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Recently I bought a "so called" intro book on number theory "Elementary number theory by burton" after reading some online recommendations to self learn number theory; but it is too much dry for a beginner like me and it feels like the author already assuming that reader is expert in algebra, proofs, combinatorics, math induction etc.. which I am not, if i was, why would I want an introductory number theory book. It is not about what material is in this book but HOW it is explained, it is intentionally written that way. anyways, is there any book that would be easy to read and has in depth and detailed explanations, step by step and goes slow in progress, some visual example would be very helpful but not necessary, should not be a typical coffee table book either but an standard text with easiest examples. I am not an student neither am in that age or mind, I just developed interest in number theory after reading "Journey through genius". it was very interesting book though.

Thanks.

Asim
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  • My copy of the 6th (2007) edition Burton's book, the only edition I have, begins with a chapter on mathematical induction and the binomial theorem (with lots of exercises for practice with these concepts), and the material is essentially that which can be found in many standard college algebra texts (e.g. see Chapter 10 in David Cohen's College Algebra, which incidentally is an excellent reference to have on hand if your school algebra background in these topics is weak). (continued) – Dave L. Renfro Apr 13 '21 at 13:13
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    FYI, Burton's book, and pretty much any of the standard undergraduate level number theory texts, are designed for (U.S. perspective follows; subtract about 1.5 to 2 years for many other countries) 3rd or 4th year mathematics majors (thus, the 3 or 4 semester calculus sequence and maybe a discrete mathematics course would have been completed). That said, Number Theory with Applications by Anderson/Belll (1997) is a bit more leisurely written with more details and exposition in the text material. – Dave L. Renfro Apr 13 '21 at 13:13
  • Agree on the most u said. But excercises in this book are more advanced than what is presented in the book, – Asim Apr 13 '21 at 14:15
  • To be fair, a lot of number theory is based on these topics and or methodologies. Pigeonhole principle ( from combinatorics) can even be used to give a supporting argument for why Fermat's little theorem (from modular-arithmetic) should hold. the visuals might be hard. can you understand mathologer videos on youtube ? – Roddy MacPhee Apr 13 '21 at 21:04
  • @RoddyMacPhee thanks but no, i just want a book that is a little less difficult than the one i mentioned. – Asim Apr 13 '21 at 21:14
  • You might find this site helpful: http://math.gordon.edu/ntic/ntic/frontmatter-1.html – PM 2Ring Apr 14 '21 at 09:18
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    Does this answer your question? Books on Number Theory for Layman –  Jul 23 '21 at 06:58

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I read a lot of Silverman's A Friendly Introduction to Number Theory and enjoyed it quite a bit. It's written in a down to earth style, and was actually intended to sort of woo non-math majors.

Recently I became aware that Rosenlicht wrote a book with Andre Weil entitled A Beginner's Guide to Number Theory. It's based on a series of lectures by the latter at the university of Chicago. I have high hopes for it, based on the fact that I'm familiar with Rosenlicht's work, and even took one of his classes.

I have heard good things about Baker's book. He won a Field's medal.

I haven't seen Davenport' s Higher Arithmetic, but love the title.

Do remember that any book at all will tend to assume a certain amount of mathematical maturity.

I am currently reading Vinogradov's Elements of Number Theory, and find there are not many prerequisites. It's nicely written, and includes various exercises with solutions.

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    @Asim: I have Davenport's book and Vinogradov's book, and if anything, they're pitched at a higher mathematical maturity level than Burton's book. For example, the material on mathematical induction and combinatorics reviewed in Burton's book is not even reviewed in these other two books (the reader is assumed to know this), and the exposition is more concise than in Burton's book (and a lot more concise than the Anderson/Bell book I previously mentioned). I don't have Silverman's book, but it sounds like it might be better for you than any of these four books. (continued) – Dave L. Renfro Apr 14 '21 at 18:39
  • Also, I just saw a book on my bookshelf that I had overlooked before that might be a good fit for you --- Excursions in Number Theory by Ogilvy/Anderson. I especially recommend looking at this, given that you've just read Journey through Genius by Dunham. – Dave L. Renfro Apr 14 '21 at 18:42
  • @DaveL.Renfro Thanks for the info, i'd seen preview pages of Silverman's book it is good but too expensive and i am looking for a old editions of textbooks because they are very affordable and have lot of material very similar to their current versions. how is Rosen's book "NT and its applications" compared to Burtons? – Asim Apr 14 '21 at 18:59
  • @Asim: I don't have a copy of Rosen's book or know anything about it. Number theory is not something I know much about and I only have a few NT books (as compared to real analysis or general topology or set theory). Besides the Ogilvy/Anderson book (not expensive for used copy), maybe look through the titles of English translations of the Russian books from the series "Topics in Mathematics" and "Popular Lectures in Mathematics" and "Little Mathematics Library". Examples: 1 and 2 – Dave L. Renfro Apr 14 '21 at 19:24
  • I think I might be able to get you a free copy of Silverman's book. Mine was free, but that was a while back. I will look into it if you like. –  Apr 15 '21 at 02:06
  • @ChrisCuster yes of course. Thanks – Asim Apr 15 '21 at 05:19
  • Send an email to [email protected], and ask for an evaluation copy. Include your mailing address. –  Apr 17 '21 at 20:16