Course Description
MGF1106 – Mathematics for Liberal Arts I is a 3-credit lecture course designed as a general education mathematics course for non-STEM majors. It surveys a broad set of mathematical topics chosen for their everyday relevance and intellectual reach, rather than for technical depth or as preparation for further mathematics. Topics typically include sets and Venn diagrams, mathematical logic, systematic counting, probability, statistics, and selected geometry topics.
MGF1106 is a terminal mathematics course for non-STEM majors. It does not serve as a prerequisite for Precalculus (MAC1140 or MAC1147), Calculus (MAC2233 or MAC2311), 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 29 Florida public institutions, including the University of Florida, Florida State University, Florida Atlantic University, Miami Dade College, Broward College, St. Petersburg College, and most Florida College System 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.
Learning Outcomes
Required Outcomes
Upon successful completion of MGF1106, students will be able to:
- Apply set theory concepts, including set notation, subsets, intersection, union, complement, and Venn diagrams to solve problems involving classification and counting.
- Apply mathematical logic, including statements, truth tables, logical connectives, conditionals (and their converse, inverse, and contrapositive), quantifiers, and the analysis of arguments for validity.
- Apply systematic counting principles — the multiplication principle, permutations, and combinations — to real-world counting problems.
- Compute and interpret basic probabilities, including theoretical and empirical probability, conditional probability, expected value, and applications to games of chance, insurance, and decision-making.
- Apply descriptive statistics, including the construction and interpretation of frequency distributions, measures of central tendency (mean, median, mode), measures of dispersion (range, variance, standard deviation), and the normal distribution.
- Distinguish among population, sample, parameter, and statistic, and recognize the principles of survey design, random sampling, and bias.
- Apply selected geometric concepts and formulas — area, perimeter, volume, and surface area — to practical problems.
- Communicate mathematical reasoning and solutions clearly in written form using proper mathematical notation.
- Use quantitative reasoning to evaluate claims, advertisements, and statistics encountered in everyday life.
Optional Outcomes
Depending on instructor and institutional emphasis, students may also:
- Apply voting theory and the mathematics of social choice: voting methods, fairness criteria, weighted voting, the mathematics of apportionment.
- Explore graph theory and networks: Euler and Hamilton circuits, the traveling salesman problem, scheduling.
- Engage with fractal geometry, self-similarity, and the Mandelbrot set.
- Apply consumer mathematics: simple and compound interest, annuities, mortgages, credit cards.
- Investigate number systems and number theory: numeration systems across cultures, modular arithmetic, prime numbers.
- Apply fair division and game theory at an introductory level.
- Use computer-based tools (Excel, MyMathLab, ALEKS, Hawkes Learning) for computation and visualization.
Major Topics
Required Topics
- Sets: Set notation and terminology; subsets and proper subsets; intersection, union, and complement; cardinality of sets; Venn diagrams; the cardinal number formula; problem solving with sets.
- Mathematical Logic: Statements and quantifiers; logical connectives (negation, conjunction, disjunction, conditional, biconditional); truth tables; equivalent statements; converse, inverse, and contrapositive; symbolic arguments; Euler diagrams for syllogisms.
- Systematic Counting: The fundamental counting principle; permutations and combinations; arrangements with restrictions.
- Probability: Sample space and events; theoretical and empirical probability; probability of compound events; conditional probability; expected value; the binomial distribution at an introductory level.
- Statistics: Population vs. sample; sampling methods; descriptive vs. inferential statistics; frequency distributions; measures of central tendency; measures of dispersion; the normal distribution and z-scores.
- Geometry (Selected): Polygons; perimeter, area, and volume formulas; the Pythagorean theorem; similar and congruent figures.
Optional Topics
- The Mathematics of Social Choice: Voting methods (plurality, Borda count, instant-runoff, approval voting); Arrow's theorem; weighted voting systems; apportionment methods (Hamilton, Jefferson, Webster, Huntington-Hill).
