Invitation to Number Theory by Oystein Ore (PDF)

Description

Number theory has been instrumental in introducing many of the most distinguished mathematicains, past and present, to the charms and mysteries of mathematical research. The purpose of this simple little guide will have been achieved if it should lead some of its readers to appreciate why the properties of nubers can be so fascinating. It would be better still if it would induce you to try to find some number relations of your own; new curiosities devised by young people turn up every year. In any case, you will become familiar with some of the special mathematical concepts and methods used in number theory and will be prepared to embark upon the study of the more advanced books in its rich literature.

User’s Reviews

Editorial Reviews: About the Author Oystein Ore- received his PhD in Oslo and went on to teach at Yale University.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐I use this book to teach my dauter and it goes very well. I agree with the other review that some exercises look tedious, but surprisingly she likes these exercises — it seems that she wants to experiment with numbers. After all, number theory is about making experiments with numbers and finding a pattern.

⭐Not as amazing as his graph theory book but a decent introduction nonetheless.

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