Math 4051 Course Outline

Math 4051: Computer Exploration and Generation of Data

Course Description

Prerequisite:

MATH 2120 or MATH 2241, and STAT 2122 or STAT 2223.

This course includes an introduction to a major spreadsheet, such as Excel. Assigned projects may be selected from a range of topics that include: Data
Analysis and Exploration; Dynamical Models and Difference Equations (Epidemics, Harvesting Models, Population Dynamics,
Predator-Prey Models); Physical Models (projectile motion, including air resistance, orbits of celestial bodies, heat propagation);
Combinatorics and Probability (birthday problem, genetics, simulation of distributions); Optimization (inventory control,
apportionment algorithms); Financial Mathematics (Stock Price Simulation, Pricing of Derivatives); Business Simulations (Net
Present Value Comparisons and Risk Evaluation, Sensitivity Analyses).

Required Text:

Mathematical Modeling with Excel, by Brian Albright, Jones and Bartlett (ISBN-13: 978-0-7637-6566-8). We will
begin using this text around week 5 through the end of the semester. Other lecture materials are provided via the course Canvas page.

Day Topic
1 Syllabus; What is Mathematical Modeling Assignment
2 Introduction to Excel – Approximating Areas
3 Extension of Approximation Techniques
4 Extension of Approximation Techniques (Continued)
5 Extension of Approximation Techniques (Continued)
6 Pivot Tables
7 Pivot Tables and Large Data Sets
8 Statistics Review – z and t Tests
9 Factor Analysis – ANOVA
10 Factor Analysis – More Tools (Including Fisher’s LSD)
11 Working Class for Project 1 – Individual Project
12 Working Class for Project 1 – Individual Project
13 Intro to Mathematical Modeling with Excel Text; Scroll Bars
14

Ch4 – Discrete Dynamical Systems

4.1 – Introduction
4.2 – Long Term Behavior
15 Ch4 – Discrete Dynamical Systems
4.3 –Growth of Bacteria Population; Equilibrium Values
16 Ch4 – Discrete Dynamical Systems
4.4 – Linear Predator-Prey Model
4.6 – Epidemics
17 Working Class for Project 2 – Group Project
18 Working Class for Project 2 – Group Project
19 Ch5 – Differential Equations
5.1 – Introduction; Newton’s Law of Cooling
20 Ch5 – Differential Equations
5.2 – Euler’s Method
21 Ch5 – Differential Equations
5.3 – Quadratic Population Model; Equilibrium Values
22 Ch5 – Differential Equations
5.5 – Lanchester Combat Models
23 Working Class for Project 3 – Group Project
24 Working Class for Project 3 – Group Project
25 Ch6 – Simulation Modeling
6.1 – Introduction
6.2 – Monte Carlo Simulations
26 Ch6 – Simulation Modeling
6.3 – Additional Simulation Examples
27 Working Class for Project 4 – Individual Project
28 Concluding thoughts about Math 4051; Final Exam Expectations Revisited
FINAL EXAM