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Lecture Notes: Discrete Mathematics
GMU Math 125-001 Spring 2007
Alexei V Samsonovich
Any theoretical consideration, no matter how fundamental it is, inevitably relies on key
primary notions that are accepted without definition. In our case, examples of notions that
we shall accept without definitions are: an object, a value, a concept, a symbol, to name
just a few. In fact, most English words used here are not defined yet expected to be
understood. Given this agreement, our first step is to give useful definitions of the key
terms, notations and concepts wisely selected among others. Below in this text, whenever
a key term is introduced, it is typed in bold italic. Synonyms are listed in parentheses. An
example follows immediately.
Discrete mathematics (sometimes understood as finite mathematics) is the study of
mathematical structures that do not support or require the notion of continuity. In
particular, all computer implementations of continuous mathematical structures inv...

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