I second this - Mathematics for the Million is truly a classic that belongs in this category that the story author referred to. It should be handed out to every child at a reasonable age, so that they can use it as an extra-curricular guide as they learn their way through the horrors of school-taught math.
The best math book ever has to be Calculus Made Easy [amazon.com] by Silvanus Thompson and edited by Martin Gardener.
I studied Calc for 4 semesters to get a Math Minor for my B.S. degree. I can honestly say I left college with little idea what calculus was. Within 4 chapters of this book, by and large, I got what I'd been missing: a practical descriptive answer for "What the heck is calculus?".
Two recommendations:
Infinity and the mind (Rudy Rucker). [amazon.com] -Mostly about infinity, paradoxes, etc,etc. I've seen this material in lots of other popularization books but Rucker seems to really enjoy it rather than just explain it. Hooked me on his work.
The book of numbers (John Conway, Richard Guy). [amazon.com] Just beautiful.
I recently took Infinity and the Mind from the school library, and I'd like to warn you to take what it says with a pinch of salt. It is wrong and over-simplified (Whilst claiming it is the truth) in many places!
Could it be that the lay-person wouldn't be interested in any book about math, no matter how well written?
In the UK, at least, Simon Singh's book on Fermat's last theorem was very successful, so they can be interested. However, most Maths books, even 'popular' Maths books, are awful for the lay-person.
I wasn't stating that as the assumption - I was stating that they wouldn't be interested in reading a/book/ about it enough for it to be "classic," no matter how well it was written.
"Moby Dick" is a classic. "The Adventures of Huckleberry Finn" (sp?) is a classic.
The *lay person* won't find a *math book* worthy of being a "classic" anything. It will be, at best, something they read when they're feeling like dorks.
That being said, don't project your own interests onto the masses. The lay person simply
The lay person has only as much use for high level theoretical mathematics as high level theoretical mathematics is able to accurately model reality. In other words, not very much.
Can you show me something that CAN be accurately modeled- to any degree of precision- with mathematics? I can't think of one. Estimated, sure. Close enough to achieve some great things, sure. But to any degree of precision? Not even close. And to most of the nuanced, grey scale problems in the average layman's life, hardly at all. Most lay people never need calculus- compound interest is the most complex calculus problem they ever use, and it's equally solvable by itera
The key word here is "ANY" degree of precision- close enough to achieve some great things is NOT equal to any degree of precision. Achieving great things is also not equal to achieving common things that can be achieved in other ways. Mathematics is not the end-all way to model the universe, yet. It's close. It's as close as the number of bytes of precision you want to do it in. But it will NEVER model the universe completely- and it's unreasonable to expect lay people to be interested in a method that
Part of learning mathematics is learning to communicate your thoughts in an unambiguous manner. This is an important and useful lesson even for lay persons such as yourself.
The ambiguousness is on purpose- the world is not unambiguous and neither is humanity- thus learning to communicate your thoughts in an unambiguous manner is neither important nor usefull in all situations, and can sometimes be uttlerly non-usefull.
A mathematician is like a guy with a hammer to whom every problem looks like a nail- so
How do people tell which problems are mathematical and which problems are non-mathematical?
An easy way is to take a concept from mathematics itself. The definition of a function. For any n-dimentional function, there should be n-1 solutions for any given input. Non-mathematical problems have MULTIPLE right answers- they are ambiguous not only in the original question, but also in the solution.
Why is that you want to take hammers out of the hands of lay people?
THERE IS A story about two friends, who were classmates in high school, talking about their jobs. One of them became a statistician and was working on population trends. He showed a reprint to his former classmate. The reprint started, as usual, with the Gaussian distribution and the st
Just because mathematics and science shows us some surprising correlations, does NOT mean that every problem can be solved with mathematics or every theory can come from science. This essay only proves the point behind WHY lay people can be utterly uninterested in Mathematics and still be completely functioning human beings.
Recently in my journal entry on Atheism and Iltheism I pointed this out- that it is equally plausible, from all we now know about energy and brain chemistry, that a soul exists as that
The lay person, on the other hand, is definately not going to be interested.
There's that assumption again. Your wife may not be interested in math, but fortunately there are other lay people who are. (And, frankly, anyone who is competent in calculus can't really be considered uninterested in math.)
