What Is A Good Book To Learn Number Theory Mathematics Stack Exchange

Bonisiwe Shabane

-Oct 30, 2025, 3:50 AM

what is a good book to learn number theory mathematics stack exchange

Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Explore Teams Connect and share knowledge within a single location that is structured and easy to search. What would be a good book to learn basic number theory?

If possible a book which also has a collection of practice problems? Thanks. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. I have just finished a master's degree in mathematics and want to learn everything possible about algebraic number fields and especially applications to the generalized Pell equation (my thesis topic), $x^2-Dy^2=k$, where $D$ is... I have a solid foundation in modern algebra and elementary number theory as well as analysis. Does anyone have any suggestions?

I am currently reading Harvey Cohn's 'Advanced number theory' with slow but marked progress. Thanks. I know of very few more endearing books on the subject than Ireland and Rosen's A Classical Introduction to Modern Number Theory. Though Mariano's comment above is no doubt true and the most complete answer you'll get, there are a couple of texts that stand apart in my mind from the slew of textbooks with the... The first leaves off a lot of algebraic number theory, but what it does, it does incredibly clearly (and it's cheap!). It's "Number Theory I: Fermat's Dream", a translation of a Japanese text by Kazuya Kato.

The second is Cox's "Primes of the form $x^2+ny^2$, which in terms of getting to some of the most amazing and deepest parts of algebraic number theory with as few prerequisites as possible, has... For something a little more encyclopedic after you're done with those (if it's possible to be "done" with Cox's book), my personal favorite more comprehensive reference is Neukirch's Algebraic Number Theory. Marcus's Number Fields is a good intro book, but it's not in LaTeX, so it looks ugly. Also doesn't do any local (p-adic) theory, so you should pair it with Gouvêa's excellent intro p-adic book and you have a great first course in algebraic number theory. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Ask questions, find answers and collaborate at work with Stack Overflow for Teams.

Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Explore Teams Connect and share knowledge within a single location that is structured and easy to search. As a physic undergraduate with some knowledge of calculus (Lebesgue integral, stochastic analysis, complex analysis) I'm interested in learning about number theory. Goal: Find the best Number Theory books according to the internet (not just one person's opinion). As an Amazon Associate, we earn from qualifying purchases (at no extra cost to you).

reference request - Books on Number Theory for Layman - Mathematics Stack Exchange Software engineer whose passion for tracking book recommendations from podcasts inspired the creation of MRB. Lead investor at 3one4 Capital whose startup expertise and love for books helped shaped MRB and its growth. We've researched and ranked the best number theory books in the world, based on recommendations from world experts, sales data, and millions of reader ratings. Learn more The Epic Quest to Solve the World's Greatest Mathematical Problem

Sarah-Jayne BlakemoreThe book is great because Simon Singh has this ability to write about the driest and most complex scientific or mathematical concepts and issues, and somehow make them come alive. (Source) Kirk BorneNew Perspective on Fermat's Last Theorem: https://t.co/YeaHQ6iadB by @granvilleDSC @DataScienceCtrl #abdsc #Mathematics See the best-selling book "Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem": https://t.co/dqenmvUw0A by @SLSingh https://t.co/deyMhQTQLU (Source) Steve Jurvetson[Steve Jurvetson recommended this book on the podcast "The Tim Ferriss Show".] (Source) Number theory, for those of us new this field, is a branch of mathematics that deals with the properties and relationships of integers, such as divisibility, primes, congruences, modular arithmetic, Diophantine equations, cryptography, and... Concepts from number theory underpin many other areas of mathematics, such as algebra, analysis, and geometry.

Number-theoretic ideas, for example, are fundamental in the study of algebraic number fields and elliptic curves. If we talk about some practical applications then, this discipline is one of the backbone (if not the backbone) of modern cryptography. Techniques like RSA encryption, which secure online transactions and communications, are based on the properties of prime numbers and modular arithmetic. Even some internet security protocols, to say the least, rely on number-theoretic algorithms. Understanding these principles is crucial for developing new methods to protect data and privacy. The field offers a wealth of problems that are easily understood even by those with basic mathematical knowledge, but whose solutions can be extraordinarily complex and elegant- and that is one of the major...

Here are five books that I think are suitable for learning number theory (for beginners to advanced). This is an easy-to-follow book, has lots of illustrative examples, and also comes with a bunch of exercises/practice problems at the end of each section. It covers the basic topics of number theory, such as the Euclidean algorithm, Fermat’s little theorem, Euler’s theorem, quadratic reciprocity, primitive roots, continued fractions, and more. It also introduces some applications of number theory, such as encryption, coding theory, and computational complexity. It’s fun to go through. Highly recommend if you are just starting.

Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Explore Teams Connect and share knowledge within a single location that is structured and easy to search. I'm currently trained in Algebra, Calculus and Statistics in high school level.

Basically, I've no knowledge at all in number theory as this subject is not taken seriously in my country.

What Is A Good Book To Learn Number Theory Mathematics Stack Exchange

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I Am Currently Reading Harvey Cohn's 'Advanced Number Theory' With

The Second Is Cox's "Primes Of The Form $x^2+ny^2$, Which

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