Anytime a professor offers an outside of class time "problem solving" session shortly prior to a test, they are letting you know they failed to teach all of the problem solving skills and especially never related practical knowledge. While I can appreciate the dedication it demonstrates on the part of the professor, they should be doing their jobs and putting it in the classroom to begin with.
Wow, I can't believe how wrong this is --- clearly you misunderstood your role in the classroom as a student. In class, a professor should explain the concepts and techniques, but you shouldn't expect them to teach you step-by-step methods of how to solve every single problem in the subject area --- there isn't enough class time for that.
The most important part of the learning process happens outside of class --- when you work and struggle towards learning on your own by working through the problems. Your professor in class is a guide in your learning journey, but they can't do the learning for you --- you need to put in the effort yourself!
When a professor schedules an extra "problem solving" session, they are letting you know they can't be there to hold your hand through that most important and difficult part of the learning process --- the part where you work and learn on your own --- but they understand that you probably got stuck at some point in that process, and are willing to spend their own valuable time to help you get unstuck.
You have a fundamental misunderstanding of how teaching & learning works. Rote and memorization are essential first steps --- get the techniques down, so that you can free up your higher-level reasoning for understanding. You will never understand math if you can't do math.
I guess you would also ask sports coaches to stop doing drills in their practice sessions?
-- Doing practice lay-ups and free-throws over and over is so boring, let's just explain to the kids how to do them, and then throw them into a game.
-- Practicing your swimming strokes is so boring, let's just explain to the kids how to swim, and then throw them in the pool and the swim meet, and they'll do just great.
Yeah, right.
Your analogy about painting is way off, as well. Have you never heard of artists practicing techniques by copying works by the masters? Never seen an art student in a museum with a sketchbook in hand?
The problem with most students is that they expect to be taught, but they don't expect to have to put any effort themselves into learning. Then, when they don't learn, it must have been the teacher's fault...
Having sat through a number of maths classes, and lectures, I find that the people teaching the subject, often fail to appreciate that what they find easy is not necessarily the case for others. This means they don't show the necessary steps or fail to find techniques to facilitate the understanding. Sometimes its almost as if they want to make maths hard to learn. Of course people end up get anxious since they end up feeling stupid.
Having taught a number of math classes, I find that the people taking the subject often fail to appreciate that learning math takes a considerable amount of effort outside of class. You should not expect to go to math lectures for three hours a week and have the subject poured into your brain in that short amount of time. You should expect that there will be times in a math class when you don't understand what the instructor is saying. It is your responsibility as a student to go over and reconstruct what the instructor did in class. Keep track of the things you didn't understand and then actually spend some time thinking about them! If you still can't figure them out on your own, then ask questions about them later.
Although we talk about car analogies here, in order to make things easy to understand to the, I find the same can benefit maths. By trying to understand what the skill set of your audience is and adapting the teaching helps. For example the 'sum' sign looks hard until (if amongst computer people) you explain its just a 'for each' with addition and the 'pi' sign is a 'for each' with multiplication. In certain cases it is equivalent to the linguistic differences between English and Chinese, in that they both can talk about the same thing, but the way in which they do so is not the same.
Math is taught in an abstract way because that is its power: we want mathematical facts to be as widely applicable as possible. If all the instructor teaches is car analogies, then that is all the students will learn, and will end up being lost when they need to apply the same facts to chemical processes, for example. As well, an instructor is usually not guaranteed that all his/her students are computer science majors, so tailoring examples to the audience is not always practical. There isn't time in class to come up with one analogy for the biology majors, and another analogy for the chemistry majors, and then make it really abstract for the math majors, etc. Again, it is the student's responsibility to grapple with the concepts and notation on their own, and if they still can't figure it out, then ask for help!
GOOGLE READS YOUR EMAIL. When you sign up with google, you AGREE TO LET THEM DO IT FOR FUN AND PROFIT.
Not if you have a legally binding contract with them in which Google agrees that they will NOT read your email. My institution is also considering switching to GMail, and I recently attended an FAQ presentation on the process. One of the points stressed is that the contract with Google will explicitly state that university data is the property of the university and/or its faculty/employees, and that Google can't touch it other than actually providing the contracted services.
Mathematics is a product of human invention.
Human invention is a product of the natural universe.
Therefore, by the transitive property, mathematics is a product of the natural universe.