This is an important issue because the future of our society depends on our ability to produce citizens who have the intellectual ability/curiosity to understand how the society actually works. Math is a big p
(And, frankly, anyone who is competent in calculus can't really be considered uninterested in math.)
It's possible, for a good student to be competant in something that they're not interested in- simply because they ARE interested in something else that depends on that topic.
I would define interest transitively. Thus, if I am interested in A, which depends on B, I think it's reasonable to say that I'm interested in (at least) the subset of B that is relevant to A.
Without such interest, no one could ever learn a complex topic like calculus.
Note that A can be something very practical (like graduating from high school) at the same time that B is very abstract (like calculus).
I would define interest transitively. Thus, if I am interested in A, which depends on B, I think it's reasonable to say that I'm interested in (at least) the subset of B that is relevant to A.
But chances are, you're only interested in that subset- and will stop learning there.
Without such interest, no one could ever learn a complex topic like calculus.
Not entirely true- some people DO have an interest in mathematics for the sake of the mathematical puzzle- and for them, calculus is a shortcut to the t
I just checked and the first five pages of GEB are about Bach. Nothing complex.
One of the great things about GEB is that it completely obliterates the standard humanities vs. sciences distinction.
I find the anti-science attitude particularly irritating because I've heard it a lot from otherwise intelligent "Liberal Arts" people.
Tell me, do you think the average lay person could understand the first five pages of _Moby Dick_, or a Shakespeare play, or an Emily Dickinson poem? I think not -- yet I don't hear anyone dissuading them from trying.
What's the practical benefit of, say, reading Jane Austen in high school? None. Yet the main complaint you hear is that "I don't want to learn algebra because I'll never use it in my real life".
Why are "average" people discourgaged from learning about science and math?
I guess my point is this. Of all the books you listed, GEB is the only one that there is no possible way (IMHO) that the average person has a chance of comprehending. It is not an entry level text to math and logic. Jane Austen or Moby Dick can be read as a (good) story, as can any other novel, ignoring the deepr subtext. This is not going to happen with GEB.
If you had the average american start reading GEB, a short distance into the novel they are going to decide you are crazy for suggesting it. Why not
Why not try a much more approachable book about science, say Darwin's Voyage of the Beagle, and don't tell them they are going to learn about science?
I agree that some scientific topics will be more approachable than pure math. I limited myself to math books because that was the topic of the original post.
GEB is not approachable (to the average person).
True, but I did not find _Moby Dick_ or Shakespeare very approachable either. That didn't stop my high school English teachers from assigning them.
Tell me, do you think the average lay person could understand the first five pages of _Moby Dick_, or a Shakespeare play, or an Emily Dickinson poem? I think not -- yet I don't hear anyone dissuading them from trying.
You obviousely didn't go to MY high school- where only the smart kids trying to get college credit ahead of schedule read anything by Herman Melville or Emily Dickinson, and the only required play for Shakespeare was Romeo and Juliet- and for that they showed the movie instead of having kids
Mr. Tortise says that the average lay person could not understand the first five pages of Godel, Escher, Bach if their life depended on it.
Achilles says, 'I think you mean "couldn't be bothered to" rather than "could not." In my experience most people are guilty of lack or interest rather than actual stupidity.'
I would agree. Especially when so many people end up in a profession that pays the bills when they would rather be doing something else (whether they were able to do it or chose not to for other reasons). I thought the Derbyshire book was excellent, well written and went well beyond the typical mathematical biography/history and really delved into the mathematics.
I started reading books on mathematics or mathematicians after listening to an Audible version of A Beautiful Mind. Other books of the same ge
I consider myself a lay person. I always did poory in mathematics because I did not care about it. The reason I did not care, is that throughout high school no one could show me a use for it. Granted, certain function such as compounded interest held me with a grand fascination - but the rest bored me to no end.
I am always looking for "laypersons" math books, because after reading Richard Feynmans (non-math) works, I want to understand his Physics Lectures.
Hey buddy - got six quarters for a dollar? Consider yourself "shown".
I am not speaking of general math - rather I am speaking of the esoteric stuff such as "new math" stuff that has no "purpose" other than to be a neat trick.
