{"product_id":"an-introduction-to-mathematical-reasoning-numbers-sets-and-functions-hardback-9780521592697","title":"An Introduction to Mathematical Reasoning; Numbers, Sets and Functions (Hardback) 9780521592697","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eAn Introduction to Mathematical Reasoning\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eNumbers, Sets and Functions\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eThe purpose of this book is to introduce the basic ideas of mathematical proof and reasoning to students starting university mathematics.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003ePeter J. Eccles (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521592697, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 11 December 1997\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e364 pages\u003cbr\u003e23.5 x 15.7 x 2.4 cm, 0.705 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'The book is written with understanding of the needs of students …' European Mathematical Society\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory, topics which include many fundamental ideas which are part of the tool kit of any mathematician. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. Over 250 problems include questions to interest and challenge the most able student as well as plenty of routine exercises to help familiarize the reader with the basic ideas.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePart I. Mathematical Statements and Proofs: 1. The language of mathematics\u003cbr\u003e 2. Implications\u003cbr\u003e 3. Proofs\u003cbr\u003e 4. Proof by contradiction\u003cbr\u003e 5. The induction principle\u003cbr\u003e Part II. Sets and Functions: 6. The language of set theory\u003cbr\u003e 7. Quantifiers\u003cbr\u003e 8. Functions\u003cbr\u003e 9. Injections, surjections and bijections\u003cbr\u003e Part III. Numbers and Counting: 10. Counting\u003cbr\u003e 11. Properties of finite sets\u003cbr\u003e 12. Counting functions and subsets\u003cbr\u003e 13. Number systems\u003cbr\u003e 14. Counting infinite sets\u003cbr\u003e Part IV. Arithmetic: 15. The division theorem\u003cbr\u003e 16. The Euclidean algorithm\u003cbr\u003e 17. Consequences of the Euclidean algorithm\u003cbr\u003e 18. Linear diophantine equations\u003cbr\u003e Part V. Modular Arithmetic: 19. Congruences of integers\u003cbr\u003e 20. Linear congruences\u003cbr\u003e 21. Congruence classes and the arithmetic of remainders\u003cbr\u003e 22. Partitions and equivalence relations\u003cbr\u003e Part VI. Prime Numbers: 23. The sequence of prime numbers\u003cbr\u003e 24. Congruence modulo a prime\u003cbr\u003e Solutions to exercises.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical foundations [\u003ca title=\"See our other books on Mathematical foundations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20foundations%20%5BPBC%5D%22\"\u003ePBC\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46005905752344,"sku":"9780521592697","price":101.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521592697i_3c78bb9b-8732-4024-b5be-919e31f485cd.jpg?v=1691370146","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/an-introduction-to-mathematical-reasoning-numbers-sets-and-functions-hardback-9780521592697","provider":"Freshly Printed Books","version":"1.0","type":"link"}