02104 2200253 4500999001700000008004100017020001800058082001500076100002500091245006900116260005500185300003300240365002200273490006000295504005100355520121100406650001601617650002001633650002401653650001901677700001801696942001201714952012401726 c32099d32099231006b xxu||||| |||| 00| 0 eng d a9781470471484 a513.2bCIO aCioaba, Sebastian M. aBridge to advanced mathematics : from natural to complex numbers bAmerican Mathematical Society,c2023aProvidence : axiii, 525 p. ;bill.,c26 cm b89.00cUSDd86.10 aPure and applied undergraduate texts, 1943-9334 ;vv.58 aIncludes bibliographical references and index. aMost introduction to proofs textbooks focus on the structure of rigorous mathematical language and only use mathematical topics incidentally as illustrations and exercises. In contrast, this book gives students practice in proof writing while simultaneously providing a rigorous introduction to number systems and their properties. Understanding the properties of these systems is necessary throughout higher mathematics. The book is an ideal introduction to mathematical reasoning and proof techniques, building on familiar content to ensure comprehension of more advanced topics in abstract algebra and real analysis with over 700 exercises as well as many examples throughout. Readers will learn and practice writing proofs related to new abstract concepts while learning new mathematical content. The first task is analogous to practicing soccer while the second is akin to playing soccer in a real match. The authors believe that all students should practice and play mathematics. The book is written for students who already have some familiarity with formal proof writing but would like to have some extra preparation before taking higher mathematics courses like abstract algebra and real analysis. aMathematics aComplex Numbers aEuclidean Algorithm aPeano's Axioms aLinde, Werner 2ddccBK 00102ddc406513_200000000000000_CIO70942705aDAIICTbDAIICTd2023-10-03g7662.90o513.2 CIOp034352r2023-10-06yBK