I was deeply impressed by Richard Feynmans chapter on his reviewing high school math books. He was livid that a number of things being taught were useless. He wanted the books to teach the students not only what they were learning, but why. One example has him in an uproar because there was a question about taking the average tempurature of a number of stars. This made Feynman angry because there is no reason to get an average star tempurature for a number of stars, it is just not something that you do. Feynman called it "a trick to get the students to add".
Furthermore, he was furious at a physics problem in one book, that had wrong answers, and in fact, Feynman actually performed the experiment listed in the book, and found out the "observed" results were wrong. The author did not even take the time to DO the experiment listed.
Again, this made him furious because he felt that teaching students math in a deceptive manner would never give them a feeling as to where the math can take you in fields in the sciences. I agree.
So, I don't want to learn fluff. I was at a disadvantage because I was just told "learn this" and in answer to the question of "why?" I was only given "so you can pass the exams."
In high school I deeply wanted the answers to some questions in Physics, that were available with mathematics, but I was not shown these, and I developed an unfortunate disgust with mathematics because of this.
So many people here on slashdot can take me to task for being bad at math - and I know I am. I don't know if you would have been so interested in it either if it was drilled into you in a dull manner, and a feeling that it lacked a purpose.
Am I learning math now? Yes, but then I understand much more about the why, the how, and the history now than I did then. I don't know about the rest of you but I detest rote learning. So take me to task on my math skills if you wish (or my typing:) ) but I can see enough in myself that I want to change, and I am making the effort. Not all people can say the same of themselves.
Actually, it was even more stupid: The book was asking what the total temperature was of all the stars. Averaging temperatures at least makes some kind of sense, but you won't convince me that two people put together in a room have a temperature of 72 degres Celsius.
Just want to say Good Luck:) That was an inspiring post.
Personally, I quite like abstract maths myself. I'm perfectly happy (happier, in-fact) with Maths which doesn't do anything useful - but of all the people I know, only one other person doesn't mind maths without a purpose.
throughout high school no one could show me a use for it
Everything you learned in high-school math was known before the Renaissance.
EVERYTHING.
Arithmetic predates civilization. High-school algebra is arguably prehistorical: the solution to the quadratic equation was known to EVERY ancient civilization that left behind written records. Plane geometry was formalized by the Greeks about 2400 years ago. The symbols for the trigonometric functions date back to the 1200s. Given thousands of years of history,
I learnt a _lot_ of maths at high school which is post-renaissance - complex numbers, differential and integral calculus, the uses of logarithms, the Binomial Theorem, cartesian coordinate geometry,... Oh, and we were shown the utility of some of this stuff, at least.
Of course, this was about 40 years ago, and in Australia. I don't know what they teach young people at school these days (although judging from what my kids were taught, it isn't much).
you went to an excellent high school... you must not be american.
Sorry to disagree with your generalization, but I live in the United States and had all of the above mathematics and more in high school. While I admit that not all of the teachers were up to par, I believe the opportunity is available at most high schools.:) We also were expected to use a lot of the above in real-world applications in high school physics, etc.
Heh funny stuff. I attended the Illinois Mathematics and Science Academy, so I can't really complain about not getting a decent education... but the grades 7 through 9 had been the dullest I've ever had. Interestingly, most of my vivid memories and "neat useful things" that I learned belong in 6th grade, which I attended in
Scuola Media di Constantino Nivola,
Frutti D'Oro,
CA, 09012, Italia
1) Grasp of basic french. I can't speak it anymore, but I will understand some of it.
2) Graphing - and I mean with
Interesting story, andreyw. I would say that 7th through 12th grade were the biggest waste of MY time ever. I too only learned about things on my own, through compulsive reading (anything I could get my hands on) and some computer programming. I'm very lucky I was able to survive in College, because I had no study skills to speak of (even with my above 4.0 grade average). It's funny, but I learned the most from my Cross Country and Track teams. Namely, hard work and self-respect. Not things you learn
This is something that always surprises me, each time I hear or read that (some) people in the USA don't do calculus until university. Admittedly, we were only taught how to differentiate and integrate polynomials, but we _were_ taught the concept of a limit, so it was a reasonable grounding.
However, it was interesting when I returned to university about 10 years ago (having failed big-time in the late 60s, for the obvious reasons) - I approached the woman who was teaching differential equations, as I didn
The Binomial Theorem itself may be quite old, but I think its application to combinatorial mathematics, probability, etc comes from the 17th and 18th centuries. The same can be said for most of the mathematics of complex numbers (de Moivre's Theorem, Argand diagrams, etc).
