MAT-101 Mathematics for Liberal Arts
This course is intended for the liberal arts student. The purpose of this course is to share the excitement and enjoyment of contemporary mathematical thinking. The course answers the question, "What do mathematicians do, practice, or believe in?" The use of mathematics in areas of business and industry, politics, networking and telecommunication will be studied with the intent to develop reasoning ability, logical thinking, critical reading, and written and oral communication. The topics are selected so that they are self-contained. This course carries SUNY General Education Mathematics (and Quantitative Reasoning) credit.
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Course Outline
Course Description
This course is intended for the liberal arts student. The purpose of this course is to share the excitement and enjoyment of contemporary mathematical thinking. The course answers the question, "What do mathematicians do, practice, or believe in?" The use of mathematics in areas of business and industry, politics, networking and telecommunication will be studied with the intent to develop reasoning ability, logical thinking, critical reading, and written and oral communication. The topics are selected so that they are self-contained. This course carries SUNY General Education Mathematics (and Quantitative Reasoning) credit.
Credit Hours
3Semester(s) Course Will Be Offered
Fall, Spring, Summer
SUNY General Education Course
- Mathematics and Quantitative Reasoning
Course Learning Outcomes
- Understand and execute algorithms to navigate through and solve problems.
- Via the topics studied throughout the course, make connections between the historical context and applications to current society.
- Describe and use the process of abstraction to model real world problems.
- Evaluate obtained results for reasonableness.
Topic Outline
- The following three topics are mandatory for this course:
- 1. Voting theory and weighted voting
- a. Preference schedules
- b. Fairness conditions and Arrow's impossibility theorem
- c. Voting methods: plurality, instant runoff, Borda count, and Copeland's
- d. Weighted voting systems
- e. Banzhaf and Shapley-Shubik power indices
- 2. Graph theory
- a. Graphs, vertices, and edges
- b. Shortest path and Dijkstra's algorithm
- c. Euler circuits and Eulerization
- d. Hamilton paths and circuits
- e. Weighted graphs and the traveling salesperson problem
- f. Spanning trees
- 3. Modular arithmetic with applications to cryptography
- a. Substitution ciphers and the Caesar cipher
- b. Modular arithmetic and modular formulas for the Caesar cipher
- c. Transposition ciphers and modular formulas for them
- d. Public-key encryption and RSA
- Each section of this class must cover at least two topics selected from the following list. Selection may be made based on instructor preferences or student interest. More than two of these topics may be covered if time permits.
- 4. Scheduling
- a. Digraphs
- b. Priority lists and list processing algorithms
- c. Critical path algorithms
- 5. Apportionment and fair division
- a. Apportionment criteria and issues
- b. Apportionment methods: Hamilton's, Jefferson's, Webster's, Huntington-Hill, and Lowndes'
- c. Fair division methods: divider-chooser, lone divider, last diminisher, and sealed bids
- 6. Set theory
- a. Set terminology (set, elements, and subsets)
- b. Set operations (union, intersection, and complement)
- c. Set cardinalities
- d. Venn diagram representations of sets
- 7. Counting systems
- a. Roman numerals
- b. Incan quipu
- c. Mayan numerals
- d. Hindu-Arabic (place value) number system
- e. Place value systems in alternative bases
- 8. Fractals
- a. Self-similarity and iterated fractals
- b. Fractal dimension
- c. Complex numbers and the complex plane
- d. The Mandelbrot set
- 9. Symbolic logic
- a. Boolean logic and operations (conjunction, disjunction, negation, and conditionals)
- b. Truth tables
- c. Quantifiers and predicates
- d. Arguments and fallacies
- 10. Game theory
- a. Modeling using games and game matrices
- b. Symmetric and asymmetric information
- c. Alternate-move and simultaneous-move games
- d. Zero-sum and non-zero-sum games
- e. Nash equilibria
- f. The prisoner's dilemma