{"product_id":"the-art-of-proof-basic-training-for-deeper-mathematics-9781493940868","title":"The Art of Proof: Basic Training for Deeper Mathematics","description":"Preface.- Notes for the Student.- Notes for Instructors.- Part I: The Discrete.- 1 Integers.- 2 Natural Numbers and Induction.- 3 Some Points of Logic.- 4 Recursion.- 5 Underlying Notions in Set Theory.- 6 Equivalence Relations and Modular Arithmetic.- 7 Arithmetic in Base Ten.- Part II: The Continuous.- 8 Real Numbers.- 9 Embedding Z in R.- 10. Limits and Other Consequences of Completeness.- 11 Rational and Irrational Numbers.- 12 Decimal Expansions.- 13 Cardinality.- 14 Final Remarks.- Further Topics.- A Continuity and Uniform Continuity.- B Public-Key Cryptography.- C Complex Numbers.- D Groups and Graphs.- E Generating Functions.- F Cardinal Number and Ordinal Number.- G Remarks on Euclidean Geometry.- List of Symbols.- Index.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=AUTH-3889780\"\u003eMatthias Beck\u003c\/a\u003e, \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=AUTH-4146664\"\u003eRoss Geoghegan\u003c\/a\u003e\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 08\/23\/2016\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 182\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.81lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 10.00h x 7.00w x 0.44d\u003cbr\u003e\u003cb\u003eISBN13:\u003c\/b\u003e 9781493940868\u003cbr\u003e\u003cb\u003eISBN10:\u003c\/b\u003e 1493940864\u003cbr\u003e\u003cb\u003eBISAC Categories:\u003c\/b\u003e\u003cbr\u003e- \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=CAT-MAT\"\u003eMathematics\u003c\/a\u003e | \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=BISAC-MAT018000\"\u003eLogic\u003c\/a\u003e\u003cbr\u003e- \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=CAT-MAT\"\u003eMathematics\u003c\/a\u003e | \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=BISAC-MAT002000\"\u003eAlgebra | General\u003c\/a\u003e\u003cbr\u003e- \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=CAT-MAT\"\u003eMathematics\u003c\/a\u003e | \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=BISAC-MAT034000\"\u003eMathematical Analysis\u003c\/a\u003e\u003cbr\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eAbout the Author\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eMatthias Beck received his initial training in mathematics in Würzburg, Germany, received his Ph.D. in mathematics from Temple University, and is now associate professor of mathematics at San Francisco State University. He is the recipient of the 2013 MAA Haimo Award for Distinguished College or University Teaching of Mathematics. He is the author of a previously published Springer book, \u003ci\u003eComputing the Continuous Discretely\u003c\/i\u003e (with Sinai Robins). \u003c\/p\u003e\u003cp\u003eRoss Geoghegan received his initial training in mathematics in Dublin, Ireland, received his Ph.D. in mathematics from Cornell University, and is now professor of mathematics at the State University of New York at Binghamton. He is the author of a previously published Springer book, \u003ci\u003eTopological Methods in Group Theory\u003c\/i\u003e.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Default Title","offer_id":44548121198829,"sku":"9781493940868","price":67.48,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0550\/8097\/6621\/products\/img_75429e11-79ec-4ccf-a915-700f4930fcf7.jpg?v=1701635364","url":"https:\/\/sureshotbooks.com\/es\/products\/the-art-of-proof-basic-training-for-deeper-mathematics-9781493940868","provider":"SureShot Books Publishing LLC","version":"1.0","type":"link"}