Top Ten Math Books on Number Theory

Number theory is a part of math that’s devoted primarily to the study of the integers, or in terms understood by all, it’s arithmetic. Distinguished authors have written and published books about number theory; one is as interesting as the next.

If you’re a math enthusiast or someone excited to learn more about mathematics, here’s a list of top ten math books on number theory. Each one is an excellent read and leaves the reader with plenty to think about and gives math students some interesting problems to solve.

Number Theory

George E. Andrews, noted mathematics scholar covers topics including fundamental theorem of arithmetic, combinatorial and computational number theory and a great deal more. Of note, the author has included exercises for constructing numerical tables on your own or by using a computer. Appropriate as a basic introduction to number theory books for beginners, the author also holds the interest of students of more advance levels.

Elementary Number Theory: Second Edition

Authored by Underwood Dudley, a popular and respected writer explains many of the basics in his elementary number theory books. This second edition book includes nearly 1,000 exercises and problems to challenge the reader. Elementary Number Theory: Second Edition is a solid book for beginners and good refresher for students ready to advance to the next level.

Number Theory: A Lively Introduction with Proofs, Applications, and Stories

The author takes a compelling look at numerical topics and concepts and their roles. The book is well – written and speaks to a wide audience. Color illustrations, drawings and diagrams are used to show math problems and theories that involve the reader and help to make learning easier. James Pommersheim’s book on Number Theory is true to its secondary title: A Lively Introduction with Proofs, Applications and Stories“.

The Book of Numbers

If you already like studying math, you might find yourself loving it after reading one of the best number theory books written. It’s fun, educational and easy to comprehend. Diagrams and color pictures help learners visualize math concepts to understand how it all works. The Book of Numbers was written by John H. Conway and Richard Guy.

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Fundamentals of Number Theory was written by William J. LeVeque about the basics of number theory as related to algebraic concepts. Well – written and comprehensive, LeVeque talks about early number theory and continues on through problems to solve, tables, graphs, symbols and more. This is among the good books on number theory that contain content that is appropriate for math majors as well as beginning grad students.

Number Theory: Structures, Examples, and Problems

Written by Titu Andreescu and Dorin Andrica, Number Theory: Structures, Examples, and Problems gets a top rating from readers and students for its problem solving approach, depth of content and inclusion of sophisticated open problems and puzzles. Stimulating and challenging for beginner math students. Appropriate for high school and undergrad college students and any interested in learning more about number theory.

Elementary Theory in Numbers

Written by William J. LeVeque, Elementary Theory of Numbers is a short book that should appeal to math students and anyone new to exploring number theory. Recommended as a self-tutorial but handy as a guide or refresher for students. Although it’s only about 120 pages long it’s considered one of the top ten math books on number theory.

Excursions in Numbers

Excursions in Numbers contains a variety of challenging math problems that include prime numbers, number patterns and many more. Great for anyone who loves challenging math problems and puzzles and has a high school math education. Fun and interesting read by Stanley Ogilvy and John T. Anderson.

Number Theory: A Historical Approach

Written by John J. Watkins, an award – winning teacher, Number Theory covers math topics from soup to nuts while telling stories about many of the great mathematicians responsible for theoretical discoveries and developments. Number Theory: A Historical Approach is full of compelling biographical facts and events. It’s an enjoyable read for every math lover and interesting even to the non-mathematician.

Unsolved Problems in Number Theory

Unsolved Problems in Number Theory was written by Richard Guy. Along with complex problems for solving by different levels of math students and scholars. The book also contains valuable references to Neil Sloane’s Online Encyclopedia of Integer Sequences. Third edition promises to be as exciting and well received as the first two editions.