Work is very much different. Now some businesses do testing on there employees... but it's not as bad as school...
When you drop math... you drop creativity, the ability to learn other subjects, to stay focused, and most importantly... to stay curious...
--
There I finally was smart enough to save this as plain text lol.
Dude, just enroll at the beginning level(for you) at a local Junior College. While the books are fine you'll get to ask questions and iteract with others more and less knowledgeable than you. That is more valuable than sitting in your room studying concepts with no one to bounce ideas to. Never too late for you!! Good Luck
I especially recommend the volume entitled Mathematics as a general introduction to that topic.
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How. I understand the area under a graph is the intergral of the formula of the graph, but if you have an everyday shape, chances are its not created by a known mathematical formula. how do you work out the area using calculus?
Ahh... Now we discover the joy of Infinite Series. Infinite series allows you to do all sorts of things to (arbitrary) precision. (Arbitrary in that it won't spit back an answer to 300 decimal places unless you make the program you write run through the loop 300 times...)
Basically, here's the idea. You can do a regression of the known points on the graph to come up with a function (formula) to describe the relationship. Regressions come from infinite series, but are used in a plug-and-play format in statistics courses. Also annoyingly, Excel 95 and up includes the capability to do them in the Data Analysis tools, OpenOffice does not yet [grumble grumble]. Anyway, once you have a function, you simply integrate it to find the area.
My favorite part of all this is that the series usually gives you a nice long sum of little polynomial expressions, which are individually and collectively easy to integrate.
Practical applications? Fourier Transforms and Fast Fourier Transforms. They allow you to express any function (audio waveform?) as a sum of different overlapping sinewaves. From there, you can do all the math you want on them. MP3 and Ogg codecs do this.
Fire and Meat. Yummy.
For physics, try reading The Cosmic Code by Heinz Pagels. I knew nothing about physics before reading, yet I found the concepts easy to understand.
Thomas! Calculus and Analytic Geometry Look in used book stores. If you find an original edition (two volumes) look for the infamous problem whose "solution is intuitively obvious to the most casual observer" (the problem is worth of a PhD's thesis). I love Thomas CnAC. It is one of the few books that is complete, rigorous and yet still accessible.
For maths you might want to try the books of Ian Stewart.
The desire to understand the world and the desire to reform it are the two great engines of progress -- Bertrand Russell
It is rare that somebody can write science book that are actually enjoyable to read. I found these two books excellent.
Besides science fiction, Asimov wrote quite a few good non-fiction books on the sciences, etc.
- "History shows again and again how nature points out the folly of men" -- Blue Oyster Cult, 'Godzilla'
For Fourier Analysis, _Who is Fourier_ by the Transnational College of LeX. For QM, their book on QM. For math, science and education in general, ask Alan Kay's people at Squeakland, http://www.squeakland.org. Math books don't have to be paper, you know.
There is a website TDLC.COM that helped me a lot with caluclus. It doesn't always explain the "mechanics", but, there are links to background information and articles to help understand. There are also "getting at the concept" sections at the beginning of each chanpter. The available range on books on line is pretty good as well. I have been out of calculus for a while now, but still maintain my subscription...
College textbooks (the ones for freshman/intro courses) might be a good place to look. They don't "squeeze in all the facts required by state law" like high school textbooks do, and they usually provide a more scientifically and mathematically valid description of a subject than books written for the general public. Books written for the general public sometimes dumb things down.
I was taking a stats class when a coworker (bluecollar) implied that it would be a useful class. Most of what I learned in that class was useful only in abstract where I could think of applicable uses for calculus while I was sitting in class. Stats I was trying to stay awake thinking I'll never use 90% of this; calculus I'm going on tangents in my notes with how I can use this stuff.
Heroscape, it's like legos combined with anachronistic wargames.
I learn tons of stuff from just browsing around wikipedia.org. They're a good site, just check the facts if they seem dubious. If it's wrong, change it! It's a wiki. Maybe it's not the *best* educational resource, but I think it's good enough! It has excelent math/science articles in particular, as well as the best today-in-history articles I've found on or off the web.
Is that book in the public domain?
CAPS LOCK: ITS LIKE THE CRUISE CONTROL FOR AWESOME
"Math For Adults" probably is the art of encoding pr0n in an efficient
way. JPEG and MPEG come to mind....
It is a textbook that deals with concepts not just dry facts and it is written by the other genius named Linus that the 20th century produced.