QED
Ticket draws are different than lotteries. With lotteries the number of possible winning numbers is fixed, so buying more tickets (with different numbers) increases the size of the numerator while the denomenator remains fixed, so playing two sets of numbers truly gives you twice the odds of winning. With ticket draws, every ticket you buy increases not only the tickets you hold but also increases the total number of tickets in the drum to be drawn from, so your increase in odds is not just a multiple.
For example, suppose there is a draw where 99 tickets have already been sold. You buy one ticket, so now there are 100 tickets sold and you have a 1/100 chance of winning. You buy another ticket (before anyone else does), so now you hold two tickets out of the 101 tickets sold, so your chances are now 2/101, which is *slightly* less than twice your chances with just the one ticket.
... Most people don't "listen" to music. They use it as a soundtrack to their sad pathetic lives as they schlep their bodies to and from work, or put it on as background during dinner, or an ambient enhancement while reading or cruising the web, or as something to hide the sounds of bedsprings while they fuck their paramour du jour...
... Because I can't fit my stereo system into my office, and I like working to music...
part of me wonders how effective a PhD would be at teaching high school students. Honestly, if you have a degree in Physics and can't find a job, I'm not sure I want you in front of students as you must be a horribly weird person.
What a small-minded comment. Not everyone is just after the money, you know. Most people who go to the trouble of getting a PhD have a passion for the subject, and often that is accompanied by a passion for sharing the subject through teaching. Have you ever considered that the person wanted to teach high school students, rather than viewing it as some sort of fallback job?
mini-itx.com is taking pre-orders for the pico-ITX -- I don't see anywhere on the site where they are taking pre-orders for the mobile-ITX that the article is actually about.
the ER/EI (energy return over energy invested) for hydrogen always is and always will be NEGATIVE.
You mean the ER/EI ratio will be less than one. Perhaps you should go back to grade school and learn about fractions again. Or did you mean the net energy produced will be negative?
So why isn't there cheap 100mbps service even in urban areas? This population density argument gets trotted out in every discussion like this, but it doesn't explain why I have to pay $25 or $30 per month for 4mbps DSL in a city with a population of 2.5 million (in the city proper, 4.5 million including surrounding sattelite suburb cities).
The story is not in italics, ie. it is not a quote from a user-submitted story -- it is written by the Slashdot editor who posted it, in this case CmdrTaco...
Hmm, it doesn't take much geometry to be able to calculate the derivatives of the trigonometric functions from first principles, and from there it is easy to calculate their Taylor series. So this naive definition of trigonometry using triangles is really not so useless after all. Sure there may be other ways of thinking of the trigonometric functions which are better for other applications, but for the argument at hand (that sin is not "closed form"), it serves pretty well.
Are you suggesting the concept of angle has to be defined in terms of infinite series? Go read a basic math book or something. Angles and trigonometry are at their core just basic geometry.
All you need to assume is that you have some way of accurately measuring lengths. Create a circle whose radius is length 1 unit. If you have two radii of the circle, you can define the angle between those two line segments as the length of the arc of the circle subtended.
Then the relationship between sin and angle is very straightforward using the basic geometric concept of lengths of sides of triangles.
Digression: if you really think about it, functions like sin(x) and ln(x) are really not closed form either - they are infinite series.
What the hell are you talking about?
sin has a very concrete definition - given some angle, it is the ratio of two particular sides of a triangle which contains that angle. That's basic trigonometry...
And ln also has a very concrete definition -- in fact there are several ways to do it. One way: Define ln(x) (for x>1) to be the area of the region under the graph of 1/x from 1 to x. For 0<x<1, define ln(x) to be the negative of the area of the region under the graph of 1/x from x to 1.
Nickel mining giant INCO grows a quarter million seedlings a year just for its regreening efforts in the small city (and surrounding area) of Sudbury, Ontario, Canada.
You've got the wrong term. "Hoosier" is an American term -- it's what you call someone who plays on any of Indiana University's sports teams. See here.
You're thinking of "hoser". A hoser is anyone you don't like. See here for other definitions. It originates from the "Great White North" program on SCTV, hosted by Bob and Doug Mckenzie. See here for a synopsis of the show.
Slashdot Mirror
Anytime a professor offers an outside of class time "problem solving" session shortly prior to a test, they are letting you know they failed to teach all of the problem solving skills and especially never related practical knowledge. While I can appreciate the dedication it demonstrates on the part of the professor, they should be doing their jobs and putting it in the classroom to begin with.
