A GUIDE TO ELEMENTARY NUMBER THEORY

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Underwood Dudley was born in New York City in 1937. He has bachelors and masters degrees from the Carnegie Institute of Technology and received the Ph.D. degree (number theory) from the University of Michigan in 1965. He taught at the Ohio State University and at DePauw University from which he retired in 2004. He is the author of three books on mathematical oddities The Trisectors Mathematical Cranks and Numerology an elementary number theory text and is the editor of two collections of mathematical pieces. He has edited the College Mathematics Journal the Pi Mu Epsilon Journal and two of the Mathematical Association of Americas book series. He has served as the MAAs Plya lecturer and has received its Distinguished Service Award. He is a member of the MAA the American Mathematical Society and the Society for Industrial and Applied Mathematics.An introductory guide to elementary number theory for advanced undergraduates and graduates.A concise introduction to elementary number theory which covers the material from a first course in the subject and which can also be used as a refresher text for those already familiar with the subject. It is suitable for advanced undergraduates and graduate students or anyone interested in the subject.A concise introduction to elementary number theory which covers the material from a first course in the subject and which can also be used as a refresher text for those already familiar with the subject. It is suitable for advanced undergraduates and graduate students or anyone interested in the subject.A Guide to Elementary Number Theory is a short exposition of the topics considered in a first course in number theory. It is intended for those who have had some exposure to the material before but have halfforgotten it and also for those who may have never taken a course in number theory but who want to understand it without having to engage with the more traditional texts which are often extensive and dense. Number theory has an impressive history which this guide investigates. Rather than being a textbook with exercises and solutions this guide is an exploration of this interesting and exciting field. Its important results are all included usually with accompanying proofs: the Quadratic Reciprocity Theorem is proved as Gauss did it. The material has been chosen to be maximally broad whilst remaining concise and accessible.Introduction: 1. Greatest common divisors: 2. Unique factorization: 3. Linear diophantine equations: 4. Congruences: 5. Linear congruences: 6. The Chinese Remainder Theorem: 7. Fermats Theorem: 8. Wilsons Theorem: 9. The number of divisors of an integer: 10. The sum of the divisors of an integer: 11. Amicable numbers: 12. Perfect numbers: 13. Eulers Theorem and function: 14. Primitive roots and orders: 15. Decimals: 16. Quadratic congruences: 17. Gausss Lemma: 18. The Quadratic Reciprocity Theorem: 19. The Jacobi symbol: 20. Pythagorean triangles: 21. x4+y4z4: 22. Sums of two squares: 23. Sums

Data Publikacji: 2010-03-25
Wymiary: 228 mm 152 mm 14 mm 320 gr