These are aimed at 17-18 year olds taking 'A-Levels' which are generally accepted to be about as academically challenging as the average US college education (e.g. resolution refutation and skolem's in a math book for 17 year olds in the UK!). I found they not only go into depth about the concepts and ideas, but they are often backed up with online sections and countless exercises and examples. There are 'A-Levels' for just about every classical subject under the sun so plenty of books around.
You can problably get a load of them from Amazon or something.
I saw a cheap trig book at B&N last week. I almost bought it, but I really want a book that teaches math as it applies to computer related subjects such as graphics. I couldn't find anything specific to it, but of course it was only B&N (not online). They tend to not carry many tech titles.
Category Theory can be used as an intuitive branch of mathematics, and a great book for math newbies is available. Check it out.
ISBN: 0-19-513427-3, 1998, Oxford University Press. This is a concise and readable summary of the history, philosophy and theories of science. I had a bit more science and math education than you claim, but it was a long time ago. This book really helped me to appreciate the accomplishments of those who contributed to the scientific endeavor. It won't teach you the particulars of any one of the sciences, but it will help you to put them all into a context for further study.
Standard college course work is pretty much learning formulas. Until I had to implement math/physics in grad school research, I didnt deeply understand them. I wonder if there are good books on math and physics for game developers? I saw some good books at SIGGRAPH last week on computer algorithms for game developers covering some of math and physics. When you actually *do* some of this stuff, then you learn it better.
Michael Spivak has a couple of books on calculus that are very comprehensive. His "Calculus" proves everything from first priciples so to speak. If you really want a full understanding of calculus and analysis then I suggest Calculus by Spivak
Hopefully someone will find these interesting:
CALCULUS
Quick Calculus by Kleppner and Ramsey.
This book is designed to teach you step by step all the calculus you would learn in 2+ semesters of college calculus classes. It is workbook style. That is they teach you something and then have you work individual problems. I tought myself calculus in 10th grade by using this book.
PHYSICS:
The Feynman Lectures on Physics:
I've only read volume 1 but I have 2 and 3 queued up. These are good for getting an understanding of how and why physics works if you know a fair amount about calculus and you've taken some physics (high school at least). THESE WILL NOT teach you how to solve physics problems (as far as I can tell they don't publish the problem set anymore).
Schaum's Outlines: Physics for Scientists and Engineers by Michael E Browne
This one will give you practical problems to solve and practice with, plus a concise explanation of topics that Feynman blew past you too quickly.
STATISTICS and DATA ANALYSIS:
It's hard to recommend anything specifically here because it's a hard subject to teach and I've never found a great book.
Principles of Statistics by M.G. Bulmer (dover)
It's an inexpensive paperback and it gives a very good overview of the basic concepts of statistics.
An introduction to error analysis by John R Taylor
I haven't read this book but I've had it recommended. If you want to understand why you need to be skeptical of numerical data, you at least need to know something about this subject.
Statistics for Experimenters by Box Hunter and Hunter
This is another one that's supposed to be a great book. If you want to do experiments and analyze the results you need to study this subject.
MATHEMATICS:
Mathematics books are often aweful, and what makes a good mathematics book is very personal (ie. your learning style), so here's a general list of subjects and why you should study them.
Calculus and differential equations Without calculus you can't do physics effectively. see my recommendation for Quick Calculus above. Differential equations are effective for modelling the behavior of physical systems.
Linear Algebra This topic forms the basis of several important fields, such as signal processing, statistics, differential equations, and much of numerical analysis.
Topology This is a field that will teach you more about important properties of functions, and of sets. It's basically about invariance: properties that do not change when you transform something (continuously)
Combinatorics or discrete math This is about counting, probability, and sequences of numbers. It's entertaining and important for computer science.
AS FOR MATH BOOKS:
The thing to know is that there is a huge variability in math books. I'd recommend starting with cheap Dover paperbacks and trying several in a particular field. Once you've exhausted those (either too poorly written or too complicated for you) at least you haven't spent a lot of money.
If you need more after the Dover paperbacks, move on to something hardback and expensive but sit down in the book store and read through it first. Does the author take pains to explain things, or just use a flurry of symbols?
Remember you can't start at the top. Work your way up a mathematical subject, preferrably with some application or core reason that drives you.
((lambda (x) (x x)) (lambda (x) (x x))) http://www.endpointcomputing.com a scientific approach to custom computing.
Just wonder if there are any good online sites that can help adults who aren't fortunate enough to have the opportunity to properly learn math, science, or whatnots that most think are _basic_skills_ ?
Thank you !
Muchas Gracias, Señor Edward Snowden !
