## Resources for Math 15: Logic, Sets & Probability

Note: Different sections of Math 15 may cover different topics selected from the following list, and not necessarily in the order given. Choose your topic and then select the resource you want.

### Topic 1: Introduction to Logic

Statements and Logical Operators, Logical Equivalence, Tautologies and Contradictions, The Conditional and the Biconditional, Tautological Implications and Tautological Equivalences, Rules of Inference, Arguments and Proofs

### Topic 2: Sets and Counting

Sets, The Number of Elements in a Set, The Multiplication Principle, The Addition Principle, Permutations, Combinations

### Topic 3: Probability

Sample Spaces and Events, Introduction to Probability, Principles of Probability, Counting Techniques and Probability, Conditional Probability and Independence, Bayes' Theorem and Applications, Bernoulli Trials

 Topic Summary: Click Here On-Line Tutorials: Sample Spaces & Events Estimated Probability Empirical Probability Abstract Probability Conditional Probability and Independence Bayes' Theorem and Applications Extra Topic On-Line: Sampling Distributions & Central Limit Theorem True-False Quiz: Click Here Review Exercises: Click Here On-Line Tools: Java Monty Hall Simulation (This simulation of the game show is based on the principles of conditional probability.)

### Topic 4: Statistics

Random Variables and Distributions, Mean, Median, and Mode, Variance and Standard Deviation, Normal Distributions

 Topic Summary: Click Here True-False Quiz: Click Here Review Exercises: Click Here On-Line Tools: Histogram and Probability Distribution Generator Probability Distribution Generator and Grapher for Bernoulli Trials Normal Distribution Utility Normal Distribution Table

### Topic 5: Calculus Applied to Probability

(For students with a calculus background)
Continuous Random Variables and Histograms, Probability Density Functions: Uniform, Exponential, Normal, and Beta, Mean, Median, Variance and Standard Deviation, Creating a Family Trust