Ask HN: Best Mathematics book for complete noobie? • Hacker News Board

Re: Ask HN: Best Mathematics book for complete noobie?

#41

Post by billswift » Tue, Aug 11, 2009, 5:32 PM UTC

If you want to DO math, nothing beats working through a decent textbook. I have worked through several since I'm approaching 50 and don't use math enough to keep my skills up (and like any skill, you have to keep practicing to stay decently competent in math). The best Precalculus textbook I have used is Swokowski's "Algebra and Trigonometry with Analytic Geometry" which is clear, concise, and has lots of problems.

If you want to learn ABOUT math, Davis and Hersch's "The Mathematical Experience" is a fairly easy read about philosophy of math, how it is used, and a bit about studying math.

Eric Temple Bell's "Mathematics: Queen and Servant of Science" is a bit dated but an excellent history of math for someone interested in learning to do advanced math; the author's a bit biased towards algebra over analysis, number theory, and geometry, but not excessively so. Its biggest lack is only one short chapter on probability and statistics. This is not a particularly easy read since it covers things in some depth, but I think it is worth the effort.

Re: Ask HN: Best Mathematics book for complete noobie?

#42

Post by timwiseman » Tue, Aug 11, 2009, 5:34 PM UTC

seanstickle wrote: post #40

timwiseman wrote: post #31

Earlier quoted context omitted.

I will join with anatoly in disagreeing. The Elements are a beautiful piece of literature and I recommend reading them for a historical understanding. (I have not read them through by any means, but I have read segments which are magnificent). As for understanding mathematics and its techniques, there are now much better methods. Our understanding of mathematics and methods of learning (not to mention our simple cult…

You say that "our understanding of mathematics and methods of learning have changed substantially since then". While I of course agree that we now have a lot more mathematics, including non-Euclidean geometry, I don't see what thay has to do with the value of Euclid and the other ancient mathematicians. I'm not recommending Euclid and Appolonius as a complete mathematical education, but a good place to start. What ar…

Invalidates? Absolutely none. Good mathematics is eternal and the Elements has some beautiful mathematics.

What I meant to say is that in the fullness of time they have been expanded on and surpassed. You can still learn good and valid mathematics from Euclid, but you can learn it better form more modern sources.

As one example amoung many, good modern geometry books will let the reader know about the existence of non-Euclidean geometry and its differences, even if the focus is on traditional Euclidean geometry.

Also, modern books will use modern notation. Notation of course does not affect the ideas which are what is important, but someone trying to learn math today will need to learn the notation so that they can read other more advanced books that will assume the reader knows that stuff. Not to mention, notation can make things easier or harder (try doing multiplication in Roman Numerals).

Finally, many things that were proven tediously before have easier proofs developped over time, often with the ability to take recourse in Algebra. For the same reason, many open questions in Euclid's time now have answers.

Re: Ask HN: Best Mathematics book for complete noobie?

#43

Post by seanstickle » Tue, Aug 11, 2009, 6:02 PM UTC

timwiseman wrote: post #42

seanstickle wrote: post #40

Earlier quoted context omitted.

You say that "our understanding of mathematics and methods of learning have changed substantially since then". While I of course agree that we now have a lot more mathematics, including non-Euclidean geometry, I don't see what thay has to do with the value of Euclid and the other ancient mathematicians. I'm not recommending Euclid and Appolonius as a complete mathematical education, but a good place to start. What ar…

Invalidates? Absolutely none. Good mathematics is eternal and the Elements has some beautiful mathematics. What I meant to say is that in the fullness of time they have been expanded on and surpassed. You can still learn good and valid mathematics from Euclid, but you can learn it better form more modern sources. As one example amoung many, good modern geometry books will let the reader know about the existence of no…

What you say makes a lot of sense.

However, notation actually does affect the ideas, and deeply. Euclid did not consider 1 a number, for perfectly sound reasons. Multiplication is a very different animal in Euclid's math, and his proportions are not just funny-looking fractions.

Overall, you are right. If someone is looking to get a broad survey of mathematics, Euclid is not a good source. But to start from scratch and learn rigorous math-by-proof, he has no equal.

Re: Ask HN: Best Mathematics book for complete noobie?

#44

Post by bgutierrez » Tue, Aug 11, 2009, 6:03 PM UTC

rickdangerous1 wrote: post #14

I'm in the similar situation as you (OP). My high school education was interrupted quite badly and 13 years after graduating I lack confidence in my comp sci endeavors because my maths sucks so bad. I'd be interested to hear of any hackers who have missed education milestones (like high school maths) but gone and successfully filled in the gaps. The reason I'm asking is because I'm kind feeling that things like maths…

I left school when I was 16 to do homeschool, which turned out to be nothing more than my parents buying me books when I asked for them and nothing more.

