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A Bridge to Advanced Mathematics

From Natural to Complex Numbers
Buch | Softcover
525 Seiten
2023
American Mathematical Society (Verlag)
978-1-4704-7148-4 (ISBN)
CHF 142,95 inkl. MwSt
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Most 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.

Sebastian M. Cioaba, University of Delaware, Newark, DE. Werner Linde, Friedrich-Schiller University Jena, Germany.

Natural numbers $/mathbb{N}$
Integer numbers $/mathbb{Z}$
Rational numbers $/mathbb{Q}$
Real numbers $/mathbb{R}$
Sequences of real numbers
Complex numbers $/mathbb{C}$
Epilogue
Sets, functions, and relations
Bibliography
Index

Erscheinungsdatum
Reihe/Serie Pure and Applied Undergraduate Texts
Verlagsort Providence
Sprache englisch
Maße 178 x 254 mm
Gewicht 272 g
Themenwelt Mathematik / Informatik Mathematik Allgemeines / Lexika
Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Logik / Mengenlehre
ISBN-10 1-4704-7148-5 / 1470471485
ISBN-13 978-1-4704-7148-4 / 9781470471484
Zustand Neuware
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