MGF 1107 — Math for Liberal Arts — Syllabus
Prerequisites: C (2.0) or better in MAT 1033, or SAT Math score of 440 or better, or ACT Math score of 19 or better, or Elementary Algebra CPT score of 72 or better.
Course Description: This course meets twice a week for 75-minute lecture sessions and twice a week for 50-minute help sessions. The course is intended for students who do not need to take calculus as part of their major degree program. The course fulfills 3 semester hours of the Gordon Rule Computation requirement and also 3 hours of the General Education Quantitative Methods requirement, provided a grade of C-minus or better is achieved. There are typically four midterm exams plus an optional cumulative final exam.
Text: Excursions in Modern Mathematics, 6th Edition, by Tannenbaum
Course Content
Chapter 1: The Mathematics of Voting (2-3 hours of lecture)
1.1: Preference Ballots and Preference Voting
1.2: The Plurality Method
1.3: The Borda Count Method
1.4: The Plurality-with-Elimination Method
1.5: The Method of Pairwise Comparisons
1.6: Rankings (This section is omitted.)
Chapter 2: Weighted Voting Systems (2-3 hours of lecture)
2.1: Weighted Voting Systems
2.2: The Banzhaf Power Index
2.3: Applications of the Banzhaf Power Index
2.4: The Shapley-Shubik Power Index
2.5: Applications of the Shapley-Shubik Power Index
Chapter 3: Fair Division (6-7 hours of lecture)
3.1: Fair-Division Games
3.2: Two Players: The Divider-Chooser Method
3.3: The Lone-Divider Method
3.4: The Lone-Chooser Method
3.5: The Last-Diminisher Method (This section is omitted.)
3.6: The Method of Sealed Bids
3.7: The Method of Markers
Chapter 4: The Mathematics of Apportionment (3-4 hours of lecture)
4.1: The Apportionment Problem
4.2: The Mathematics of Apportionment: Basic Concepts
4.3: Hamilton's Method and the Quota Rule
4.4: The Alabama Paradox
4.5: The Population and New-States Paradoxes
4.6: Jefferson's Method
4.7: Adams's Method
4.8: Webster's Method
Chapter 5: Euler Circuits (2-3 hours of lecture)
5.1: Routing Problems
5.2: Graphs
5.3: Graph Concepts and Terminology
5.4: Graph Models
5.5: Euler's Theorems
5.6: Fleury's Algortithm
5.7: Eulerizing Graphs (This section is omitted.)
Chapter 6: The Traveling-Salesman Problem (3-4 hours of lecture)
6.1: Hamilton Circuits and Hamilton Paths
6.2: Complete Graphs
6.3: Traveling-Salesman Problems
6.4: Simple Strategies for Solving TSPs
6.5: The Brute-Force and Nearest-Neighbor Algorithms
6.6: Approximate Algorithms
6.7: The Repetitive Nearest-Neighbor Algorithm
6.8: The Cheapest-Link Algorithm
Chapter 7: The Mathematics of Networks (3-4 hours of lecture)
7.1: Trees
7.2: Minimum Spanning Trees
7.3: Kruskal's Algorithm
7.4: The Shortest Distance Between Three Points
7.5: The Shortest Network Linking More Than Three Points – Conclusion
Chapter 8: The Mathematics of Scheduling (3-4 hours of lecture)
8.1: The Basic Elements of Scheduling
8.2: Directed Graphs (Digraphs)
8.3: The Priority-List Model for Scheduling
8.4: The Decreasing-Time Algorithm
8.5: Critical Paths
8.6: The Critical-Path Algorithm
8.7: Scheduling with Independent Tasks
Chapter 9: Spiral Growth in Nature (2-3 hours of lecture)
9.1: Fibonacci Numbers
9.2: The Equation x2 = x + 1 and the Golden Ratio
9.3: Gnomons
9.4: Gnomonic Growth
Chapter 10: The Mathematics of Population Growth (3-4 hours of lecture)
10.1: The Dynamics of Population Growth
10.2: The Linear Growth Model
10.3: The Exponential Growth Model
10.4: The Logistic Growth Model
Chapter 11: Symmetry (3-4 hours of lecture)
This chapter is only covered if time permits.
11.1: Geometric Symmetry
11.2: Rigid Motions
11.3: Reflections
11.4: Rotations
11.5: Translations
11.6: Glide Reflections
11.7: Symmetry Revisited
11.8: Patterns
Chapter 12: Fractal Geometry
(This chapter is generally omitted due to time constraints.)
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