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.

Foundations of Knowledge & Learning: This course is part of the University of South Florida’s Foundations of Knowledge and Learning (FKL) Core Curriculum. It is certified for Mathematics and Quantitative Reasoning and will meet the following four dimensions: Critical Thinking, Inquiry-based Learning, Scientific Processes, and Quantitative Literacy. Students enrolled in this course will be expected to participate in the USF General Education assessment effort. This might involve answering questions that measure quantitative reasoning skills (but are not directly related to the course), responding to surveys, or participating in other measurements designed to assess the FKL Core Curriculum learning outcomes.

Text: Excursions in Modern Mathematics, 7th Edition, by Tannenbaum

Course Content

Chapter 1. The Mathematics of Voting: The Paradox of Democracy (2-3 hours of lecture)

1.1: Preference Ballots and Preference Schedules
1.2: The Plurality Method
1.3: The Borda Count Method
1.4: The Plurality-with-Elimination Method (Instant Runoff Voting)
1.5: The Method of Pairwise Comparisons
1.6: Rankings (This section is omitted.)

Chapter 2. The Mathematics of Power: Weighted Voting (2-3 hours of lecture)

2.1: An Introduction to Weighted Voting
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. The Mathematics of Sharing: Fair Division Games (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: Making the Rounds (3-4 hours of lecture)

4.1: Apportionment Problems
4.2: Hamilton's Method and the Quota Rule
4.3: The Alabama and Other Paradoxes
4.4: Jefferson's Method
4.5: Adams's Method
4.6: Webster's Method

Chapter 5. The Mathematics of Getting Around: Euler Paths and Circuits (2-3 hours of lecture)

5.1: Euler Circuit Problems
5.2: What is a Graph?
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 Mathematics of Touring: 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: The Cost of Being Connected (3-4 hours of lecture)

7.1: Trees
7.2: Spanning Trees
7.3: Kruskal's Algorithm
7.4: The Shortest Network Connecting Three Points
7.5: Shortest Networks for Four or More Points

Chapter 8. The Mathematics of Scheduling: Chasing the Critical Path (3-4 hours of lecture)

8.1: The Basic Elements of Scheduling
8.2: Directed Graphs (Digraphs)
8.3: Scheduling with Priority Lists
8.4: The Decreasing-Time Algorithm
8.5: Critical Paths
8.6: The Critical-Path Algorithm
8.7: Scheduling with Independent Tasks

Chapter 9. The Mathematics of Spiral Growth: Fibonacci Numbers and the Golden Ratio (2-3 hours of lecture)

9.1: Fibonacci's Rabits
9.2: Fibonacci Numbers
9.3: The Golden Ratio
9.4: Gnomons
9.5: Spiral Growth in Nature

Chapter 10. The Mathematics of Money: Spending it, Saving It, and Growing It (3-4 hours of lecture)

10.1: Percentages
10.2: Simple Interest
10.3: Compound Interest
10.4: Geometric Sequences
10.5: Deferred Annuities: Planned Savings for the Future
10.6: Installment Loans: The Cost of Financing the Present

Chapter 11. The Mathematics of Symmetry: Beyond Reflection (3-4 hours of lecture)

This chapter is only covered if time permits.
11.1: Rigid Motions
11.2: Reflections
11.3: Rotations
11.4: Translations
11.5: Glide Reflections
11.6: Symmetry as a Rigid Motion
11.7: Patterns

Chapter 12. The Geometry of Fractal Shapes: Naturally Irregular (This chapter is generally omitted due to time constraints.)

Miscellaneous University/College Policies:

You are encouraged to take notes and may tape the lectures, but neither your notes nor your tapes are to be sold.
All unauthorized recordings of class are prohibited. Recordings that accommodate individual student needs must be approved in advance and may be used for personal use during this semester only; redistribution is prohibited.
Students in need of academic accommodations for a disability may consult with the Office of Students with Disabilities Services (SDS) in SVC 1133 to arrange appropriate accommodations. Students are required to give reasonable notice (typically 5 working days) prior to requesting an accommodation.
Students who anticipate the necessity of being absent due to the observation of a major religious holiday must provide notice of the date in writing to the instructor by the second class meeting.
Contingency Course Plan: In the event of an emergency, it may be necessary for USF to suspend normal operations. During this time, USF may opt to continue delivery of instruction through methods that include but are not limited to: Blackboard, Elluminate, Skype, and e-mail messaging and/or alternate scheduling. It is the responsibility of the student to monitor the main USF website, e-mails and MoBull messages for important information about the closure. For information about the continuation of instruction, students are directed to their individual blackboard course sites.
S-U Policy: Students who want to take this course for a grade of S-U (Satisfactory-Unsatisfactory) must sign the S-U Contract no later than the end of the third week of classes. There will be no exceptions. For further information on S-U grades, please consult the undergraduate catalog. Note: Gordon Rule Math courses cannot be taken for an S-U grade.
“I” Grade Policy: A grade of “I” indicates incomplete work and will only be assigned when most of the coursework has already been completed with a passing grade. For further information on “I” grades, please consult the undergraduate catalog.

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