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Mathematics & Statistics

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. 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.

[textbook]

Text: Excursions in Modern Mathematics, 9th Edition, by Tannenbaum

Course Content

1 The Mathematics of Elections (2-3 weeks)
1.1 The Basic Elements of an Election
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 Fairness Criteria and Arrow’s Impossibility Theorem

2 The Mathematics of Power (omit)
2.1 An Introduction to Weighted Voting
2.2 Banzhaf Power
2.3 Shapley-Shubik Power
2.4 Subsets and Permutations

3 The Mathematics of Sharing (omit)
3.1 Fair-Division Games
3.2 The Divider-Chooser Method
3.3 The Lone-Divider Method
3.4 The Lone-Chooser Method
3.5 The Method of Sealed Bids
3.6 The Method of Markers

4 The Mathematics of Apportionment (2-3 weeks)
4.1 Apportionment Problems and Apportionment Methods
4.2 Hamilton's Method
4.3 Jefferson's Method
4.4 Adams's and Webster's Methods
4.5 The Huntington-Hill Method
4.6 The Quota Rule and Apportionment Paradoxes

5 The Mathematics of Getting Around (omit)

6 The Mathematics of Touring (omit)

7 The Mathematics of Networks (omit)

8 The Mathematics of Scheduling (omit)

9 Population Growth Models (omit)
9.1 Sequences and Population Sequences
9.2 The Linear Growth Model
9.3 The Exponential Growth Model
9.4 The Logistic Growth Model

10 Financial Mathematics (2-3 weeks)
10.1 Percentages
10.2 Simple Interest
10.3 Compound Interest
10.4 Retirement Savings
10.5 Consumer Debt

11 The Mathematics of Symmetry (omit)

12 Fractal Geometry (omit)

13 Fibonacci Numbers and the Golden Ratio (If time allows.)
13.1 Fibonacci Numbers
13.2 The Golden Ratio
13.3 Gnomons
13.4 Spiral Growth in Nature

14 Censuses, Surveys, Polls, and Studies (2 weeks)
14.1 Enumeration
14.2 Measurement
14.3 Cause and Effect

15 Graphs, Charts, and Numbers (1-2 weeks)
15.1 Graphs and Charts
15.2 Means, Medians, and Percentiles
15.3 Ranges and Standard Deviations

16 Probabilities, Odds, and Expectations (omit)

17 The Mathematics of Normality (omit)

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