The Kemeny Lectures on Finite Mathematics

TSILB¹

Version 0.11, 22 October 2001.

Topics

• Compound statements and truth tables
• Example: equivalence and implication
• Introduction to tree diagrams
• Excerpt: Professor Snell and the urn
• Set operations (review)
• Counting problems
• Partitions and binomial coefficients
• What is 0!?
• Partitions and binomial coefficients (review)
• How many subsets?
• Pascal's triangle
• Binomial coefficients and Pascal's triangle (review)
• Introduction to probability
• Introduction to probability (review)
• Simulation in probability
• Two examples: binomial coefficients and odds
• The birthday problem
• Conditional probability (preview)
• Advice on exam-taking
• To add, or to multiply?
• Conditional probability
• Conditional probability (review)
• Venn diagram probability examples
• Example: true-false test strategy
• Example: gerrymandering
• Example: false positives and false negatives
• Coin tossing (preview)
• Coin tossing and binomial probabilities
• Coin tossing and binomial probabilities (review)
• Example: onditional probabilities by reversing the tree
• Example: getting exactly half heads
• Example: take the negation
• Plotting binomial probabilities; introduction to CLT
• The Central Limit Theorem
• Excerpt: applications of the CLT
• GAME DELAYED--DOG ON FIELD

Raw lectures

• Lecture 1
• Lecture 3
• Lecture 4
• Lecture 5
• Lecture 6
• Lecture 7
• Lecture 8
• Lecture 9
• Lecture 10
• Lecture 11
• Lecture 12
• Lecture 13
• Lecture 14
• Lecture 15
• Lecture 16
• Lecture 17

Footnotes

...TSILB¹

This Space Intentionally Left Blank. Contributors include: John G. Kemeny; Anne Huggins. Additional work by: Peter Doyle. Copyright (C) 2001 Peter G. Doyle. Based on works Copyright (C) 1983-1998 Anne Huggins. This work is freely redistributable under the terms of the GNU Free Documentation License.