Sets, Groups, and Mappings
An Introduction to Abstract Mathematics
Seiten
2019
American Mathematical Society (Verlag)
978-1-4704-4932-2 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-4932-2 (ISBN)
Introduces the world of advanced mathematics using algebraic structures as a unifying theme. Having no prerequisites beyond precalculus and an interest in abstract reasoning, the book is suitable for students who are looking for an entry into discrete mathematics, induction and recursion, groups and symmetry, and plane geometry.
This book introduces students to the world of advanced mathematics using algebraic structures as a unifying theme. Having no prerequisites beyond precalculus and an interest in abstract reasoning, the book is suitable for students of math education, computer science or physics who are looking for an easy-going entry into discrete mathematics, induction and recursion, groups and symmetry, and plane geometry. In its presentation, the book takes special care to forge linguistic and conceptual links between formal precision and underlying intuition, tending toward the concrete, but continually aiming to extend students' comfort with abstraction, experimentation, and non-trivial computation.
The main part of the book can be used as the basis for a transition-to-proofs course that balances theory with examples, logical care with intuitive plausibility, and has sufficient informality to be accessible to students with disparate backgrounds. For students and instructors who wish to go further, the book also explores the Sylow theorems, classification of finitely-generated Abelian groups, and discrete groups of Euclidean plane transformations.
This book introduces students to the world of advanced mathematics using algebraic structures as a unifying theme. Having no prerequisites beyond precalculus and an interest in abstract reasoning, the book is suitable for students of math education, computer science or physics who are looking for an easy-going entry into discrete mathematics, induction and recursion, groups and symmetry, and plane geometry. In its presentation, the book takes special care to forge linguistic and conceptual links between formal precision and underlying intuition, tending toward the concrete, but continually aiming to extend students' comfort with abstraction, experimentation, and non-trivial computation.
The main part of the book can be used as the basis for a transition-to-proofs course that balances theory with examples, logical care with intuitive plausibility, and has sufficient informality to be accessible to students with disparate backgrounds. For students and instructors who wish to go further, the book also explores the Sylow theorems, classification of finitely-generated Abelian groups, and discrete groups of Euclidean plane transformations.
Andrew D. Hwang, College of the Holy Cross, Worcester, MA.
Logic and proofs
An introduction to sets
The integers
Mappings and relations
Induction and recursion
Binary operations
Groups
Divisibility and congruences
Primes
Multiplicative inverses of residue classes
Linear transformations
Isomorphism
The symmetric group
Examples of finite groups
Cosets
Homomorphisms
Group actions
Euclidean geometry
Euler's formula
Index
| Erscheinungsdatum | 02.09.2019 |
|---|---|
| Reihe/Serie | Pure and Applied Undergraduate Texts |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 736 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-4932-3 / 1470449323 |
| ISBN-13 | 978-1-4704-4932-2 / 9781470449322 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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