Nope, it's still under copyright-- but it is already on the Web with permission of the London Mathematical Society!
On Computable Numbers, with an Application to the Entscheidungsproblem
I can understand why they allow publishing on the web, with those ugly colours, no one will ever read it...
Evolution of Language Through The Ages: 6000 BC : ungh, grrf, booga 2000 AD : grep, awk, sed
One of the subjects that really put it all together for me was Linear Algebra. It doesn't require calculus so much as a certain mathematical sophistication. The book that made it interesting for me was "linear algebra and its applications" by Gilbert Strang
All generalizations are false, including this one. Mark Twain
The correct path, is to go to a highly regarded 4 year school, and then transfer into the private university from there.
Heck, you could get a 4.0 GPA and not transfer into any of those schools from a community college. Elite private universities take fewer than a hundred transfer students a year, and they usually get many thousands of qualified applicants - many of those from highly regarded 4-year schools. If your goal is to go to an Ivy League school, go right after high school or not at all. It's still hard, but you're probably 10x more likely to get in.
You dont go from community college straight to Harvard, you go from community college, to a state school, to an elite private school and then you go to Harvard on the graduate level.
Not trying to discourage you, just being realistic. If you don't believe me, look up the statistics for transfer students at one of those schools and see how different they are from first-year acceptance rates.
I know people who have gone to Harvard on the graduate level. You dont need to go as an undergrad, sure going as an undergrad makes it easier but on the graduate level you can transfer into most of these schools easily because not alot of people actually go to graduate school.
You can transfer into an elite private school from a state school, that stuff happens all the time, yes you need very good grades, but its a step by step process, you move up the ladder piece by piece and step by step.
You start in a community college, you do well and you transfer into a state school, you do well there and then you transfer into a private school, you do well in the private school and then you can transfer into an elite private school.
My sister has done this, so it does happen and its fairly common, its not common however to be accepted into Harvard on the undergraduate level and most people who get degrees from Harvard or any of these ivy league schools are graduate students.
The average undergrade GPA in Harvard Business School is 3.5, this is Harvards most elite school next to their law school. There around 2000 enrolled.
The Law school is extremely difficult to get in, the average GPA is 3.7 or 3.9. 13% of those who apply are accepted.
This means I have a 13% chance of getting in, if my GPA is above 3.7.
Harvard Medical school, under 1000 enrolled, EXTREMELY difficult to get into, with only 5% being accepted. Average GPA of 3.8.
So its not impossible to get into Harvard, if you have a GPA of over 3.5, like I said over and over in many of my posts. You have about a 13% chance of getting in, I think I'm one of that 13%, it may sound unrealistic, but self esteem is not one of my flaws.
If you use Linux, please help development of Autopac
Ok, Mechanics, but theres a limited number of mechamics in this country, the number grows smaller every year, and eventually only mexicans and people from other countries will be doing these kinds of jobs.
Truckers? Nurses? Ok I admit those jobs will be needed, but like I said before eventually there wont be a shortage or nurses or truckers as we lose more jobs, more people with degrees will become nurses and truckers.
Like I said, yes you can get a degree from a community college, you can get certified, but when it comes to actually having job security, this is where your professional degree beats out the cerfication from the community college.
If you use Linux, please help development of Autopac
That's how we used to measure areas under curves in gas chromatography before there were such things as digital integrators (early 1970s)... have the output of the GC go to a chart recorder, then cut all the different curves out, weigh them all then weigh them individually. It wasn't perfect, but it worked well enough to get me a degree in chemistry!
Sorry to sound contrarian, but PLEASE! You, or your sorry companions failed the course because you didn't see the obvious answer. And before you run off on "why should I have to do that, they should teach it right the first time!" consider that its simply a game. How much of anything you learn in any school, at any level, is actually used in real life? 30%? Maybe!
1. AUDIT THE TOUGH COURSES BEFORE TAKING THEM FOR CREDIT. and/or...
2. Be a Gym major, get a 4.0 and go to Georgetown, MIT or Stanford for grad school. Audit the courses and sail into grad school instead of the slobs who ACTUALLY struggled through the tough ones and can't get in because of their 2.9 GPA.
That's what I learned in my math courses: How to play the game.
I happen to like Stewart's Calculus with Vectors book. Covers from precalc (quick review) all the way through 3-d vector calculus. Lots of problems and decent examples. I used this book as an undergrad to learn calc, but even as a grad student I often find it invaluable as a reference.
Don't become a regular here, you will become retarded. -- Yoda the Retard
Why is it Americans insist on shortening mathematics to math?
