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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.
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.
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
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.
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.
"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")
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
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.)
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
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!
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.
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.
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?
The mathematical/physics books put out by Dover Books are decent. They give you a good overview and background of the subject. The subjects range from Number Theory, Information Theory, Magnetism, Mathematics, Physics, Probablility,etc.
The Dover books are usually inexpensive, and some are good references. As a text for the non-mathematician, they're probably inappropriate. What they do cover is usually in depth but also don't pull punches. For example, the opening chapter of "Modern Algebra" jumps directly into set theory without a good treatment of reals, naturals, integers, etc.. Yes, the whole point of the chapter is to introduce these, but talking about isomorphic and abelian groups in the initial pages to a math neophyte is perhaps not the best approach.
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.
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
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:
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
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
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.
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.)
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!
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Okay, I'm going to overlook the fact that the primary poster of the thread is pursuing personal edification, and not a particular educational track, so the fact that grades are given doesn't seem to be a relevant concern in his case.
Let me see if I can be helpful in this sub-thread. I'm an adjunct faculty member at a community college, I've taught for going on two years now. I'll speculate that I'm teaching in the same region you're going to school, based on the 4-year institutions you're looking at.
If I could give one crucial insight to my students, that I usually have to bite my tongue on, it's this. 4-year schools have expectations which are an order of magnitude beyond those of 2-year community colleges. My biggest challenge in teaching now is to take my experiences at a 4-year (state) school and dial them way down to a level where my students can pass the course, with some getting A's. Maybe my two best students in a class of 20 seem to be doing work that would be appropriate at a 4-year school.
I would encourage you to not shy away from any courses at a community college. The hardest class in your school will be just a taste of what you'll be asked to do at any 4-year school. You need to find this out about yourself, if you can function at this level, sooner rather than later. If you're worried about passing a math course at a community college, the honest truth is, Harvard is not in the cards. My guess is that a school like Harvard is not going to distinguish much past "4.0 or not 4.0?" when looking at a GPA from a community college.
Not to say that other colleges you mention are not a possibility. I write quite a few recommendations for my students to go to Northeastern and BU, but even those are generally just my "A" students.
We know where leadership by an anti-intellectual "strongman" who scapegoats minorities and likes boisterous rallies goes
A much better book is Riordan's, The Hunting of The Quark.
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
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.
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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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...
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.
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.
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".
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.
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.
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.
I wonder if there are good books on math and physics for game developers?
O'Reilly publishes a book called "Physics for Game Developers" and Charles River Media publishes a book called "Mathematics for 3D Game Programming and Computer Graphics." Both are quite good.