Mathematics, Statistics & Computer Science
University of Wisconsin-Stout
Jarvis Hall Science Wing 231
Menomonie, WI 54751-0790
COURSE NUMBER/TITLE:
MATH-710 Introduction to Industrial Mathematics
CREDITS:
3
COURSE DESCRIPTION:
Introduction to mathematical methods with direct applications in
business and industry, including mathematical aspects of quality control,
Monte Carlo methods, linear programming, model fitting, frequency
domain methods, difference and differential equations, graph theory, and
report writing.
TEXTBOOK: Industrial Mathematics, A Course in Solving Real-World Problems, 1st Ed., by Friedman and
Littmann (adopted Fall 2014)
COURSE OBJECTIVES:
Upon successful completion of this course, the student will be able to:
1. Come to an understanding of applied mathematics reasoning, including the ability to use various
types of numerical methods to model problems, and the ability to use simulations to solve problems.
2. Understand and apply recursive methods to solve problems, including the use of finite differences.
3. Understand and apply how graphs of points joined by lines can model a variety of problem
situations, including critical path analysis, graph coloring problems, minimal spanning trees, and
bin-packing techniques.
4. Analyze data and apply probability concepts to solve problems.
5. Use mathematically correct terminology and notation and construct correct direct and indirect
proofs.
6. Express statements with the precision of formal logic.
7. Present solutions to applied problems in written and oral form.
COURSE OUTLINE:
1. Introduction to Industrial Mathematics Problems (objective 1)
a. Possible Problems:
i. Crystal Precipitation Problem
ii. Air Quality Modeling Problem
2. The Mathematical Model (objectives 1, 3, 4, and 5)
a. Modeling Techniques Including
i. Monte Carlo Methods
ii. Graph Theory
iii. Linear Programming
iv. Frequency Domain Methods
b. Possible Scenarios to Model
i. Electron Beam Lithography
ii. Development of Color Film Negative
3. Analysis of the Solution (objectives 1, 3, 4, and 5)
a. Solution Techniques Including
i. Monte Carlo Methods
4.
5.
6.
ii. Graph Theory
iii. Linear Programming
iv. Frequency Domain Methods
b. Possible Scenarios to Consider:
i. How Does a Catalytic Converter Function?
ii. The Photocopy Machine
An Introduction to Logic and Proof (objectives 2, 5, and 6)
a. Statements, Connectives, Quantifiers
b. Truth Tables
c. Logical Equivalence
d. Methods of Proof
i. Direct Proofs
ii. Proofs by Mathematical Induction
iii. Proofs by Contradiction, Counterexamples
e. Applications: Recursive Definitions, Algorithms
Combinatorics (objective 2)
a. Recurrence Relations
b. Generating Functions
c. Method of Iteration
d. Permutations and Combinations
Report Writing (objectives 4, 5, 6, 7)
a. The Formal Technical Report
b. The Progress Report
c. The Problem Statement
Updated 2/2016
12/2012