Elementary number theory
by Underwood Dudley · first published 1969
80% recommend20% neutral
Why HN recommends it
Easy-to-follow introduction with many inline exercises, key problems and extra problems written for an active reader; a good fit for self-study and covers the basics well for students and the curious.
Summarised by Claude from recommending comments
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That's cool -- you might like Underwood Dudley's book on Elementary Number Theory. It has a similar set of topics, and I think it has more exercises and contains some solutions. And it's inexpensive!
on “An Illustrated Theory of Numbers (2017)” ↗…on any topic which interests you, read through it, and do a significant number of the exercises. You might try Epp's Discrete Mathematics, Hefferon's Linear Algebra, Colley's Vector Calculus, Dudley's Elementary Number Theory, Spivak or Apostol's Calculus (these go far beyond ordinary freshman calculus), Pinter's A Book of Abstract Algebra, among many others. Some of these books are expensive to buy new, but just buy older…
on “Ask HN: Is there a website specialized in mathematics courses?” ↗Of recent gems: Elementary Number Theory by Underwood Dudley is easy to like. You can really see how it was written with an active reader in mind, with a good and doable set of inline excercises, key problems and additional problems. The material…
on “Ask HN: How to learn mathematical proofs from scratch?” ↗"Elementary Number Theory" by Underwood Dudley is great. Also, I enthusiastically second tokenadult's recommendations of all of Stillwell's books, which has quite rightly been voted to the top.
on “Ask HN: Exploring math without a teacher?” ↗The answer is always Elementary Number Theory by David Burton. I read this book since 7th grade.
on “Ask HN: Math books that made you significantly better at math?” ↗…personally like to get a book, see if I like the topic, and if I do then get another book so that I can compare them. You might try one of these elementary books on number theory: https://www.amazon.com/Elementary-Number-Theory-Second-Mathe... https://www.amazon.com/Introduction-Number-Theory-MIT-Press/... https://artofproblemsolving.com/store/book/intro-number-theo... Combinatorics and graph theory are reasonable too, but…
on “Ask HN: Books or courses to understand college level mathematics?” ↗…good math materials out there at higher levels, but generally speaking they will cover one subject at a time, as this is what creators enjoy creating. For example one book I like is Underwood Dudley's Elementary Number Theory (can be bought cheaply online) -- and one reason is that the author gives elementary proofs which mimic the structure of the higher-level formalism (i.e. abstract algebra), so that this formalism feels…
on “Ask HN: Does this math education idea make sense?” ↗…tricky for self study IMO. If you already graduated maybe follow some MOOC. I'd actually recommend Number theory if you want more fun or if you are interested in Cryptography which is related to CS. Elementary Number Theory throws you tons of questions that even a toddler can understand but you might hit bam head on walls for nights to prove them.
on “How Not to Learn Cryptography (2014)” ↗…my interest in all of Mathematics (BTW, I'll be glad if you recommend any Abstract Algebra books): - Calculus, Howard Anton. - Calculus, Spivak - Advanced Engineering Mathematics, Erwin Kreyszig - Elementary Number Theory, David Burton. Computer Science/Engineering: - Data Structures and Algorithms, Adam Drozdek - Digital Design, Morris Mano - David Patterson and John Hennesey's books - Mastering Embedded Linux Programming,…
on “Ask HN: The book that did it for you in math and/or CS?” ↗…pretty good. His number theory text is also great (used it in my number theory course, it was better than the instructor). Avoid the 6th edition, not worth the extra cash. Link: http://www.amazon.com/Elementary-Number-Theory-Kenneth-Rosen...
on “Math to support self-taught CS” ↗…looks interesting — how did you choose which topics to cover? Were they influenced by what would be easy to illustrate? My knowledge of number theory is limited to the (very) early chapters of Burton's Elementary Number Theory or Niven & Zuckerman's book, so I'm wondering how this book differs in its choice of contents. (The presentation of course is outstanding.)
on “An Illustrated Theory of Numbers (2017)” ↗…verifying one's solutions. Programmers have another advantage over other mathematics students: you can test your understanding of the mathematics by writing actual programs. For example, if you're reading an elementary number theory book and learn about the Chinese Remainder Theorem, you can write an actual program/function for finding solutions to a system of modular congruences. As computers require a level of precision greater…
on “Books I Recommend” ↗…been struggling with which paper to use to implement the Lambda Calculus (I prefer original source material, because I feel that I learn a little more that way). I started with "An Unsolvable Problem of Elementary Number Theory" [1], but have now temporarily settled on Church's book "The Calculi of Lambda-Conversion" [2] which is a bit more explanatory and is less focused on the decision problem. Curious if you have a recommendation?…
on “Show HN: The first complete open source implementation of Turing's famous paper” ↗