Discrete Transition to Advanced Mathematics

Name: Discrete Transition to Advanced Mathematics
Price: 21.41 USD
Availability: InStock
ISBN: 9780534405182

ISBN-10: 0534405185

ISBN-13: 9780534405182

Edition: 2004

Authors: Bettina Richmond, Thomas Richmond

List price: $170.95

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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…

Book details

List price: $170.95
Copyright year: 2004
Publisher: Brooks/Cole
Publication date: 7/21/2003
Binding: Hardcover
Pages: 450
Size: 7.50" wide x 9.25" long x 0.75" tall
Weight: 1.892
Language: English




Sets And Logic


Sets


Set Operations


Partitions


Logic and Truth Tables


Quantifiers


Implications



Proofs


Proof Techniques


Mathematical Induction


The Pigeonhole Principle



Number Theory


Divisibility


The Euclidean Algorithm


The Fundamental Theorem of Arithmetic


Divisibility Tests


Number Patterns



Combinatorics


Getting from Point A to Point B


The Fundamental Principle of Counting


A Formula for the Binomial Coefficients


Combinatorics with Indistinguishable Objects


Probability



Relations


Relations


Equivalence Relations


Partial Orders


Quotient Spaces



Functions and Cardinality


Functions


Inverse Relations and Inverse Functions


Cardinality of Infinite Sets


An Order Relation for Cardinal Numbers



Graph theory


Graphs


Matrices, Digraphs, and Relations


Shortest Paths in Weighted Graphs


Trees



Sequences


Sequences


Finite Differences


Limits of Sequences of Real Numbers


Some Convergence Properties


Infinite Arithmetic


Recurrence Relations



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



Continued Fractions


Finite Continued Fractions


Convergents of a Continued Fraction


Infinite Continued Fractions


Applications of Continued Fractions