MAT 210: Topics in Finite Mathematics

Introduction

What is finite mathematics? Though there is no easy answer to this question, a brief answer would include "mathematics that works outside of the notion of continuity." The realm of continuity is the realm of calculus. Consequently, mathematical modeling of real life problems that are limited to discrete (finite packs of) data or information falls into realm of finite mathematics. Hence, computer scientists should not miss taking finite mathematics since by its very nature a computer works with discrete data. However, finite mathematics goes further than discrete mathematics even though they are closely related. Finite mathematics is more about learning mathematical modeling techniques that can be applied to real world problems.

For example, a system of linear equations is a modeling technique that can be applied to many real world situations, including business and economics, finance, life sciences, social sciences, computer sciences and the physical sciences. Hence, in finite mathematics we learn methods to solve systems of linear equations. Of course, not all situations in the real world are bound by equality and therefore we need to learn how to model using inequalities and how to solve a system of linear inequalities. These techniques form the basis of linear programming. Techniques learned in finite mathematics are the basis of Operations Research that has applications in transportation, shipping, scheduling and optimization.

Basic financial mathematics is also in the realm of finite mathematics with a particular emphasis in compound interest, future values of annuities, present values of annuities and amortization. Probability and statistics have to work with discrete distributions and the basis for these fields is set theory. In finite mathematics we begin with set theory and then introduce the concepts of probability including conditional probability, independence of events, and Bayes' Theorem. We then extend these concepts to counting techniques and binomial probability.

As part of finite mathematics we will learn about stochastic processes that are mathematical models that have evolved over time in a probabilistic way. We will study a Markov Chain which is a special kind of stochastic process. Again, all these models have applications in business and economics, life sciences, social sciences, computer sciences and physical sciences.

Finite mathematics will be one of the most interesting and applicable mathematics course in your program.

Description

UW Colleges Catalog Course Description for MAT 210 Topics in Finite Mathematics - 3 credits.
Matrices, linear programming and applications, probability, Markov chains and mathematics of finance.

Prerequisite. A grade of C or better in MAT 110 or MAT 124 or equivalent, or placement based on placement test score. MS

Proficiencies

Institutional proficiencies assigned to this course

Successful completion of this course will enhance the student's ability to:

  • Interpret and synthesize information and ideas
  • Select and apply scientific and other appropriate methodologies
  • Solve quantitative and mathematical problems
  • Interpret graphs, tables, and diagrams

Department-specific proficiencies assigned to this course

By completing this course, students will be able to:

  • Formulate and solve applications as systems of linear equations or linear inequalities
  • Formulate and solve applications of linear systems in matrix form
  • Interpret and solve applications using matrix operations
  • Distinguish standard and nonstandard linear programming problems
  • Use the simplex method
  • Interpret and solve practical applications as linear programming problems
  • Recognize simple annuities
  • Be able to distinguish present and future values in practical applications
  • Count large finite sets
  • Construct probability models
  • Distinguish the relative frequency model from the uniform probability model
  • Distinguish a Markov chain from an arbitrary stochastic process

Requirements

Hardware

  • Some course work cannot be completed on a Mac. Students must have access to a PC for this course, and the PC must have a CD Player and speakers.
  • Calculator (in addition to the MS Excel software requirement below)
    • Minimum calculator requirement is a full scientific calculator with statistical functions, combination and permutation calculation capability. (Students must have a manual for their calculator with instructions and keystroke operations.)
    • Recommended calculator requirement is a calculator with a full graphing capability. (Students must have a manual for their graphing calculator with instructions and keystroke operations.)

Software

  • Microsoft Word (with Equation Editor installed) and Microsoft Excel
    The most current edition of MS Office (containing MS Word, MS Excel and other valuable programs) is now available to University of Wisconsin students through the Wisconsin Integrated Software Catalog.
  • Shockwave/Flash
  • RealPlayer
  • QuickTime
  • MathXL Player and Test Gen plug-ins
  • Adobe Reader

About the Instructors

  • Photo of Michael BartlettMichael Bartlett
    Assistant Professor, Mathematics
    BEd, Avondale College
    BA, Pacific Union College
    MM, University of Newcastle
    MC, University of Western Sydney