{"product_id":"a-primer-of-analytic-number-theory-from-pythagoras-to-riemann-hardback-9780521813099","title":"A Primer of Analytic Number Theory; From Pythagoras to Riemann (Hardback) 9780521813099","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eA Primer of Analytic Number Theory\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eFrom Pythagoras to Riemann\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eAn undergraduate-level 2003 introduction whose only prerequisite is a standard calculus course.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJeffrey Stopple (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521813099, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 23 June 2003\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e398 pages\u003cbr\u003e23.4 x 15.5 x 3 cm, 0.75 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 general style is user-friendly and interactive … a well presented and stimulating informal introduction to a wide range of topics …'. Proceedings of the Edinburgh Mathematical Society\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis 2003 undergraduate introduction to analytic number theory develops analytic skills in the course of studying ancient questions on polygonal numbers, perfect numbers and amicable pairs. The question of how the primes are distributed amongst all the integers is central in analytic number theory. This distribution is determined by the Riemann zeta function, and Riemann's work shows how it is connected to the zeroes of his function, and the significance of the Riemann Hypothesis. Starting from a traditional calculus course and assuming no complex analysis, the author develops the basic ideas of elementary number theory. The text is supplemented by series of exercises to further develop the concepts, and includes brief sketches of more advanced ideas, to present contemporary research problems at a level suitable for undergraduates. In addition to proofs, both rigorous and heuristic, the book includes extensive graphics and tables to make analytic concepts as concrete as possible.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Sums and differences\u003cbr\u003e 2. Products and divisibility\u003cbr\u003e 3. Order and magnitude\u003cbr\u003e 4. Counterexamples\u003cbr\u003e 5. Averages\u003cbr\u003e 6. Prime number theorems\u003cbr\u003e 7. Series\u003cbr\u003e 8. The Basel problem\u003cbr\u003e 9. Euler's product\u003cbr\u003e 10. The Riemann zeta function\u003cbr\u003e 11. Pell's equation\u003cbr\u003e 12. Elliptic curves\u003cbr\u003e 13. Symmetry\u003cbr\u003e 14. Explicit formula.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Number theory [\u003ca title=\"See our other books on Number theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Number%20theory%20%5BPBH%5D%22\"\u003ePBH\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":46005461483800,"sku":"9780521813099","price":114.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521813099_6046f200-d696-41c6-a92b-b1445bf6618a.jpg?v=1691368319","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/a-primer-of-analytic-number-theory-from-pythagoras-to-riemann-hardback-9780521813099","provider":"Freshly Printed Books","version":"1.0","type":"link"}