Invitation to Number Theory available in Paperback
- Pub. Date:
- American Mathematical Society
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.
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Invitation to Number Theory (New Mathematical Library Series, Vol. 20) based on 0 ratings. 2 reviews.
Ore's text is part of the Anneli Lax New Mathematical Library series published by the Mathematical Association of America. The texts in this series are designed to expose high school students to topics not normally covered in the high school curriculum in order to stimulate them to study mathematics further. Ore's text on number theory fulfills this purpose admirably. Ore's text begins with a discussion of historical topics in number theory including Pythagorean triples, polygonal numbers, and magic squares. These discussions stimulate the reader to explore Ore's subsequent discussion of prime and composite numbers, divisibility, primality testing, numeration systems, and modular arithmetic. Ore's exposition is lucid and the examples he uses to illustrate the theorems and definitions are well-chosen. I like the fact that he kept returning to the same examples (Pythagorean triples, perfect and amicable numbers, Fermat primes, and Mersenne primes) because the reader gains a fuller sense of their properties. Ore's treatment is generally rigorous. Thus the reader should be prepared to read slowly with pencil in hand, check the details, and complete the exercises at the end of the sections. The exercises, of which I wish there were more, are generally tractable. However, they require thought and effort. Answers to some of the exercises are in the back of the text. Many of the exercises are thought-provoking, but others simply require numerous calculations. I found the latter tedious. Also, you should know that Ore assumes that you know how to write proofs using mathematical induction, so you should study how to do so before working your way through the text. I think that once you have worked your way through Ore's text you will want to study number theory further.