I did my GED and dropped out of college, so I think that I can relate to how you feel. There's a huge inferiority complex that comes from having less education than others. Filling in the gaps is difficult but I've found that whenever I fill something in, I've benefited pretty quickly. Lately I realized that I sucked at systems programming concepts, so I've been reading about that, which has been really helpful. I make a living as a programmer, but I have to continually be studying to try and fill in gaps before I'm hurt by lack of knowledge.

If someone can work through a discrete math textbook and do the exercises, I think they could get a lot out of it. Calculus has some important ideas, but I think the discrete math is much more relevant to every day programming. I took a course last year at my community college that used Discrete Mathematics with Applications, by Susanna S. Epp. I don't recall it requiring higher math than algebra, but it did require sharp thinking. Concrete Mathematics: A Foundation for Computer Science is probably a good textbook, but I haven't used it, so can't say anything about it.

Re: Ask HN: Best Mathematics book for complete noobie?

#45

Post by ottbot » Tue, Aug 11, 2009, 6:11 PM UTC

I think Kreyszig's Advanced Engineering Mathematics is an excellent text in applied math.

I'm not sure where you're at or what direction you want to study, but once you're familiar with calculus concepts this text is a good place to go to deal with ODE and analysis.

Re: Ask HN: Best Mathematics book for complete noobie?

#46

Post by bddbbdb » Tue, Aug 11, 2009, 6:29 PM UTC

michael_dorfman wrote: post #2

What kind of math do you want to learn? There's a lot of great resources out there, but you need to be more specific. For example: I really enjoyed Gilbert Strang's course on Linear Algebra, available as a series of video lectures on MIT OCW ( http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/Cours... ). If you are interested in Discrete mathematics, Knuth's "Concrete Mathematics" is a great book--but it might n…

Concrete Mathematics is (as it says itself) intended for first year grad students. It is certainly good, but it is NOT for a "complete noobie". I am in a similar situation, and am finding Vellman's "How to Prove It" extremely useful. Having poked around the edges of math for about a year, I finally realized that proofs are central to mathematical maturity... No more eyes crossing when I read a new CS textbook!

Re: Ask HN: Best Mathematics book for complete noobie?

#47

Post by brg » Tue, Aug 11, 2009, 6:35 PM UTC

Here is some general advice.

First have some kind of goal. Do you want to be able to determine the orbit of an planet, evaluate the complexity of algorithms and computing models, study human interactions as walks on graphs, or use statistics to model and predict complex systems. Decide on this first, don't wonder around mathematics aimlessly.

Secondly, work the books. Maths can not be learned by observation, and reading proof after proof is simply observation. Memorize proofs, work from your current point back to first principles, and do all the problems you can. Of course there will be times when you simply can not find a means to start on a problem, and at that time find help or try and come back to the problem later.

Re: Ask HN: Best Mathematics book for complete noobie?

#48

Post by brg » Tue, Aug 11, 2009, 6:37 PM UTC

If you have some decent background in reasoning and logic, I would suggest Linear Algebra Done Right by Sheldon Axler. It provides a general introduction in mathematical reasoning as well as providing a strong framework for maths needed in many fields.

http://www.amazon.com/Linear-Algebra-Right-Sheldon-Axler/dp/...

Re: Ask HN: Best Mathematics book for complete noobie?

#49

Post by revertts » Tue, Aug 11, 2009, 6:55 PM UTC

mahmud wrote: post #3

"An Introduction to Mathematical Reasoning" by Peter J Eccels. Teaches the vocabulary of mathematics, just the basics you need to think like a mathematician, not a mathematics user like most science texts. "How To Solve It" George Polya. Heurists and problem solving skills, by a great mathematician. Do a google search, specially in the sci.math newsgroup. Again, read books by mathematicians for mathematicians; they'r…

How To Solve It is a great recommendation.

I had a physics professor that did an amazing job of teaching problem solving; even though the class wasn't directly to my major, it was probably the single most useful class I ever took. Next semester I read How To Solve It and realized that the way he taught followed closely to what Polya lays out.

Re: Ask HN: Best Mathematics book for complete noobie?

#50

Post by jaja » Tue, Aug 11, 2009, 8:06 PM UTC

"Scientific Notation and Other First Principles: Comprehensive Mathematics for Lawyers and Politicians," by Jacob Herwitz. Penguin, 1992.

Great introductory text which starts from algebraic first principles and goes through pretty much everything up until differential equations. Very thorough.