A bridge to advanced mathematics : from natural to complex numbers
著者
書誌事項
A bridge to advanced mathematics : from natural to complex numbers
（The Sally series, Pure and applied undergraduate texts ; 58）
American Mathematical Society, c2023
- :pbk.
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注記
Includes bibliographical references (p.515-516) and index
内容説明・目次
内容説明
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.
目次
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
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