Just a note to highly recommend this book, by David Deutsch, Professor of Physics at Oxford University and world leader in the field of Quantum Computing. Dr Deutsch provides a first rate discussion of the weirdnesses of Quantum Mechanics, and uses the Many Worlds interpretation of QM to resolve them. Along the way he writes intelligently about topics as diverse as evolution and the theory of computing. Aimed at the layman, this is an excellent introduction to the field, tying in elements from many different disciplines with an ease not seen since (the also excellent) Godel, Escher, Bach by Douglas Hofstadter.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
Reading your post- I couldn't help but plug your local community college. As a community college graduate who went on to get a B.S. in
Math from a top 50 ranked school, I highly recommend this route.
In my experience, a CC faculty may not be the best overall, but each department nearly always has at least one great instructor. If you go to your local CC and talk to members of the math department, explaining your situation, you will get hooked up with the right people and classes.
The main downside of this option is the fixed schedule, but that can also be an advantage if you think that you may lose intrest with the self-study option. It is at least worth looking into.
Check out Journey through Genius: The Great Theorems of Mathematics. It's a good read. Not mathematically rigorous, it covers important theorems in mathematics with a nice balance of math and historical context.
It covers topics such as Euclid and the Infinitude of Primes, Archimedes' Determination of Circular Area, the Bernoulli brothersand Harmonic Series, and Fermat's Theorem.
Look, if you didn't learn this stuff the first time around, you probably don't have it in you to learn it on your own. Go take a few courses at a community college if you really want the skills. If you just to think about 'cool stuff,' read some general interest books like A Brief History of Time or even The Physics of Star Trek. It'll make you more interesting at summer block-parties, but not much else.
Here is a listing of free books that might be relevant.
Find free books.
Bitter about BYU here too. A few gripes:
Professors who came to class totally unprepared (they hadn't looked at their lecture notes since teaching the material the previous semester).
Class sizes that were totally ridiculus (Most classes were 300 students - even my senior year - I got a bs in zoology - the department got reorganized after I left) I was in a class with 900 students once.
TA's do all the teaching - I wasn't aware that I'd be paying other students to teach me - I mistakenly thought I was going to be taught by professors.
Religion Professors that didn't know anything about religion. I didn't research professors very well and just took who ever was available that fit my schedule. Big Mistake! (For those who don't know: Religion is required at BYU - it's a religious school)
There are at least another half dozen complaints I have about BYU. And yes, I realize that mostly it's my problem if I had a poor educational experience at BYU, but I wouldn't recommend that school to anyone, ever.
Nobody found this yet? Google served up this link to the paper:
http://www.abelard.org/turpap2/tp2-ie.asp
Second, some books:
Third, don't skimp on the methematics! Mathematics, especially calculus, underlies all of modern science. You can't really understand most of the science without understanding calculus, and if you understand calculus, much of the science will simply fall into place.
Finally, don't be too proud or stubborn to actually go back to school. You can enroll in a night course at the local community college for less than the cost of a bare-bones PC-clone. A little actual instruction goes a lot farther than a whole lot of unaided reading. You might also have some fun. (it's amazing how much fun learning is when you're not worried about getting the piece-of-paper)
If you can learn the basics of physics and math, you will be able to cope with (if not master) just about anything. Anything you weren't actually taught, you will be able to get a reasonable grasp of after a few days (sometimes only a few hours) of reading and thinking. If something takes longer than that, you have hit upon a trully difficult subject and may need to look for a course to take.
When I was a BSEE undergraduate, I had to endure Kreyszig's "Advanced Engineering Mathematics". It is a horrible book if you're trying to learn differential equations. A much, much better book is "Applied Differential Equations" by Murray R. Spiegel.
Circle the wagons and fire inward. Entropy increases without bounds.
Has anyone mentioned Prime Obsession by John Derbyshire? Like Kanigel's book, it only deals with a subset of math (in this case the Riemann hypothesis), but it's brilliantly lucid, and well-explained enough to both make you feel quite smart and actually teach you something.
My kid is a little young for this stuff but I was worried that I was gonna be left in the dust as well when the time came. I wasn't anything close to a math major in HS so these references are a big help. Thanks guys/girls!
MMORPG Fan? Prove your worth!
I love this book. Exactly what you are looking for.
2 01 781301/qid=1060262440/sr=8-1/ref=sr_8_1/102-186100 6-1032911?v=glance&s=books&n=507846
Computer Science: An Overview by Glenn Brookshear
http://www.amazon.com/exec/obidos/tg/detail/-/0