Wow, I can't believe how wrong this is --- clearly you misunderstood your role in the classroom as a student. In class, a professor should explain the concepts and techniques, but you shouldn't expect them to teach you step-by-step methods of how to solve every single problem in the subject area --- there isn't enough class time for that.
The most important part of the learning process happens outside of class --- when you work and struggle towards learning on your own by working through the problems. Your professor in class is a guide in your learning journey, but they can't do the learning for you --- you need to put in the effort yourself!
When a professor schedules an extra "problem solving" session, they are letting you know they can't be there to hold your hand through that most important and difficult part of the learning process --- the part where you work and learn on your own --- but they understand that you probably got stuck at some point in that process, and are willing to spend their own valuable time to help you get unstuck.
You have a fundamental misunderstanding of how teaching & learning works. Rote and memorization are essential first steps --- get the techniques down, so that you can free up your higher-level reasoning for understanding. You will never understand math if you can't do math.
I guess you would also ask sports coaches to stop doing drills in their practice sessions?
-- Doing practice lay-ups and free-throws over and over is so boring, let's just explain to the kids how to do them, and then throw them into a game.
-- Practicing your swimming strokes is so boring, let's just explain to the kids how to swim, and then throw them in the pool and the swim meet, and they'll do just great.
Yeah, right.
Your analogy about painting is way off, as well. Have you never heard of artists practicing techniques by copying works by the masters? Never seen an art student in a museum with a sketchbook in hand?
The problem with most students is that they expect to be taught, but they don't expect to have to put any effort themselves into learning. Then, when they don't learn, it must have been the teacher's fault...
Having sat through a number of maths classes, and lectures, I find that the people teaching the subject, often fail to appreciate that what they find easy is not necessarily the case for others. This means they don't show the necessary steps or fail to find techniques to facilitate the understanding. Sometimes its almost as if they want to make maths hard to learn. Of course people end up get anxious since they end up feeling stupid.
Having taught a number of math classes, I find that the people taking the subject often fail to appreciate that learning math takes a considerable amount of effort outside of class. You should not expect to go to math lectures for three hours a week and have the subject poured into your brain in that short amount of time. You should expect that there will be times in a math class when you don't understand what the instructor is saying. It is your responsibility as a student to go over and reconstruct what the instructor did in class. Keep track of the things you didn't understand and then actually spend some time thinking about them! If you still can't figure them out on your own, then ask questions about them later.
Although we talk about car analogies here, in order to make things easy to understand to the, I find the same can benefit maths. By trying to understand what the skill set of your audience is and adapting the teaching helps. For example the 'sum' sign looks hard until (if amongst computer people) you explain its just a 'for each' with addition and the 'pi' sign is a 'for each' with multiplication. In certain cases it is equivalent to the linguistic differences between English and Chinese, in that they both can talk about the same thing, but the way in which they do so is not the same.
Math is taught in an abstract way because that is its power: we want mathematical facts to be as widely applicable as possible. If all the instructor teaches is car analogies, then that is all the students will learn, and will end up being lost when they need to apply the same facts to chemical processes, for example. As well, an instructor is usually not guaranteed that all his/her students are computer science majors, so tailoring examples to the audience is not always practical. There isn't time in class to come up with one analogy for the biology majors, and another analogy for the chemistry majors, and then make it really abstract for the math majors, etc. Again, it is the student's responsibility to grapple with the concepts and notation on their own, and if they still can't figure it out, then ask for help!
GOOGLE READS YOUR EMAIL. When you sign up with google, you AGREE TO LET THEM DO IT FOR FUN AND PROFIT.
Not if you have a legally binding contract with them in which Google agrees that they will NOT read your email. My institution is also considering switching to GMail, and I recently attended an FAQ presentation on the process. One of the points stressed is that the contract with Google will explicitly state that university data is the property of the university and/or its faculty/employees, and that Google can't touch it other than actually providing the contracted services.
decimation means 1 out of ten killed
Decimation means reduced to one-tenth. That is, 9 out of 10 killed.
Mathematics is a product of human invention. Human invention is a product of the natural universe. Therefore, by the transitive property, mathematics is a product of the natural universe. QED
Ticket draws are different than lotteries. With lotteries the number of possible winning numbers is fixed, so buying more tickets (with different numbers) increases the size of the numerator while the denomenator remains fixed, so playing two sets of numbers truly gives you twice the odds of winning. With ticket draws, every ticket you buy increases not only the tickets you hold but also increases the total number of tickets in the drum to be drawn from, so your increase in odds is not just a multiple.
