AspenPlus/DCS901/DMCS

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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}}
  • 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}}
  • 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.