Sets, Groups, and Mappings
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Sets, Groups, and Mappings: An Introduction to Abstract Mathematics(Pure and Applied Undergraduate Texts)

Sets, Groups, and Mappings: An Introduction to Abstract Mathematics(Pure and Applied Undergraduate Texts)


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About the Book

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.

Table of Contents:
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

About the Author :
Andrew D. Hwang, College of the Holy Cross, Worcester, MA.


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Product Details
  • ISBN-13: 9781470449322
  • Publisher: American Mathematical Society
  • Publisher Imprint: American Mathematical Society
  • Height: 254 mm
  • No of Pages: 416
  • Sub Title: An Introduction to Abstract Mathematics
  • Width: 178 mm
  • ISBN-10: 1470449323
  • Publisher Date: 30 Oct 2019
  • Binding: Hardback
  • Language: English
  • Series Title: Pure and Applied Undergraduate Texts
  • Weight: 736 gr


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Sets, Groups, and Mappings: An Introduction to Abstract Mathematics(Pure and Applied Undergraduate Texts)
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