- Graph Theory and Networks: Graphs and digraphs; Euler paths and circuits; Hamilton circuits and the traveling salesman problem; minimum-cost spanning trees; scheduling.
- Geometry of Symmetry and Fractals: Symmetry types; the Mandelbrot set and Julia sets; fractal dimension.
- Consumer Mathematics: Simple interest, compound interest, annuities, amortization, mortgages, credit-card finance.
- Number Systems: Hindu-Arabic, Roman, Babylonian, and Mayan numeration; bases other than 10; modular arithmetic.
- Fair Division and Game Theory: Cake-cutting algorithms, the Adjusted Winner method, simple two-person games.
Resources & Tools
- Most-adopted textbooks at Florida institutions: A Survey of Mathematics with Applications by Angel, Abbott, and Runde (Pearson) — widely used at SPC, FSCJ, MDC, and others; Excursions in Modern Mathematics by Peter Tannenbaum (Pearson) — used at UF; Mathematics: Its Power and Utility by Karl Smith; Mathematical Ideas by Miller, Heeren, and Hornsby.
- Open-access alternatives: Hacking Mathematics (FSU's free web-based text); OpenStax-aligned course packs increasingly common as zero-textbook-cost options at Florida community colleges.
- Online learning platforms: MyMathLab / MyLab Math (Pearson); WebAssign; Hawkes Learning; ALEKS; institution-specific platforms.
- Calculators: A scientific calculator is typically sufficient. Some institutions allow graphing calculators on certain assessments. Students should check with their instructor.
- Tutoring and support: Institution math labs and tutoring centers (free, walk-in); Khan Academy modules on probability, statistics, logic, and sets (free); Paul's Online Math Notes (free).
- Software for projects: Microsoft Excel or Google Sheets (for statistical exercises and consumer math).
Special Information
Articulation and Transfer
MGF1106 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.
Important: Not for STEM Majors
MGF1106 is explicitly designed as a terminal mathematics course for liberal arts majors. It does not satisfy the mathematics requirement for any of the following majors:
- Engineering (any field)
- Computer Science or Computer Engineering
- Mathematics, Physics, Chemistry, Biology, or other natural sciences
- Business administration, accounting, finance, or economics
- Pre-medical, pre-dental, pre-pharmacy, pre-physical-therapy programs (which require chemistry-and-biology-track gen-ed math)
- Most pre-health professions in general
- Architecture, surveying
Students considering any of those programs should take MAC1105 (College Algebra) instead, which serves both as a Gordon Rule math course and as a prerequisite for further STEM-track mathematics. If you are uncertain about your major, choose MAC1105 over MGF1106 — switching from MGF1106 to MAC1105 typically requires a complete re-take.
Credit-Overlap Rules
MGF1106 has overlapping credit with MGF1107 (Mathematics for Liberal Arts II) at some institutions, and overlap rules apply with related courses such as MGF1113 and MGF1119 — credit is awarded for only one of MGF1106 / MGF1113 / MGF1119 at most institutions. Students who have already completed MGF1106 with a C or better cannot retake it for credit.
Prerequisites and Placement
The standard prerequisite is appropriate score on the institution's mathematics placement test, completion of any required developmental mathematics coursework (typically MAT1033 or MAT0028C), or completion of MAC1105 with a minimum grade of C. Placement requirements vary by institution; check your specific institution's catalog.
Course Format and Workload
MGF1106 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 possibly quizzes or projects. The course is generally considered moderate in difficulty — students who struggled with high-school algebra often find MGF1106 more accessible than MAC1105 because the topics are conceptually independent and don't build cumulatively in the same way as the algebra-precalculus-calculus track.
Course Code Variations
Florida institutions title this course variously: "Mathematics for Liberal Arts I," "Math for Liberal Arts," "Foundations of Mathematical Reasoning," "Liberal Arts Mathematics 1," and "Math to Stats Pathway" all refer to the same SCNS course. The core topical coverage (sets, logic, counting, probability, statistics) is consistent across institutions; the optional topics (voting theory, graph theory, fractals, consumer math) vary considerably.