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(Ebook PDF) How to Prove It A Structured Approach 2nd Edition by Daniel Velleman 0521675995 9780521675994 Full chapter

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How to Prove It A Structured Approach 2nd Edition Daniel J. Velleman Digital Instant Download

Author(s): Daniel J. Velleman
ISBN(s): 9780521675994, 0511159439
Edition: 2
File Details: PDF, 23.87 MB
Year: 2006
Language: english
SKU: EB-2099730 Category: Tag:

How to Prove It A Structured Approach 2nd Edition by Daniel J. Velleman – Ebook PDF Instant Download/Delivery: 0521675995, 978-0521675994
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Product details:

ISBN 10:         0521675995
ISBN 13: 978-0521675994
Author:          Daniel J. Velleman

Geared to preparing students to make the transition from solving problems to proving theorems, this text teaches them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5
 

How to Prove It A Structured Approach 2nd Table of contents:

  • Chapter 1: Propositional Logic

    • Basic Propositional Logic
    • Logical Connectives
    • Truth Tables
    • Equivalence of Propositions
    • Proofs Using Propositional Logic

  • Chapter 2: Logical Proofs

    • Direct Proofs
    • Proof by Contradiction
    • Proof by Contrapositive
    • Proof by Cases
    • Mathematical Induction

  • Chapter 3: Set Theory

    • Basic Set Operations
    • Set Relations and Functions
    • Proofs Involving Sets
    • Venn Diagrams
    • Cartesian Products and Relations

  • Chapter 4: Functions and Relations

    • Functions: Definitions and Properties
    • Inverse Functions
    • Compositions of Functions
    • Equivalence Relations
    • Partially Ordered Sets

  • Chapter 5: Proofs in Number Theory

    • Divisibility and Primes
    • The Division Algorithm
    • Greatest Common Divisors and Least Common Multiples
    • Mathematical Induction in Number Theory
    • Modular Arithmetic

  • Chapter 6: Proofs in Combinatorics

    • Basic Counting Principles
    • Permutations and Combinations
    • The Pigeonhole Principle
    • Binomial Coefficients
    • Inclusion-Exclusion Principle

  • Chapter 7: Proofs in Graph Theory

    • Basic Graph Definitions
    • Graph Representations
    • Eulerian and Hamiltonian Paths
    • Graph Coloring
    • Planar Graphs and Graph Isomorphisms

  • Chapter 8: Proofs in Calculus

    • Limits and Continuity
    • The Intermediate Value Theorem
    • The Mean Value Theorem
    • Sequences and Series
    • Proofs Involving Derivatives and Integrals

  • Chapter 9: Advanced Proof Techniques

    • Proof by Construction
    • Proof by Exhaustion
    • Proofs Involving Infinity
    • Uniqueness Proofs
    • Proofs in Topology and Geometry

  • Chapter 10: Applications of Proofs

    • Proofs in Computer Science
    • Proofs in Cryptography and Security
    • Proofs in Algebra and Linear Algebra
    • Proofs in Logic and Philosophy

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