For example, suppose there is a draw where 99 tickets have already been sold. You buy one ticket, so now there are 100 tickets sold and you have a 1/100 chance of winning. You buy another ticket (before anyone else does), so now you hold two tickets out of the 101 tickets sold, so your chances are now 2/101, which is *slightly* less than twice your chances with just the one ticket.
In the case of the Seagate Momentus 7200.1 (I have one as well), that 600,000 number comes right from the data sheet (PDF).
Pot, meet kettle.
part of me wonders how effective a PhD would be at teaching high school students. Honestly, if you have a degree in Physics and can't find a job, I'm not sure I want you in front of students as you must be a horribly weird person.
What a small-minded comment. Not everyone is just after the money, you know. Most people who go to the trouble of getting a PhD have a passion for the subject, and often that is accompanied by a passion for sharing the subject through teaching. Have you ever considered that the person wanted to teach high school students, rather than viewing it as some sort of fallback job?
The official kernel site says 2.6.23 is only on release candidate 1.
mini-itx.com is taking pre-orders for the pico-ITX -- I don't see anywhere on the site where they are taking pre-orders for the mobile-ITX that the article is actually about.
the ER/EI (energy return over energy invested) for hydrogen always is and always will be NEGATIVE.
You mean the ER/EI ratio will be less than one. Perhaps you should go back to grade school and learn about fractions again. Or did you mean the net energy produced will be negative?
If you divide both sides by P you are throwing away the possibility that P=0.
The proper thing to do is to manipulate it as
P=NP
P-NP=0
(1-N)P=0
=> P=0 or N=1
So why isn't there cheap 100mbps service even in urban areas? This population density argument gets trotted out in every discussion like this, but it doesn't explain why I have to pay $25 or $30 per month for 4mbps DSL in a city with a population of 2.5 million (in the city proper, 4.5 million including surrounding sattelite suburb cities).
What's a Pastafarian? Is it an Italian immigrant living in Jamaica?
No, they all put worms and leeches in their mouths...
What you have linked to appears to be about a Futurama movie, not more Futurama episodes...
Who is this person?
The story is not in italics, ie. it is not a quote from a user-submitted story -- it is written by the Slashdot editor who posted it, in this case CmdrTaco...
Hmm, it doesn't take much geometry to be able to calculate the derivatives of the trigonometric functions from first principles, and from there it is easy to calculate their Taylor series. So this naive definition of trigonometry using triangles is really not so useless after all. Sure there may be other ways of thinking of the trigonometric functions which are better for other applications, but for the argument at hand (that sin is not "closed form"), it serves pretty well.
Are you suggesting the concept of angle has to be defined in terms of infinite series? Go read a basic math book or something. Angles and trigonometry are at their core just basic geometry.
All you need to assume is that you have some way of accurately measuring lengths. Create a circle whose radius is length 1 unit. If you have two radii of the circle, you can define the angle between those two line segments as the length of the arc of the circle subtended.
Then the relationship between sin and angle is very straightforward using the basic geometric concept of lengths of sides of triangles.
Digression: if you really think about it, functions like sin(x) and ln(x) are really not closed form either - they are infinite series.
What the hell are you talking about?
sin has a very concrete definition - given some angle, it is the ratio of two particular sides of a triangle which contains that angle. That's basic trigonometry...
And ln also has a very concrete definition -- in fact there are several ways to do it. One way: Define ln(x) (for x>1) to be the area of the region under the graph of 1/x from 1 to x. For 0<x<1, define ln(x) to be the negative of the area of the region under the graph of 1/x from x to 1.
Nickel mining giant INCO grows a quarter million seedlings a year just for its regreening efforts in the small city (and surrounding area) of Sudbury, Ontario, Canada.
You've got the wrong term. "Hoosier" is an American term -- it's what you call someone who plays on any of Indiana University's sports teams. See here.
You're thinking of "hoser". A hoser is anyone you don't like. See here for other definitions. It originates from the "Great White North" program on SCTV, hosted by Bob and Doug Mckenzie. See here for a synopsis of the show.
Actually, I'm pretty sure it's "You'll queer the deal."