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

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

#31

Post by timwiseman » Tue, Aug 11, 2009, 3:48 PM UTC

seanstickle wrote: post #8

I heartily endorse reading the classic works of geometry as a way to both the subject as well as a way of thinking about math, proof, and argumentation. Start with Euclid's _Elements_, and then move onto Archimedes' short books on levers and floating bodies, Apollonius's wonderful treatise on conic sections, and Ptolemy's _Almagest_. They are excellent for self-education, providing both geometrical knowledge in itsel…

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 culture in general) have changed substantially since then, the most obvious point being the development of non-Euclidean geometry.

To add to the list of books already mentioned consider Numeracy. It was influential for me when I was an undergraduate and touches on numerous topics. Also, if you want to start at the beginniner, there is a very good book called Chapter Zero that starts with nothing and is easily accessible to anyone willing to study it.

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

#32

Post by thunk » Tue, Aug 11, 2009, 3:58 PM UTC

It's not strictly math, and I can't recommend it from experience, but I've always been curious what a beginner's reaction to _Structure and Interpretation of Classical Mechanics_ might be. It's free here:

http://mitpress.mit.edu/SICM/book.html

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

#33

Post by papaf » Tue, Aug 11, 2009, 4:10 PM UTC

I came back to doing maths after a gap of over a decade. I found the student survival guide very clear and useful. I imagine it would be excellent to someone who is not good at maths.

I read the guide every evening while I was cooking (its not a difficult read) and my maths improved greatly.

http://www.netcomuk.co.uk/~jenolive/ http://www.amazon.com/Maths-Students-Survival-Self-Help-Engi...

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

#34

Post by zppx » Tue, Aug 11, 2009, 4:16 PM UTC

That's depends on what you want to learn and for why, well, some people want to understand the formalism of a theory, as theoretical computer science or theoretical physics where others are only interested in applications, so I will take a generalist approach in the topics, yes topics not books, that I will advise you to learn. Unless the book is awful (and there are many out there that are) it will makes no difference which book you pick, you generally will not "read" a math book, the only case in which you will is when it's a book for divulgation (as Polya's "How To Solve It"). For me the basics is: Statistics (Descriptive and some Probability), Calculus, the idea of Limits, Derivatives and Integrals (for Multiple Variables) and applications, Linear Algebra and also some Applications (there are many), numerical Linear Algebra is totally necessary if you want to apply it in the real world, a basics in Differential Equations, some Numerical Analysis.

If you want to learn things closer to computer science then learn something of Number Theory, some Enumerative Combinatorics and Graph Theory as well. The list is extensive because I come from a mathematical background. If you learn at least a bit of these topics them the next step will be apparent for you.

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

#35

Post by EdwardCoffin » Tue, Aug 11, 2009, 4:34 PM UTC

I've had pretty good luck using the MAA recommendations list for libraries: http://mathdl.maa.org/mathDL/19/?pa=content&sa=viewDocum...

I recommend reading Theodore Gray and Jerry Glynn's Brain Rot article for some ideas on what math skills are worth intensive study and development and which are less important: http://www.theodoregray.com/BrainRot/

There are several articles and blog postings on the topic of math self study that I found interesting and you might find useful in determining what and how to study: Developing your intuition for math: http://betterexplained.com/articles/developing-your-intuitio... Math every day (Steve Yegge): http://steve.yegge.googlepages.com/math-every-day Math for programmers (Steve Yegge): http://steve-yegge.blogspot.com/2006/03/math-for-programmers... How to read mathematics (Shai Simonson and Fernando Gouvea):http://web.stonehill.edu/compsci/History_Math/math-read.htm

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

#36

Post by CamperBob » Tue, Aug 11, 2009, 4:45 PM UTC

jimbokun wrote: post #24

brown9-2 wrote: post #17

I know this doesn't answer your question since you asked about math in general, but in case anyone ever starts a "Best Physics books for complete noobie?" thread I'd like to go ahead and suggest Brian Greene's "Fabric of the Cosmos": http://www.amazon.com/Fabric-Cosmos-Space-Texture-Reality/dp...

Maybe more on topic than you suggest, as some Physics books double as pretty good books about math. http://www.amazon.com/Road-Reality-Complete-Guide-Universe/d... OK, I haven't actually read it, but it looked like a really good book for learning a lot of interesting math when I thumbed through its contents at the library. :)

I agree with hyperbovine -- Road To Reality is a downright terrible book for the casually-interested nonprofessional, and I don't understand why it gets recommended so frequently. Roger Penrose is a bright fellow and a good writer but this book is not for the person who did OK in high school math and physics and now wants to take it to the next level.

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

#37

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

"Naive Set Theory" by Paul R. Halmos.

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

#38

Post by seanstickle » Tue, Aug 11, 2009, 5:17 PM UTC

anatoly wrote: post #29

seanstickle wrote: post #8

I heartily endorse reading the classic works of geometry as a way to both the subject as well as a way of thinking about math, proof, and argumentation. Start with Euclid's _Elements_, and then move onto Archimedes' short books on levers and floating bodies, Apollonius's wonderful treatise on conic sections, and Ptolemy's _Almagest_. They are excellent for self-education, providing both geometrical knowledge in itsel…

I completely disagree. Do not rely on ancient texts to give you understanding of what mathematics is about. They're very difficult to read, they do not teach well, and you'll know next to nothing about even basic notions of mathematics, as understood now, after you're through with them. Do read the classical texts for pleasure, to round out your education, or to understand the history of mathematics. But don't study…

I'd be curious to know what you find difficult about them, and why you think they do not teach well.

I find Euclid extraordinarily clear in his exposition of geometry. And I have not yet found a better teacher on conics than Appolonius, although Descartes comes very close with his analytic geometry.

Are there some defective constructions in the Conic Sections or in the Elements that lead you to say that "you'll know next to nothing about even basic notions of mathematics"?

It's not clear to me why you think that the ancient texts are lacking in pedagogical power, except for perhaps a personal aesthetic preference.

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

#39

Post by billswift » Tue, Aug 11, 2009, 5:18 PM UTC

babyboy808 wrote: post #16

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…

Fantastic reply, thank you. An Introduction to Mathematical Reasoning loks good, just going to read some reviews on Amazon first. Would 'How To Solve It' be aimed at someone like myself?

How to Solve It seems to be aimed at math teachers, but it is useful for almost anyone wanting to learn more math since it gives ideas about how to think about maths.

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

#40

Post by seanstickle » Tue, Aug 11, 2009, 5:20 PM UTC

timwiseman wrote: post #31

seanstickle wrote: post #8

I heartily endorse reading the classic works of geometry as a way to both the subject as well as a way of thinking about math, proof, and argumentation. Start with Euclid's _Elements_, and then move onto Archimedes' short books on levers and floating bodies, Apollonius's wonderful treatise on conic sections, and Ptolemy's _Almagest_. They are excellent for self-education, providing both geometrical knowledge in itsel…

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 are the methods of learning that we now have that invalidates Euclid and the others from being valuable teachers of mathematics?