Math 118: Finite Mathematics

Catalog Information

Title

Finite Mathematics

(Credit Hours:Lecture Hours:Lab Hours)

(3:0:3)

Offered

Fall, Winter

Prerequisite

Math 110

Description

Description: This course studies the basic elements and applications of finite mathematics. The first half of the class covers the language of set theory, principles of counting and combinatorics, probability theory for equally likely outcomes, elementary stochastic processes, conditional probabilities, and repeated experiments. The concept of a random variable is developed, along with expectation and variance. The second half of the class explores systems of linear equations and matrix algebra, linear programming, and Markov chains. This course considers a broad range of applications in business, the life sciences, and the social sciences.

Desired Learning Outcomes

1. Probability Models (21 lectures)
   • Sets Theory (3 lectures)
     • Describe sets using set-builder notation.
   • Solve problems involving set membership, subsets, intersections, unions, and complements of sets.
2. Regular surfaces
   • Regular surfaces as inverse images of regular values
   • Change of parameters
   • The tangent plane
   • The first fundamental form
   • Orientation of surfaces
3. The geometry of the Gauss map
   • Definition of the Gauss map and fundamental properties
   • The Gauss map in local coordinates
   • Minimal surfaces
4. Intrinsic geometry of surfaces
   • Isometries and conformal maps
   • Geodesics and parallel transport
   • The Gauss-Bonnet Theorem and applications
   • The exponential map

Prerequisites

Math 110

Textbooks

Possible textbooks for this course include (but are not limited to):

Finite Mathematics, 5th edition, Daniel P. Maki and Maynard Thompson, McGraw-Hill 2005