Introduction to Number Theory
by Mathew Crawford
Learn the fundamentals of number theory from former MATHCOUNTS, AHSME, and AIME perfect scorer Mathew Crawford. Topics covered in the book include primes & composites, multiples & divisors, prime factorization and its uses, simple Diophantine equations, base numbers, modular arithmetic, divisibility rules, linear congruences, how to develop number sense, and much more.
As you'll see in the excerpts below, the text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, so the student has a chance to solve them without help before proceeding. The text then includes motivated solutions to these problems, through which concepts and curriculum of number theory are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains hundreds of problems. The solutions manual contains full solutions to nearly every problem, not just the answers.
This book is ideal for students who have mastered basic algebra, such as solving linear equations. Middle school students preparing for MATHCOUNTS, high school students preparing for the AMC, and other students seeking to master the fundamentals of number theory will find this book an instrumental part of their mathematics libraries.
About the author: Mathew Crawford is the founder and CEO of MIST Academy, a school for gifted students, in Birmingham,
Alabama. He is a former instructor and curriculum developer for the Art of Problem Solving online school. He is
co-author of Art of Problem Solving's Intermediate Algebra textbook, and served on the Board of Directors of the
Art of Problem Solving Foundation. Crawford was a perfect scorer at the national MATHCOUNTS competition in
1990, and a member of the national championship team (Alabama) in 1991. He was a 3-time invitee to the Math
Olympiad Summer Program, a perfect scorer on the AIME, and a 2-time USA Math Olympiad honorable mention.
ISBN: 978-0-9773045-4-7
Text: 336 pages. Solutions: 144 pages.
Paperback. 10 7/8 x 8 3/8 x 5/8 inches.
Pricing Information
Discount Information: Additional 10% discount for orders of 5-9 copies of the same text; 20% discount for 10+ copies.
Excerpts
Table of Contents -
Excerpt 1 -
Excerpt 2 -
Index
Diagnostic Tests
- Pre-test: Students should be able to complete most or all of the pre-test before beginning this book.
- Post-test: Students who can comfortably solve most or all of the problems on the post-test will likely find this book to be mostly review.
Testimonials
"Thank you so much for Introduction to Number Theory. I have thoroughly enjoyed this book. It has introduced me to form of math that I would never have discovered on my own. I have been studying the book own my own now for three weeks. In those three weeks I have learned to not only do problems I thought were impossible, but I have learned to enjoy them. I have to say this is my favorite form of math."
10th grade student, Alabama
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