Discrete Calculus & Probability
MCS 256: Discrete Calculus & Probability
Unit 0 Outline
Introduction to Discrete Mathematics
- Algorithms, computational complexity, and recurrence relations
- Sorting example
- Gambler's ruin
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Problem-solving tactics
- Thinking recursively & recurrence relations
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The principle of mathematical induction
- Sequences
- Triangular numbers
- Unwinding/unfolding/backtracking a recurrence
- Arithmetic sequences
- Geometric sequences
- Sums of arithmetic and geometric sequences
- Financial mathematics
- Simple interest (arithmetic [linear] sequences)
- Compound interest (geometric [exponential] sequences)
- Present values of installment payments (geometric sums)
- Pascal's triangle and the binomial theorem