Number Theory

Designed for the gifted self-learner who has completed Algebra I, this supplemental high school text is ideal for summertime or other independent study. Careful exposition of the topics and well-developed examples with ample comments guide the student’s thinking, while answers to odd-numbered exercises provide feedback on the student’s progress.

The topics chosen form an introduction to the rich field of number theory. Among others, they include: divisibility, the Euclidean algorithm, prime numbers, figurate numbers, recursively-defined numbers such as Fibonacci and Lucas numbers, modular arithmetic, the Chinese Remainder Theorem, and an appendix on sets.

Applications are made to calendar systems, UPC and ISBN codes, and more. Side notes are provided to spark further interest or exploration on such topics as digital signals, the history of mathematical symbols, and numerology.

Throughout the text, students are guided to think carefully about mathematics itself, including learning the roles of definitions and proof. Such study can be an invaluable aid in maximizing a student’s understanding of high school geometry.