MAT2313

Foundations of Mathematics (3-0) 3 Credit Hours

Course Catalog

Corequisite: MAT1224.

Content: Permutations, combinations, multinational coefficients, inclusion/exclusion principle, axioms of probability, conditional probability, Bayes formula, independent events, discrete random variables, expected value,m variance, discrete random variables (Bernoulli, Binomial, Poisson, geometric, hypergeometric and Zeta random variables), continuous random variables (uniform, normal and other distributions), joint distributions, properties of expectations, limit theorems (Chebyshev's inequality, Central Limit Theorem, Law of Large Numbers)) Generally offered: Fall, Spring, Summer.

Description

Introduction to the theory of probability, through the study of discrete and continuous random variables.

Sample textbooks

• Modern Mathematical Statistics with Applications (Springer Texts in Statistics). Jay L. Devore and Kenneth N. Berk. Second Edition.
• A Probability Course for the Actuaries: A Preparation for Exam P/1, by Marcel B. Finan. Freely available online.

Topics List

Week	Topic	Sections from Finan's book	Subtopics
1-2	Populations and Samples	Chapters 1-2	The Fundamental Principle of Counting Permutations and Combinations Permutations and Combinations with Indistinguishable Objects
3-4	Probability: Definitions and Properties	Chapter 3	Basic Definitions and Axioms of Probability Properties of Probability Probability and Counting Techniques
5	Conditional Probability and Independence	Chapter 4	Conditional Probabilities Posterior Probabilities: Bayes’ Formula Independent Events Odds and Conditional Probability
6-8	Discrete Random Variables	Chapter 5	Random Variables Probability Mass Function and Cumulative Distribution Function119 Expected Value of a Discrete Random Variable Expected Value of a Function of a Discrete Random Variable Variance and Standard Deviation
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See also

• UTSA Undergraduate Mathematics Course Descriptions