So sure, there's not a great deal which has post-Renaissance underpinnings, but you could say that about most of mathematics. However, most mathematics from the 19th and 20th centuries is a bit advanced for high school students (or even m
Yes, I agree. This has the side effect we don't get to learn it, though.
In the UK, the A-Level Maths coursework by MEI does actually have a module, called Further Pure 3, which does have some more "modern" things in. However, it is too hard and my school, for one, doesn't really want to make people do it (since it will bring down our overall grades). You can see it, in DOC format, here [mei.org.uk].
I enjoy math and majored in mathematics but agree that most of the teachers I've had didn't know the power or use of what they were teaching. I had an education-major roomate ask his college math teacher for an application or example real-world use of the math they were learning and to my surprise and sadness the teacher said "Well, suppose someone comes up to you on the street and asks 'what are the roots of this polynomial?' "
Physics is what made it all work for me. If you get a decent physics teacher,
Just FYI, here [keycollege.com] is a reference to the latest edition of "The Heart of Mathematics". You can get the earlier addition new or used through Amazon.
Hint: The point was real-world application of the math.
So, yes, the physics answer is obviously better in this context because my roomate was asking for a real-world use of the math. If you think that the answer the teacher gave is a real-world application of the use or application of polynomials then you seriously need a course in critical thinking.
My roomate had asked for an application of the math they were doing.
While I totally agree with you that firing a cannon off a cliff may be an uncommon (or even useless to some) application of polynomials, it never the less IS an application of the math.
In contrast, the answer his teacher gave of solving a math problem because someone asked you to solve that math problem may be a real-world problem, but it IS NOT an application of the math.
I believe you failed to see this distinction. So to your quest
I think you're being cruel. Lots of laypersons have intellectual curiosity that may not have been fed either because they were too poor to go on to higher education, there were family problems, whatever. Not everyone who ends up without an education is dumb and uninterested. Lots of people are interested in space travel, chemistry, astronomy - why not math? I have a lady at work who is always asking me questions about some math thing or another she heard about and I've been looking for a good book li
Classic Foundations of Arithmetic - Gottlieb Frege Contributions to the Founding of the Theory of Transfinite Numbers - Georg Cantor Complete works of Spinoza - Spinoza
Flatland, and the latest "Flatterland" is a great read. I'm almost done (just abstract algebra to go!) with a math major, and it's been a wonderful journey, cumlinating in my eyes with Number theory(exploration of Primes a LOT - Mersenne, etc.) and real analysis (all proofs, all the time!) last semester. I'm giving myself a mini-calculus course this christmas break just, sadly enough i guess, for fun! It's been a while since I had to use Chain rule and all that stuff...
An irrefutably classic book on mathematics is Courant and Robbins' amazing "What is Mathematics?" (Later edited and revised by Ian Stewart). This is a fantastic book that was nevertheless written very much with the lay-person in mind. (I believe the introduction - by Courant's son? - discusses how one of the authors required his sons' brides-to-be to get through the book at least once.)
It's one of those books that you never really finish. I received it years ago for my Bar Mitzvah and I've probably read
The average person owns few, if any, books. In the US one can often expect the home to have a bible, and perhaps a couple other books, but most people have read very little. They read what they were forced to read in school, the sports section, and perhaps a few magazines written at the 5th grade level. And lest people get pissed about me dissing the sport section, let me state here that we owe a lot to sport section, as it is often written at above a 5th grade level and is likely responsible for the min
lay person? (Score:4, Insightful)
Ummm...what would its peers be? Just how many "classic" math books does the lay-person have now?
Could it be that the lay-person wouldn't be interested in any book about math, no matter how well written?
I dunnnoooo...almost sounds completely probable.
Examples of Math books for lay people (Score:5, Informative)
Re:Examples of Math books for lay people (Score:3, Insightful)
I second this - Mathematics for the Million is truly a classic that belongs in this category that the story author referred to. It should be handed out to every child at a reasonable age, so that they can use it as an extra-curricular guide as they learn their way through the horrors of school-taught math.
Re:Examples of Math books for lay people (Score:2)
Re:Examples of Math books for lay people (Score:2, Informative)
Re:Examples of Math books for lay people (Score:1)
Re:Examples of Math books for lay people (Score:1)
The best math book ever has to be Calculus Made Easy [amazon.com] by Silvanus Thompson and edited by Martin Gardener.
