## Course Catalog Description

An advanced study of probability theory. Sample spaces, random variables and their distributions, conditional probability and independence, transformations of random variables. The prerequisites are MATH 205 (Calculus III) and MATH 210 (Linear Algebra).

## Course Overview

This is the first of a two-course sequence in mathematical aspects of probability and statistics. The purpose of this first course is to introduce you to the consequences of knowable randomness in the world around us. With this knowledge, you will be better able to predict future events, which is the primary purpose of the second course, MATH 322.

## Course Objectives

By the end of this course, you should be able to

- use Monte Carlo simulation to approximate answers;
- apply rules of probability to decision-making;
- determine appropriate distributions for natural phenomena;
- calculate moments, both central and raw, for distributions;
- apply and prove the Central Limit Theorem;
- write results using correct language; and
- use computer programs to perform calculations and to typeset documents.

- Teacher: Ole Forsberg

## Course Catalog Description

The prerequisites are a satisfaction of the Mathematics Proficiency requirement. The idea of a matrix, or rectangular array of objects, is surprisingly powerful and pervasive in mathematics and its applications. This course explores the algebraic properties and uses of matrices. Topics include inverses, determinants, systems of linear equations, eigenvalues and eigenvectors, and applications to such areas as network flow, economic input-output analysis, random processes, electric circuits, game theory, and linear optimization.

## Course Overview

The purpose of this course is to introduce you to handling a powerful construct in mathematics – the matrix. Mathematics advances by giving us the tools to improve our understanding of the world around us. This course shows you why matrices are useful in describing and understanding life.

## Course Objectives

By the end of this course, you should be able to

- represent experienced phenomena in matrix form;
- perform algebra with matrices;
- calculate eigenvalues and eigenvectors of a matrix;
- use matrices to understand Markov chains;
- calculate the least squares means and lines;
- use matrices to solve questions about phenomena; and
- use Mathematica to solve problems and typeset them nicely.

- Teacher: Ole Forsberg