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Can anyone suggest some good math books?

 
 
 
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rousseau

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This thread is similar to my one on physics. Math is another area that I'm not well versed in. I've gone up to introductory calculus and statistics, but outside of that my knowledge is basically null. I feel like if I were to find some good books on different topics, though, my mind would be opened up to a wide range of interesting ideas that have never occurred to me before.

Any suggestions?
 
You generally have to pick breadth or depth, I'm assuming you want broad overviews.

Good basic overviews (basic number theory, calculus, geometry):
http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192
http://www.amazon.com/Mathematics-Nonmathematician-Dover-Books/dp/0486248232

More advanced overviews (the above, plus algebra, analysis, topology, etc):
http://www.amazon.com/All-Mathematics-You-Missed-Graduate/dp/0521797071
http://www.amazon.com/Concepts-Modern-Mathematics-Dover-Books/dp/0486284247
 
Excursions in Number Theory by C. Stanley Ogilvy and John T. Anderson. I just picked this up. It might be considered "advanced," although it really isn't - I'm reading it after all, and it is written such that you don't need knowledge of higher mathematics and you don't need to be familiar with mathematical proofs. All you need is a basic understanding of numbers that you would have picked up in school. The presentation is as rigorous as a textbook but the prose is much more informal and fun.
 
rousseau said:
This thread is similar to my one on physics. Math is another area that I'm not well versed in. I've gone up to introductory calculus and statistics, but outside of that my knowledge is basically null. I feel like if I were to find some good books on different topics, though, my mind would be opened up to a wide range of interesting ideas that have never occurred to me before.

Any suggestions?
Click to expand...
The Road to Reality, by Roger Penrose. It's nominally a physics book (and a very good one!) but actually half the book is an explanation of the math you'll need in order to have a prayer of understanding the other half.
 
For less theoretical, more numeric topics, I found that programming books (and online resources) such as Numerical Recipies were really instructive.
If you really want to learn how to solve a problem, teach a computer to do it;)
 
travc said:
For less theoretical, more numeric topics, I found that programming books (and online resources) such as Numerical Recipies were really instructive.
If you really want to learn how to solve a problem, teach a computer to do it;)
Click to expand...

Numerical Recipes in C also has a really good joke:

Numerical Recipes in C said:
Q: What's the difference between a computer scientist and a research scientist?
A: a computer scientist is trying to solve yesterday's problems on tomorrow's computer.
Click to expand...
 
Knuth’s Semi Numerical Algorithms isa good reference book. Interesting read and practical. A long chapteron random numbers. One of my favorites.


http://books.google.fr/books/about/The_Art_of_Computer_Programming.html?hl=fr&id=-XxGAAAAYAAJ




Duncan's Quality Control And IndustrialStatistics. Expensive but the best overall book on applyingprobability and statistics.


http://books.google.com.br/books/ab...trial_statistic.html?hl=pt-BR&id=h2stAAAAIAAJ








I have several calculus books. The mostuseful is Technical Calculus And Analytic Geometry by Washington.Been in print for a long time. More emphasis on how to use it thentheoretical underpinnings.


http://books.google.com/books/about/Technical_calculus_with_analytic_geometr.html?id=WjjYAAAAMAAJ






When I was starting out in the early80s I realized I had no interest in any serious academic pursuits andwhat drove me was understanding how things worked.


I was jumping into areas like heattransfer, fluid mechanics, and vibration analysis. As I was wadingthru books my great Aha! Experience. Atleast for me,was when it sunkin it was all the same mathematics. The mechanical moments of inertiawere mathematically the same moments in statistics and so on.Mathematically fluid mechanics and electromagnet fields wereidentical.


It became obvious that there were nospecial secrets, it was all the basic undergrad math sequence.Algerbra-trig, calculus, differential equations, complex variables,linear algebra,statistics, and numerical methods.






I then went back to algebra/trig andstarted working problems to get a solid proficiency. Then I wentthrough calculus again.


It paid off in the long run. Whenever Ineeded to learn some new area it was relatively easy to read books.


I took a night class in modern physicsback in the 90s. Quantum mechanics and other topics were appearing inengineering articles. It was anti climactic. Linear algebra,probability distributions, Fourier Transforms.


So, if you really want to understandmath and science, start with algebra and learn how to use it.


There is a great book written as aproject by Japanese students who had no math or science background.Background. What Is Quantum Mechanics?: A Physics Adventure .




http://www.amazon.com/What-Quantum-Mechanics-Physics-Adventure/dp/0964350440


If you wnt something worthwhile toengage in as a life long pursuit forget video games and jump in tomath. Pick a book,any book.


The net may even be detrimental. Itmakes it easy to look up short responses and answers to questionswithout ever developing any real understanding and proficiency.
 
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