# AspenPlus/DCS901/DMCS

## 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:
$\displaystyle \sum_{i=1}^{n}i=\sum_{i=1}^{n}(n-i)=\frac{n(n+1)}{2}$
• Stated otherwise:
$\displaystyle 1 + 2 + 3 + \dots + n = \frac{n(n+1)}{2}$
• Gauss' Trick 2:
$\displaystyle \sum_{i=1}^{n-1}i=\sum_{i=1}^{n-1}(n-i)=\frac{n(n-1)}{2}$
• Stated otherwise:
$\displaystyle 1 + 2 + 3 + \dots + n-1 = \frac{n(n-1)}{2}$
• See (Stein et al., 2011, p. 4).