I studied Calc for 4 semesters to get a Math Minor for my B.S. degree. I can honestly say I left college with little idea what calculus was. Within 4 chapters of this book, by and large, I got what I'd been missing: a practical descriptive answer for "What the heck is calculus?".
Re:Examples of Math books for lay people (Score:1)
Re:Examples of Math books for lay people (Score:1)
The book of numbers (John Conway, Richard Guy). [amazon.com] Just beautiful.
Re:Examples of Math books for lay people (Score:2)
Re:lay person? (Score:1)
In the UK, at least, Simon Singh's book on Fermat's last theorem was very successful, so they can be interested. However, most Maths books, even 'popular' Maths books, are awful for the lay-person.
Re:lay person? (Score:2)
Not to mention, of course, his Code Book (assuming you consider cryptography as a branch of mathematics, which I think most people do).
Re:lay person? (Score:5, Insightful)
Martin Gardner's series of Mathematical Games books certainly qualifies as classic.
I would put some of Douglas Hofstadter's books in there too. Certainly _Godel, Escher, Bach_ is highly (though not entirely) mathematical.
Richard Smullyan also has a number of very good math/puzzle books.
There are others, too, but you get the idea. I don't think you need to be professional mathematician to enjoy any of these.
Re:lay person? (Score:1)
"Moby Dick" is a classic. "The Adventures of Huckleberry Finn" (sp?) is a classic.
The *lay person* won't find a *math book* worthy of being a "classic" anything. It will be, at best, something they read when they're feeling like dorks.
That being said, don't project your own interests onto the masses. The lay person simply
Re:lay person? (Score:2)
Re:lay person? (Score:2)
Can you show me something that CAN be accurately modeled- to any degree of precision- with mathematics? I can't think of one. Estimated, sure. Close enough to achieve some great things, sure. But to any degree of precision? Not even close. And to most of the nuanced, grey scale problems in the average layman's life, hardly at all. Most lay people never need calculus- compound interest is the most complex calculus problem they ever use, and it's equally solvable by itera
Re:lay person? (Score:2)
Re:lay person? (Score:2)
The ambiguousness is on purpose- the world is not unambiguous and neither is humanity- thus learning to communicate your thoughts in an unambiguous manner is neither important nor usefull in all situations, and can sometimes be uttlerly non-usefull.
A mathematician is like a guy with a hammer to whom every problem looks like a nail- so
Re:lay person? (Score:2)
An easy way is to take a concept from mathematics itself. The definition of a function. For any n-dimentional function, there should be n-1 solutions for any given input. Non-mathematical problems have MULTIPLE right answers- they are ambiguous not only in the original question, but also in the solution.
Why is that you want to take hammers out of the hands of lay people?
That's reading an intent into my words
Re:lay person? (Score:2)
Re:lay person? (Score:2)
Recently in my journal entry on Atheism and Iltheism I pointed this out- that it is equally plausible, from all we now know about energy and brain chemistry, that a soul exists as that
Re:lay person? (Score:2)
There's that assumption again. Your wife may not be interested in math, but fortunately there are other lay people who are. (And, frankly, anyone who is competent in calculus can't really be considered uninterested in math.)
This is an important issue because the future of our society depends on our ability to produce citizens who have the intellectual ability/curiosity to understand how the society actually works. Math is a big p
Re:lay person? (Score:3, Funny)
I for one welcome our new, math-knowing, Finnish overloards!
And our math-knowing Korean overloards.
And our math-knowing... eh, forget it. At least we beat Portugal [go.com].
Re:lay person? (Score:2)
It's possible, for a good student to be competant in something that they're not interested in- simply because they ARE interested in something else that depends on that topic.
Re:lay person? (Score:2)
Without such interest, no one could ever learn a complex topic like calculus.
Note that A can be something very practical (like graduating from high school) at the same time that B is very abstract (like calculus).
Re:lay person? (Score:2)
But chances are, you're only interested in that subset- and will stop learning there.
Without such interest, no one could ever learn a complex topic like calculus.
Not entirely true- some people DO have an interest in mathematics for the sake of the mathematical puzzle- and for them, calculus is a shortcut to the t
Re:lay person? (Score:1)
Re:lay person? (Score:5, Insightful)
One of the great things about GEB is that it completely obliterates the standard humanities vs. sciences distinction.
