Invitation to Number Theory

Rating:
Summary: An appealing introduction to number theory.
Review: The purpose of Ore's text is to get the reader interested in studying number theory. It serves that purpose quite well.

The book begins by discussing the historical origins of number theory including Pythagorean triples, polygonal numbers, and magic squares. This introductory chapter whets the reader's appetite for the subsequent discussion of prime and composite numbers, divisibility, primality tests, numeration systems, and modular arithmetic. Ore's writing is lucid and he uses well-chosen examples to illustrate the theorems he discusses. I liked the fact that he kept returning to the same examples (Pythagorean triples, perfect numbers, Fermat primes, Mersenne primes) in different contexts because it gives the reader a fuller picture of their properties.

Ore's text requires only a solid grounding in high school mathematics, including proofs by mathematical induction, and a willingness to think. If you read slowly, check the details as you go along, and complete the exercises at the end of each section, you will be rewarded amply for your efforts.

The exercises, of which I wish there were more, are tractable. Answers to some of the exercises are provided at the end of the book. While many of the exercises are thought-provoking, there are others that simply require the reader to make numerous calculations. I found the latter tedious.

Ore concludes the book by providing a somewhat dated (the text was published in 1967) list of references for future study in number theory. I think that by the time you have completed working through Ore's text, you will want to explore number theory further.

Rating:
Summary: An appealing introduction to number theory.
Review: The purpose of Ore's text is to get the reader interested in studying number theory. It serves that purpose quite well.

The book begins by discussing the historical origins of number theory including Pythagorean triples, polygonal numbers, and magic squares. This introductory chapter whets the reader's appetite for the subsequent discussion of prime and composite numbers, divisibility, primality tests, numeration systems, and modular arithmetic. Ore's writing is lucid and he uses well-chosen examples to illustrate the theorems he discusses. I liked the fact that he kept returning to the same examples (Pythagorean triples, perfect numbers, Fermat primes, Mersenne primes) in different contexts because it gives the reader a fuller picture of their properties.

Ore's text requires only a solid grounding in high school mathematics, including proofs by mathematical induction, and a willingness to think. If you read slowly, check the details as you go along, and complete the exercises at the end of each section, you will be rewarded amply for your efforts.

The exercises, of which I wish there were more, are tractable. Answers to some of the exercises are provided at the end of the book. While many of the exercises are thought-provoking, there are others that simply require the reader to make numerous calculations. I found the latter tedious.

Ore concludes the book by providing a somewhat dated (the text was published in 1967) list of references for future study in number theory. I think that by the time you have completed working through Ore's text, you will want to explore number theory further.