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.
A Discrete Transition to Advanced Mathematics / Edition 1by Bettina Richmond, Thomas Richmond
Pub. Date: 07/25/2003
Publisher: Cengage Learning
Offering many elegant and surprising results, an engaging writing style, and more than 650 exercises, this mathematics text is designed to bridge the gap between computational lower-level courses, and more theoretical upper-level courses. The text is appropriate for discrete mathematics courses, as well as introductory proofs courses, and is accessible to students having two or three semesters of calculus, or introductory linear algebra. Topics include proofs, number theory, combinatorics, graph theory, divisibility tests, binomial coefficients, and Fibonacci numbers and Pascal's triangle. Annotation ©2003 Book News, Inc., Portland, OR
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