Course Description
MGF1107 – Mathematics for Liberal Arts II is a 3-credit lecture course designed as a second general-education mathematics course for non-STEM majors. The course surveys a different set of mathematical topics than its companion course MGF1106, with most institutions emphasizing the mathematics of finance, voting and apportionment theory, graph theory, number systems, elementary number theory, and (at some institutions) the history of mathematics. The goal is to develop quantitative reasoning skills and demonstrate the relevance of mathematics to real-world contexts including business, civics, and the social sciences.
MGF1107 is a terminal mathematics course for non-STEM majors. Like MGF1106, it does not serve as a prerequisite for Precalculus, Calculus, or any required mathematics course in business, computer science, engineering, the natural sciences, or mathematics. Students intending to major in any of those fields should take MAC1105 (College Algebra) instead.
The course sits within the Florida Statewide Course Numbering System (SCNS) under Mathematics > Mathematics: General and Finite and is offered at approximately 26 Florida public institutions. It satisfies the mathematics general education requirement under Florida State Board of Education Rule 6A-10.030 and counts as a Gordon Rule mathematics course. MGF1107 is commonly taken after MGF1106, but the two courses cover different topics and either can be taken first; some institutions also list MGF1107 as a stand-alone math elective for liberal-arts students.
Learning Outcomes
Required Outcomes
Upon successful completion of MGF1107, students will be able to:
- Apply the mathematics of finance: simple and compound interest, present and future value, annuities, sinking funds, amortization, and the financial decisions involved in personal loans, credit cards, mortgages, and retirement saving.
- Analyze voting methods and their fairness: plurality, plurality with elimination (instant runoff), Borda count, pairwise comparison, approval voting; criteria for fair voting (majority, Condorcet, monotonicity, independence of irrelevant alternatives); Arrow's impossibility theorem.
- Apply apportionment methods for distributing a fixed total among groups: Hamilton, Jefferson, Webster, Huntington-Hill methods; the Alabama, population, and new-state paradoxes; Balinski-Young impossibility theorem.
- Apply graph theory at an introductory level: graphs, paths, circuits, Euler paths and circuits, Hamilton paths and circuits, the traveling salesman problem, minimum-cost spanning trees, scheduling.
- Work with numeration systems: Hindu-Arabic place-value system; historical numeration systems (Egyptian, Babylonian, Roman, Mayan); positional systems in bases other than 10; conversion between bases.
- Apply elementary number theory: prime numbers and factorization, GCD and LCM, modular arithmetic and clock arithmetic.
- Communicate mathematical reasoning and solutions clearly using proper notation.
- Use quantitative reasoning to evaluate financial decisions, electoral processes, and apportionment outcomes encountered in everyday life and civic engagement.
Optional Outcomes
Depending on instructor and institutional emphasis, students may also:
- Investigate fair-division algorithms: discrete and continuous fair division, the divider-chooser method, the last-diminisher method, the method of sealed bids.
- Apply introductory game theory: two-person zero-sum games, dominant strategies, mixed strategies.
- Engage with population growth and decay models: linear, exponential, and logistic models applied to population, finance, and natural phenomena.
- Explore fractal geometry and self-similarity (some institutions cover this in MGF1107 instead of MGF1106).
- Investigate the history of mathematics: ancient Egyptian and Babylonian mathematics; Greek geometry; the development of algebra and the Hindu-Arabic numeral system; calculus.
- Complete a student project applying course concepts to a real-world problem.
Major Topics
Required Topics
- Mathematics of Finance: Percent and percent change; simple interest and the simple-interest formula; compound interest and the compound-interest formula; present value and future value; annuities and sinking funds; loan amortization; mortgages; credit-card finance; retirement investing.
- Voting Methods and Fairness: Preference ballots and preference schedules; plurality method; Borda count method; plurality-with-elimination (instant runoff); pairwise comparison method; approval voting; fairness criteria (majority criterion, Condorcet criterion, monotonicity, independence of irrelevant alternatives); Arrow's impossibility theorem.
- Weighted Voting and Apportionment: Weighted voting systems; the Banzhaf and Shapley-Shubik power indices; standard divisors and standard quotas; Hamilton's, Jefferson's, Webster's, and Huntington-Hill's apportionment methods; quota rule and apportionment paradoxes (Alabama, population, new-state); Balinski-Young theorem.
- Graph Theory and Networks: Graphs, vertices, edges, and degree; paths and circuits; Euler paths and Euler circuits; Hamilton paths and Hamilton circuits; the traveling salesman problem; nearest-neighbor and cheapest-link algorithms; minimum-cost spanning trees (Kruskal's algorithm); scheduling and digraphs.
