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9780534405182

A Discrete Transition to Advanced Mathematics

by
  • ISBN13:

    9780534405182

  • ISBN10:

    0534405185

  • Edition: 1st
  • Format: Paperback
  • Copyright: 2003-07-21
  • Publisher: Brooks Cole

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Supplemental Materials

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Summary

As the title indicates, this text is intended for courses aimed at bridging the gap between lower level mathematics and advanced mathematics. The transition to advanced mathematics presented is discrete since continuous functions are not studied. The text provides a careful introduction to techniques for writing proofs and a logical development of topics based on intuitive understanding of concepts. The authors utilize a clear writing style and a wealth of examples to develop an understanding of discrete mathematics and critical thinking skills. Including more topics than can be covered in one semester, the text offers innovative material throughout, particularly in the last three chapters (e.g. Fibonacci Numbers and Pascal's Triangle). This allows flexibility for the instructor and the ability to teach a deeper, richer course.

Table of Contents

1. SETS AND LOGIC
Sets
Set Operations
Partitions
Logic and Truth Tables
Quantifiers
Implications
2. PROOFS
Proof Techniques
Mathematical Induction
The Pigeonhole Principle
3. NUMBER THEORY
Divisibility
The Euclidean Algorithm
The Fundamental Theorem of Arithmetic
Divisibility Tests
Number Patterns
4. COMBINATORICS
Getting from Point A to Point B
The Fundamental Principle of Counting
A Formula for the Binomial Coefficients
Combinatorics with Indistinguishable Objects
Probability
5. RELATIONS
Relations
Equivalence Relations
Partial Orders
Quotient Spaces
6. FUNCTIONS AND CARDINALITY
Functions
Inverse Relations and Inverse Functions
Cardinality of Infinite Sets
An Order Relation for Cardinal Numbers
7. GRAPH THEORY
Graphs
Matrices, Digraphs, and Relations
Shortest Paths in Weighted Graphs
Trees
8. SEQUENCES
Sequences
Finite Differences
Limits of Sequences of Real Numbers
Some Convergence Properties
Infinite Arithmetic
Recurrence Relations
9. FIBONACCI NUMBERS AND PASCAL'S TRIANGLE
Pascal's Triangle
The Fibonacci Numbers
The Golden Ratio
Fibonacci Numbers and the Golden Ratio
Pascal's Triangle and the Fibonacci Numbers
10. CONTINUED FRACTIONS
Finite Continued Fractions
Convergents of a Continued Fraction
Infinite Continued Fractions
Applications of Continued Fractions

Supplemental Materials

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The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

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