Project Euler Forum

Which books would you prefer if i want to learn about number theory, factoring, different methods of finding primes and a great book on maths?

Not number theory but if you want a great book, you can start with 'Analytic Combinatorics' by Sedgwick and Flajolet. It is a very nice read on Combinatorics and will also help in solving numerous PE problems directly or using the ideas on the book.

Thanks

Anything on number theory? Which branch do you like?

Googling on "books numbertheory" gave this discussion:
https://math.stackexchange.com/question ... ber-theory
Loads of people suggest a book there. You can find your book there, I suppose.

You might like "Concrete Mathematics" By Knuth and Patashnik, or "An Introduction to the Theory of Numbers" by Niven, Zuckerman, and Montgomery. Both are pretty cheap, especially for textbooks. I believe my copy of "An Introduction to the Theory of Numbers" was 15 USD.

My "go to" book is "Elementary Number Theory" by David M. Burton. I don't even know where I got it from but the main thing I like about it is that the mathematical detail is interspersed with interesting historical details.

Both "Prime Numbers: A Computational Perspective", Pomerance & Crandall, and "A Course in Computational Algebraic Number Theory", Henri Cohen, are more technical but at the same time more focused on algorithms.

Albert H Beiler "Recreations in the Theory of Numbers" is an interesting one. It belongs to the very end of the hand-computation era, just as computers were starting to take over. The methods he describes are very different to the ones you'd use now. That's what made it fascinating for me. It's a lost tradition.

yourmaths wrote: ↑

Tue Sep 11, 2018 11:31 am

My "go to" book is "Elementary Number Theory" by David M. Burton. I don't even know where I got it from but the main thing I like about it is that the mathematical detail is interspersed with interesting historical details.

Both "Prime Numbers: A Computational Perspective", Pomerance & Crandall, and "A Course in Computational Algebraic Number Theory", Henri Cohen, are more technical but at the same time more focused on algorithms.

thanks for your suggestions. I already have Elementary Number Theory and i found it as interesting. I will check the other ones also.

I have looked at a few of the Elementary Number Theory books available at LibGen. For some like me, just starting out on Number Theory, Burton's 7th edition is a great introduction. I have worked through the first two chapters. I would definitely recommend it to any PE enthusiast. It would have been so much more fun if I had started with PE and Burton at the same time.

Great books on math:

The Man Who Knew Infinity by Robert Kanigel
Gödel, Escher, Bach by Douglas Hofstadter
The Colossal Book of Mathematics by Martin Gardner
Euclid in the Rainforest by Joseph Mazur
Four Colours Suffice by Robin Wilson
What is Mathematics Really? by Reuben Hersh
Magical Mathematics by Persi Diaconis and Ron Graham
Games of Life by Karl Sigmund
Mathenauts: Tales of Mathematical Wonder edited by Rudy Rucker
The Mathematical Principles of Natural Philosophy by Isaac Newton

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Thanks elissasmart, and
Great books on the...
Limits of Math:

Godel's Proof by Ernest Nagel and James Newman with a new Foreword by Douglas Hofstadter 2001

A World Without Time - The Forgotten Legacy of Godel and Einstein by Palle Yourgrau 2005

When Einstein Walked with Godel - Excursions to the Edge of Thought by Jim Holt 2018

Incompleteness - The Proof and Paradox of Kurt Godel by Rebecca Goldstein 2005

ps - Not recommended: Genius At Play - The Curious Mind of John Conway

Interesting books, thanks!