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Number Theory
In this book, the author solves the problem of maintaining students' interest by offering a combinatorial approach to elementary number theory.
Written by a distinguished mathematician and teacher, this undergraduate text uses a combinatorial approach to accommodate both math majors and liberal arts students. In addition to covering the basics of number theory, it offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.
Accessible Introduction: This book offers a comprehensive and accessible introduction to number theory, catering to both mathematics majors and students in education and liberal arts who require a more basic understanding of the topic. Combinatorial Approach: By taking a combinatorial approach to elementary number theory, this book offers new insights to mathematics majors while providing simple proofs for many theorems to other students. Wide Range of Topics: The book covers multiplicativity-divisibility, fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots, prime numbers, quadratic congruences, additivity, partition theory, and geometric number theory. Emphasis on Numerical Examples: The author emphasizes the value of numerical examples in number theory and demonstrates the role of computers in obtaining such examples, allowing students to derive conjectures and develop a deeper understanding of the theorems. Opportunities for Practical Application: Exercises throughout the book allow students to construct numerical tables with or without a computer, encouraging them to explore the concepts through hands-on practice.
Written by a distinguished mathematician and teacher, this undergraduate text uses a combinatorial approach to accommodate both math majors and liberal arts students. In addition to covering the basics of number theory, it offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.
Accessible Introduction: This book offers a comprehensive and accessible introduction to number theory, catering to both mathematics majors and students in education and liberal arts who require a more basic understanding of the topic. Combinatorial Approach: By taking a combinatorial approach to elementary number theory, this book offers new insights to mathematics majors while providing simple proofs for many theorems to other students. Wide Range of Topics: The book covers multiplicativity-divisibility, fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots, prime numbers, quadratic congruences, additivity, partition theory, and geometric number theory. Emphasis on Numerical Examples: The author emphasizes the value of numerical examples in number theory and demonstrates the role of computers in obtaining such examples, allowing students to derive conjectures and develop a deeper understanding of the theorems. Opportunities for Practical Application: Exercises throughout the book allow students to construct numerical tables with or without a computer, encouraging them to explore the concepts through hands-on practice.
288 pages, Paperback
First published January 1, 2012
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Displaying 1 - 6 of 6 reviews
July 9, 2016
Great review ! I fought my way through this subject 40 years ago
The presentation is consistent and if you don't fight it, brings back pleasant memories. I remember being afraid of the notation, did I really understand it? There are multiple levels of abstraction to deal with. They pop up at odd times during a reading. Keep going until no new meanings jump out at you, then put it down, wait awhile and read it again. It's nice not to worry about an examination or presentation of the material.
The presentation is consistent and if you don't fight it, brings back pleasant memories. I remember being afraid of the notation, did I really understand it? There are multiple levels of abstraction to deal with. They pop up at odd times during a reading. Keep going until no new meanings jump out at you, then put it down, wait awhile and read it again. It's nice not to worry about an examination or presentation of the material.
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May 13, 2021For clarification! I actually had to read the entirety of “Number Theory: In Context and Interactive” by Karl-Dieter Crisman, my professor for the course, but Goodreads doesn’t have that gem of a textbook 😤😤
Anyways, Number Theory is far and away the most difficult course I’ve taken, but MAN is it cool if you’re into patterns and discovering/analyzing neat mathematical systems! Shoot me a text if you wanna talk about the Riemann Zeta function, Euler Phi function, and/or Legendre symbols :-D The sense of relief upon turning my last assignment in could’ve sedated Winston Churchill though oh my goodness
Anyways, Number Theory is far and away the most difficult course I’ve taken, but MAN is it cool if you’re into patterns and discovering/analyzing neat mathematical systems! Shoot me a text if you wanna talk about the Riemann Zeta function, Euler Phi function, and/or Legendre symbols :-D The sense of relief upon turning my last assignment in could’ve sedated Winston Churchill though oh my goodness
September 12, 2024
A good introductory book for number theory, the problems were not too difficult or too many either, and the book was nice and short. I didn't really cover much after chapter 11 since they were not relevant to the course I am taking right now on Number Theory, but the rest of the book was well-written and overall not too confusing. Glad to have this one done early though, so that I can focus more on the other textbooks I have been reading over the semester.
January 3, 2026
required reading for Elementary Number Theory. It was hard to read without the lectures. The lectures make it easy to go through the book. I don't think I would've been able to just read this on my own
April 27, 2024
I expected this book was going to make me wiser about discrete mathematics in an intuitive way. Unfortunately, the book is more specific for students who are sitting exams relating with this field which is very useful for that public. So the book sharply exceeds the reading difficulty I expected and it’s is deeply mathematic.
I strongly recommend this book as a reference of proofs and definitions as the mathematical detail is enough to understand theorems in the field of number theory. In addition, it is very well explained.
I strongly recommend this book as a reference of proofs and definitions as the mathematical detail is enough to understand theorems in the field of number theory. In addition, it is very well explained.
Displaying 1 - 6 of 6 reviews