I find the anti-science attitude particularly irritating because I've heard it a lot from otherwise intelligent "Liberal Arts" people.
Tell me, do you think the average lay person could understand the first five pages of _Moby Dick_, or a Shakespeare play, or an Emily Dickinson poem? I think not -- yet I don't hear anyone dissuading them from trying.
What's the practical benefit of, say, reading Jane Austen in high school? None. Yet the main complaint you hear is that "I don't want to learn algebra because I'll never use it in my real life".
Why are "average" people discourgaged from learning about science and math?
Re:lay person? (Score:1)
Re:lay person? (Score:2)
I agree that some scientific topics will be more approachable than pure math. I limited myself to math books because that was the topic of the original post.
GEB is not approachable (to the average person).
True, but I did not find _Moby Dick_ or Shakespeare very approachable either. That didn't stop my high school English teachers from assigning them.
As
Re:lay person? (Score:1)
Re:lay person? (Score:2)
You obviousely didn't go to MY high school- where only the smart kids trying to get college credit ahead of schedule read anything by Herman Melville or Emily Dickinson, and the only required play for Shakespeare was Romeo and Juliet- and for that they showed the movie instead of having kids
Re:lay person? (Score:3, Funny)
Achilles says, 'I think you mean "couldn't be bothered to" rather than "could not." In my experience most people are guilty of lack or interest rather than actual stupidity.'
Re:lay person? (Score:1)
Re:lay person? (Score:1)
layperson (lay'pûr'sen) n. A man or woman not interested in math.
Re:lay person? (Score:1)
I started reading books on mathematics or mathematicians after listening to an Audible version of A Beautiful Mind. Other books of the same ge
Re:lay person? (Score:2, Funny)
It should become a classic, alongside with this book: Everyday Math For Dummies http://www.dummies.com/WileyCDA/DummiesTitle/produ ctCd-1568842481.html [dummies.com]
Re:lay person? (Score:3, Insightful)
I am always looking for "laypersons" math books, because after reading Richard Feynmans (non-math) works, I want to understand his Physics Lectures.
As a helpful AC http://slashdot.org/comments.pl?s [slashdot.org]
Re:lay person? (Score:2)
Hey buddy - got six quarters for a dollar?
Consider yourself "shown".
Re:lay person? (Score:4, Interesting)
Consider yourself "shown".
I am not speaking of general math - rather I am speaking of the esoteric stuff such as "new math" stuff that has no "purpose" other than to be a neat trick.
I was deeply impressed by Richard Feynmans chapter on his reviewing high school math books. He was livid that a number of things being taught were useless. He wanted the books to teach the students not only what they were learning, but why. One example has him in an uproar because there was a question about taking the average tempurature of a number of stars. This made Feynman angry because there is no reason to get an average star tempurature for a number of stars, it is just not something that you do. Feynman called it "a trick to get the students to add".
Furthermore, he was furious at a physics problem in one book, that had wrong answers, and in fact, Feynman actually performed the experiment listed in the book, and found out the "observed" results were wrong. The author did not even take the time to DO the experiment listed.
Again, this made him furious because he felt that teaching students math in a deceptive manner would never give them a feeling as to where the math can take you in fields in the sciences. I agree.
So, I don't want to learn fluff. I was at a disadvantage because I was just told "learn this" and in answer to the question of "why?" I was only given "so you can pass the exams."
In high school I deeply wanted the answers to some questions in Physics, that were available with mathematics, but I was not shown these, and I developed an unfortunate disgust with mathematics because of this.
So many people here on slashdot can take me to task for being bad at math - and I know I am. I don't know if you would have been so interested in it either if it was drilled into you in a dull manner, and a feeling that it lacked a purpose.
Am I learning math now? Yes, but then I understand much more about the why, the how, and the history now than I did then. I don't know about the rest of you but I detest rote learning. So take me to task on my math skills if you wish (or my typing
Feynman (Score:1)
Re:lay person? (Score:2)
Personally, I quite like abstract maths myself. I'm perfectly happy (happier, in-fact) with Maths which doesn't do anything useful - but of all the people I know, only one other person doesn't mind maths without a purpose.
Read this [amazon.com] -- it is truely amazing.
