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An Elementary Transition to Abstract Mathematics.

By: Contributor(s): Material type: TextTextSeries: Textbooks in Mathematics SeriesPublisher: Milton : Taylor & Francis Group, 2019Copyright date: ©2020Edition: 1st edDescription: 1 online resource (293 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781000701814
Subject(s): Genre/Form: Additional physical formats: Print version:: An Elementary Transition to Abstract MathematicsDDC classification:
  • 512.2
LOC classification:
  • QA9 .E345 2020
Online resources:
Contents:
Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Contents -- Preface -- 1. A Look Back: Precalculus Math -- 2. A Look Back: Calculus -- 3. About Proofs and Proof Strategies -- 4. Mathematical Induction -- 5. The Well-Ordering Principle -- 6. Sets -- 7. Equivalence Relations -- 8. Functions -- 9. Cardinality of Sets -- 10. Permutations -- 11. Complex Numbers -- 12. Matrices and Sets with Algebraic Structure -- 13. Divisibility in Z and Number Theory -- 14. Primes and Unique Factorization -- 15. Congruences and the Finite Sets Zn -- 16. Solving Congruences -- 17. Fermat's Theorem -- 18. Diffie-Hellman Key Exchange -- 19. Euler's Formula and Euler's Theorem -- 20. RSA Cryptographic System -- 21. Groups - Definition and Examples -- 22. Groups - Basic Properties -- 23. Groups - Subgroups -- 24. Groups - Cosets -- 25. Groups - Lagrange's Theorem -- 26. Rings -- 27. Subrings and Ideals -- 28. Integral Domains -- 29. Fields -- 30. Vector Spaces -- 31. Vector Space Properties -- 32. Subspaces of Vector Spaces -- 33. Polynomials -- 34. Polynomials - Unique Factorization -- 35. Polynomials over the Rational, Real and Complex Numbers -- Suggested Solutions to Selected Examples and Exercises -- Bibliography -- Index.
Summary: This text is intended to help students move from introductory courses to those where rigor and proof play a much greater role. The emphasis is on precise definitions of mathematical objects and rigorous proofs of properties.
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Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Contents -- Preface -- 1. A Look Back: Precalculus Math -- 2. A Look Back: Calculus -- 3. About Proofs and Proof Strategies -- 4. Mathematical Induction -- 5. The Well-Ordering Principle -- 6. Sets -- 7. Equivalence Relations -- 8. Functions -- 9. Cardinality of Sets -- 10. Permutations -- 11. Complex Numbers -- 12. Matrices and Sets with Algebraic Structure -- 13. Divisibility in Z and Number Theory -- 14. Primes and Unique Factorization -- 15. Congruences and the Finite Sets Zn -- 16. Solving Congruences -- 17. Fermat's Theorem -- 18. Diffie-Hellman Key Exchange -- 19. Euler's Formula and Euler's Theorem -- 20. RSA Cryptographic System -- 21. Groups - Definition and Examples -- 22. Groups - Basic Properties -- 23. Groups - Subgroups -- 24. Groups - Cosets -- 25. Groups - Lagrange's Theorem -- 26. Rings -- 27. Subrings and Ideals -- 28. Integral Domains -- 29. Fields -- 30. Vector Spaces -- 31. Vector Space Properties -- 32. Subspaces of Vector Spaces -- 33. Polynomials -- 34. Polynomials - Unique Factorization -- 35. Polynomials over the Rational, Real and Complex Numbers -- Suggested Solutions to Selected Examples and Exercises -- Bibliography -- Index.

This text is intended to help students move from introductory courses to those where rigor and proof play a much greater role. The emphasis is on precise definitions of mathematical objects and rigorous proofs of properties.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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