An introduction to the theory of numbers
by Ivan Morton Niven, H. S. Zuckerman, Hugh L. Montgomery · first published 1960
60% recommend40% neutral
Why HN recommends it
Standard introductory number theory text, often named as a good first book on the subject; suits those learning number theory from the ground up, including people building math skills through problem solving.
Summarised by Claude from recommending comments
Publisher Description (unedited publisher data) The Fifth Edition of one of the standard works on number theory, written by internationally-recognized mathematicians. Chapters are relatively self-contained for greater flexibility. New features include expanded treatment of the binomial theorem, techniques of numerical calculation and a section on public key cryptography. Contains an outstanding set of problems.
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An Introduction to the Theory of Numbers (Niven, Zuckerman and Montgomery) Graph theory with applications (JA Bondy and USR Murty, available online)
on “Ask HN:Math Books” ↗…Mathematics - Lang - One variable Calculus: A First Course in Calculus - Lang - Multi variable Calculus: Calculus of Several Variables - Lang - Linear Algebra: Linear Algebra - Lang - Number theory: An Introduction to the Theory of Numbers - Niven, Zuckerman, Montgomery Some more advanced stuff - Algebra: Algebra - Artin or Algebra, Chapter 0 - Aluffi - Complex Analysis: Functions of One Complex Variable I - Conway - Probability Basics:…
on “Ask HN: How to self-learn math?” ↗If you mean Hardy and Wright's Introduction to the Theory of Numbers, I agree it is excellent, but you can solve the great majority of the project Euler problems without going to quite that level. I particularly enjoyed Daniel Shank's Solved and Unsolved Problems in Number…
on “Project Euler” ↗…ones that can be used for studying now. Books that are clearly written, popular, cover their subject well. Examples: Visual Complex Analysis, Spivak’s Calculus, Linear Algebra Done Right, Hardy’s An Introduction to the Theory of Numbers.
on “Ask HN: What are the most fundamental books on computer science?” ↗…style of textbook): Davenport - The Higher Arithmetic Burkill - A First Course in Mathematical Analysis (and also A Second Course in Mathematical Analysis by Burkill and Burkill) Hardy and Wright - An introduction to the theory of numbers
on “Ask HN: Serious mathematics books that can replace a good teacher?” ↗Absolutely - Hardy and Wright's An introduction to the theory of numbers is excellent but definitely doesn't need to be restricted to postgrads - its also fine for undergraduate level number theory (indeed it was a recommended textbook when I was an undergrad). It is quite…
on ““A Course of Pure Mathematics” – G. H. Hardy (1921) [pdf]” ↗…it is knowledge of math that is barrier. I keep learning math (and, sometimes, relatively new development in math) by solving problems. To start, I would recommend reading G.H. Hardy & E.M. Wright "An Introduction to the Theory of Numbers". With LeetCode -- this is more traditional exercise in coding. I did not pay much attention to it. So, sorry, cannot provide any advice
on “Solving the first 100 Project Euler problems using 100 languages” ↗…introductory text on algebraic number theory, ideal class groups, etc., and by the end it uses these techniques to explain how Kummer proved Fermat's Last Theorem for exponents below 100. Baker's "A concise introduction to the Theory of Numbers" is exactly what it says on the tin. It has five to ten exercises per chapter, and each chapter is a fairly short introduction to a different branch of number theory, giving examples of the fundamental…
on “Ask HN: Recommendations for a good elementary text on Number Theory” ↗…C/C++, JavaScript, Java, Python, Perl, Mathematica, Fortran, and Rust. Another example is number theory. I just checked a few number theory books from my library and most used base e: Hardy & Wright's "An Introduction to the Theory of Numbers", Apostol's "Introduction to Analytic Number Theory", Baker's "A Comprehensive Course in Number Theory", Ingham's "The Distribution of Prime Numbers", Baker's "Transcendental Number Theory", Ribenboim's…
on “New proof dramatically compresses space needed for computation” ↗…arithmetic', a more novel and in some ways a more appropriate title; but it was pointed out that this might lead to misunderstandings about the content of the book." G.H. Hardy and E. M. Wright "An Introduction to the Theory of Numbers"
on “Six Math Essentials” ↗“An Introduction to the Theory of Numbers” by Hardy and Wright.
on “Classic Mathematics Books for Lifelong Learners” ↗