Re:lay person? (Score:2)
Everything you learned in high-school math was known before the Renaissance.
EVERYTHING.
Arithmetic predates civilization. High-school algebra is arguably prehistorical: the solution to the quadratic equation was known to EVERY ancient civilization that left behind written records. Plane geometry was formalized by the Greeks about 2400 years ago. The symbols for the trigonometric functions date back to the 1200s. Given thousands of years of history,
Re:lay person? (Score:2)
Of course, this was about 40 years ago, and in Australia. I don't know what they teach young people at school these days (although judging from what my kids were taught, it isn't much).
Re:lay person? (Score:2)
I had to go to the local college to learn calculus, because they didn't even offer it in my high school!
Re:lay person? (Score:1)
Re:lay person? (Score:2)
Sorry to disagree with your generalization, but I live in the United States and had all of the above mathematics and more in high school. While I admit that not all of the teachers were up to par, I believe the opportunity is available at most high schools. :) We also were expected to use a lot of the above in real-world applications in high school physics, etc.
Re:lay person? (Score:2)
Re:lay person? (Score:2)
Re:lay person? (Score:2)
However, it was interesting when I returned to university about 10 years ago (having failed big-time in the late 60s, for the obvious reasons) - I approached the woman who was teaching differential equations, as I didn
Re:lay person? (Score:2)
Differntial and Integral Calculus was 1600's, so post-renaissance, but some existed before that at any rate.
Logarithms were invented near the end of the renaissance, but the work was not published until the 1600's, also.
The Binomial Theorem is very, very old!
The Cartesian coordinate system is from the 1600's.
So although there are bits from Post-Renaissance (taking that as anything from the 17th centry onwards), there isn't really anything fr
Re:lay person? (Score:2)
So sure, there's not a great deal which has post-Renaissance underpinnings, but you could say that about most of mathematics. However, most mathematics from the 19th and 20th centuries is a bit advanced for high school students (or even m
Re:lay person? (Score:2)
"is a bit advanced for high school students"
Yes, I agree. This has the side effect we don't get to learn it, though.
In the UK, the A-Level Maths coursework by MEI does actually have a module, called Further Pure 3, which does have some more "modern" things in. However, it is too hard and my school, for one, doesn't really want to make people do it (since it will bring down our overall grades). You can see it, in DOC format, here [mei.org.uk].
For a student to take this module, they must
Re:lay person? (Score:2)
Re:lay person? (Score:2)
Physics is what made it all work for me. If you get a decent physics teacher,
Re:lay person? (Score:2)
Re:lay person? (Score:2)
Hint: The point was real-world application of the math.
So, yes, the physics answer is obviously better in this context because my roomate was asking for a real-world use of the math. If you think that the answer the teacher gave is a real-world application of the use or application of polynomials then you seriously need a course in critical thinking.
Re:lay person? (Score:2)
While I totally agree with you that firing a cannon off a cliff may be an uncommon (or even useless to some) application of polynomials, it never the less IS an application of the math.
In contrast, the answer his teacher gave of solving a math problem because someone asked you to solve that math problem may be a real-world problem, but it IS NOT an application of the math.
I believe you failed to see this distinction. So to your quest
Re:lay person? (Score:1)
Ummm...what would its peers be?
Martin Gardner's math puzzle/game books [barnesandnoble.com]? or mabye Godel, Escher, Bach [barnesandnoble.com] for the more philosophicaly inclined? Not all non-mathematicians are turned off by math...
Re:lay person? (Score:3, Insightful)
Re:lay person? (Score:1)
Foundations of Arithmetic - Gottlieb Frege
Contributions to the Founding of the Theory of Transfinite Numbers - Georg Cantor
Complete works of Spinoza - Spinoza
Re:lay person? (Score:2)
Besides, he said "for the lay-person", not "read by the lay-person". I can write a book for geeks, that doesn't mean any geek would have to read it.
Re:lay person? (Score:1)
Re:lay person? (Score:1)
It's one of those books that you never really finish. I received it years ago for my Bar Mitzvah and I've probably read
Re:lay person? (Score:2, Insightful)
Re:lay person? (Score:2)
I'm interested - have people said this to them, then? Who? Why?
Re:lay person? (Score:1)
Men of Mathematics (Score:2)
The History of Pi by Petr Beckman.