000			a
999			_c32099 _d32099
008			231006b xxu||||| |||| 00| 0 eng d
020			_a9781470471484
082			_a513.2 _bCIO
100			_aCioaba, Sebastian M.
245			_aBridge to advanced mathematics : from natural to complex numbers
260			_bAmerican Mathematical Society, _c2023 _aProvidence :
300			_axiii, 525 p. ; _bill., _c26 cm
365			_b89.00 _cUSD _d86.10
490			_aPure and applied undergraduate texts, 1943-9334 ; _vv.58
504			_aIncludes bibliographical references and index.
520			_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.
650			_aMathematics
650			_aComplex Numbers
650			_aEuclidean Algorithm
650			_aPeano's Axioms
700			_aLinde, Werner
942			_2ddc _cBK