AspenPlus/DCS901/DMCS
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Contents
- 1 Book Information
- 2 Associated Courses
- 3 Chapter 1: Counting
- 4 Chapter 2: Cryptography and Number Theory
- 5 Chapter 3: Reflections on Logic and Proof
- 6 Chapter 4: Induction, Recursion, and Recurrences
- 7 Chapter 5: Probability
- 8 Chapter 6: Graphs
- 9 Appendix A: Derivation of the More General Master Theorem
- 10 References
Book Information
- Discrete Mathematics for Computer Scientists. Written by Clifford Stein; Robert L. Drysdale; Kenneth Bogart. Boston, MA. Addison-Wesley. ISBN: 978-0132122719
Common Definitions
- corollary: A proposition inferred immediately from a proved proposition with little or no additional proof.
- lemma: An auxiliary proposition used in the demonstration of another proposition (or theorem).
- principle: A comprehensive and fundamental law, doctrine, or assumption.
- theorem:
- A formula, proposition, or statement in mathematics or logic deduced or to be deduced from other formulas or propositions.
- An idea accepted or proposed as a demonstrable truth often as a part of a general theory.
Selected Highlights
- Gauss' Trick 1:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \sum_{i=1}^{n}i=\sum_{i=1}^{n}(n-i)=\frac{n(n+1)}{2}}- Stated otherwise:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 1 + 2 + 3 + \dots + n = \frac{n(n+1)}{2}}
- Stated otherwise:
- Gauss' Trick 2:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \sum_{i=1}^{n-1}i=\sum_{i=1}^{n-1}(n-i)=\frac{n(n-1)}{2}}- Stated otherwise:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 1 + 2 + 3 + \dots + n-1 = \frac{n(n-1)}{2}}
- Stated otherwise:
- See (Stein et al., 2011, p. 4).
Associated Courses
Chapter 1: Counting
Chapter 2: Cryptography and Number Theory
Chapter 3: Reflections on Logic and Proof
Chapter 4: Induction, Recursion, and Recurrences
Chapter 5: Probability
Chapter 6: Graphs
Appendix A: Derivation of the More General Master Theorem
References
- Lipschutz, S., & Lipson, M. L. (2007) Schaum's outline of discrete mathematics (3rd ed.). New York, NY: McGraw Hill.
- Stein, C., Drysdale, R., & Bogart, K. (2011). Discrete mathematics for computer scientists. Boston, MA: Addison-Wesley.