- Numeration Systems: The Hindu-Arabic place-value system; historical numeration systems (Egyptian, Roman, Babylonian, Mayan); positional systems in other bases (base 2 binary, base 8 octal, base 16 hexadecimal); conversions between bases.
- Number Theory: Divisibility rules; primes and prime factorization; greatest common divisor and least common multiple; modular and clock arithmetic; modular arithmetic applications.
Optional Topics
- Fair Division: Discrete vs. continuous fair division; cake-cutting algorithms; the method of sealed bids; the Adjusted Winner method.
- Introductory Game Theory: Strategic decision-making; two-person zero-sum games; saddle points; mixed strategies.
- Population Growth and Mathematical Modeling: Arithmetic and geometric growth; exponential growth and decay; logistic growth; applications to ecology, finance, and disease.
- Fractal Geometry: Self-similarity; the Koch snowflake and Sierpinski triangle; the Mandelbrot set; fractal dimension.
- History of Mathematics: Selected episodes from the history of mathematical thought.
- Student Project: A capstone exercise applying course concepts to a real-world problem.
Resources & Tools
- Most-adopted textbooks at Florida institutions: A Survey of Mathematics with Applications by Angel, Abbott, and Runde (Pearson) — also used for MGF1106; Excursions in Modern Mathematics by Peter Tannenbaum (Pearson); Topics in Contemporary Mathematics by Bello, Britton, and Kaul (Cengage); Mathematical Ideas by Miller, Heeren, and Hornsby (Pearson).
- Open-access alternatives: Math in Society by David Lippman (free, OER) — covers many MGF1107 topics; OpenStax does not currently publish a liberal-arts mathematics text comparable to MGF1107.
- Online learning platforms: MyMathLab / MyLab Math (Pearson); WebAssign; Hawkes Learning; ALEKS; institution-specific platforms.
- Calculators: A scientific calculator is typically sufficient. Financial calculators (e.g., TI BA II Plus) may be useful but are not generally required.
- Tutoring and support: Institution math labs and tutoring centers (free, walk-in); Khan Academy modules on finance, graph theory, voting; Paul's Online Math Notes (free).
- Software for projects: Microsoft Excel or Google Sheets (for finance and voting calculations).
Special Information
Articulation and Transfer
MGF1107 articulates to all Florida SUS institutions and satisfies the mathematics general education requirement under Florida State Board of Education Rule 6A-10.030 ("Gordon Rule"). A grade of C or higher is required for the course to count toward the Gordon Rule. MGF1107 is commonly accepted as a second math course for AA degree purposes.
Important: Not for STEM Majors
MGF1107, like its companion MGF1106, is explicitly designed as a terminal mathematics course for liberal arts majors. It does not satisfy the mathematics requirement for STEM, business, or pre-health majors. Students considering any of those programs should take MAC1105 (College Algebra) as their math course (and MAC2233, MAC1140, or MAC1147 next, depending on their major's calculus requirement). If you are uncertain about your major, choose MAC1105 over MGF1107.
Credit-Overlap Rules
At most institutions, credit is awarded for only one of MGF1106 / MGF1107 / MGF1113 (or similar related courses) toward the general education math requirement — students should consult their institution's catalog for specific overlap rules. Many students take both MGF1106 and MGF1107 as their two math courses, but credit may be limited or constrained.
Prerequisites and Placement
The standard prerequisite is MAT1033 (Intermediate Algebra) with a minimum grade of C, MAC1105 (College Algebra) with a minimum grade of C, MGF1106 with a minimum grade of C, or appropriate placement test score. Placement requirements vary by institution.
Course Format and Workload
MGF1107 is typically a lecture course meeting three hours per week, with significant homework completed via online platforms. Expect 3–4 unit exams plus a comprehensive final, weekly homework, and (at some institutions) a student project applying mathematical concepts. The course is generally considered moderately demanding but accessible — most students find finance and voting topics intuitive once mastered.
Course Code Variations
Florida institutions title this course variously: "Mathematics for Liberal Arts II," "Survey of Mathematics," "Topics in Mathematics," "Liberal Arts Mathematics 2," and "Liberal Arts Math II" all refer to the same SCNS course. The core topical coverage (finance, voting/apportionment, graph theory, number systems) is consistent across institutions; the optional topics (fair division, game theory, growth models, fractals, history) vary widely.