MATH A100: Liberal Arts Mathematics
| Item | Value |
|---|---|
| Curriculum Committee Approval Date | 03/20/2024 |
| Top Code | 170100 - Mathematics, General |
| Units | 3 Total Units |
| Hours | 54 Total Hours (Lecture Hours 54) |
| Total Outside of Class Hours | 0 |
| Course Credit Status | Credit: Degree Applicable (D) |
| Material Fee | No |
| Basic Skills | Not Basic Skills (N) |
| Repeatable | No |
| Grading Policy | Standard Letter (S),
|
| Associate Arts Local General Education (GE) |
|
| Associate Science Local General Education (GE) |
|
| California General Education Transfer Curriculum (Cal-GETC) |
|
| Intersegmental General Education Transfer Curriculum (IGETC) |
|
| California State University General Education Breadth (CSU GE-Breadth) |
|
Course Description
This is a survey course designed for non-science majors. Topics include mathematics of finance, probability, statistics, set theory, voting methods, and other selected topics such as logic, geometry, and graph theory. PREREQUISITE: MATH A030 or higher or appropriate placement. Transfer Credit: CSU; UC.
Course Level Student Learning Outcome(s)
- Determine the winner of an election using the Plurality Method, Borda Count Method, Plurality-with-Elimination Method, or Pairwise Comparison Method.
- Use Venn diagrams to represent sets and draw conclusion about the represented sets.
- Calculate the principal, future value, or interest earned on a simple or compound interest investment.
- Organize statistical data in a meaningful way to draw appropriate conclusions.
- Calculate the probability of a simple or compound event.
Course Objectives
- 1. Apply set theory concepts to problem solving.
- 2. Use mathematical formulas to solve problems in practical applications such as borrowing money and saving money.
- 3. Apply statistical methods to analyze data.
- 4. Construct a tree diagram to represent a sample space and determine the corresponding probabilities.
- 5. Use an apportionment model to verify current apportionment numbers in the House of Representatives.
Lecture Content
Each of these topics is presented with a view toward its mathematical structure and the application of that structure to the solution of contemporary realistic problems from a wide variety of disciplines. Set Theory Definitions including subset, proper subset, and cardinality Set operations including union, intersection, difference, and complement DeMorgans Laws Venn diagrams and their applications Consumer Math/Mathematics of Finance Percents Simple interest Compound interest Installment buying Student loans Home buying including amortization Investing in stock and bonds (optional) Statistics Organizing and picturing data including frequency distributions, stem-and-leaf plots, bar graphs, and histograms Measures of average: mean, median, and mode Measures of variation: range, standard deviation, and variance Measures of position: percentiles, quartiles, boxplots, and outliers The Normal Distribution including The Empirical Rule (68-95-99.7 Rule) Probability and Counting Techniques Basic concepts of probability including events, sample spaces, "and" probabilities, "or" probabilities The Fundamental Counting Principle Permutations Combinations Determining sample spaces by using tree diagrams and tables Probability invovling permutations and combinations (optional) Odds and expected value (optional) Conditional probabilities (optional) Voting Methods Preference Tables Pluraity Method The Borda Count Method Plurality-with-Elimination Method The Pairwvise Comparision Method Approval Voting Apportionment Introduction to standard divisors and quotas Apportionment models Hamiltons Method Jeffersons Method Adams Method Websters Method Huntington-Hill Method Instructor must choose at lease one of the following three topics (i.e., Logic, Graph Theory, Geometry), and, time permitting, may choose to teach more than one topic: Logic Statements Simple Negation Compound: conjuntion, disjunction, coditional (including converse, inverse, and contrapositive), biconditional Symbolic form and notation Analysis of valid and invalid arguments, which may include: Determining validity of arguments (e.g., using truth tables) Drawing a valid conclusion from a given set of premises Classic syllogisms and fallacies (e.g., Transitive Reasoning/Law of Syllogism, Affirming the Conclusion/Fallacy of the Converse) Graph Theory Definitions including graph, vertices, edges, equivalent graphs, degree, loop, bridge, path, and circuit Eulers paths and Euler circuits Eulers Theorem and Fleurys Algorithm Hamilton paths and circuits Traveling Salesperson problem Brute Force Method Nearest Neighbor Method Cheapest Link Algorithm Geometry Angles and lines Polygons Circles Three-dimensional figures Geometric measurements (e.g., permiter, area, surface area, volume, length of the sides of a right triangle using the Pythagorean Theorem) If time permits, instructor may elect to cover any of the topics in areas II and IV identified as optional. Instructor m ay also elect to cover any topics selected from areas of student interest or instructor expertise that are not listed here.
Method(s) of Instruction
- Lecture (02)
- DE Live Online Lecture (02S)
Instructional Techniques
Although the primary instructional mode is the lecture/demonstration method emphasizing approaches to problem solving, significant class time is reserved for student questions and class discussion. Lectures are enhanced by video, film, audio, and slide presentations.
Reading Assignments
Students will spend approximately 1-2 hours per week on readings as assigned from textbook selection
Writing Assignments
Writing is required on homework assignments and quizzes (hours included in out-of-class calculation)
Out-of-class Assignments
Writing is required on homework assignments and quizzes; however, the applications nature of the course requires proficiency demonstration of problem-solving skills. (Approximately 4-5 hours per week)
Demonstration of Critical Thinking
Grades are determined by student performance on unit tests which evaluate problem-solving techniques and understanding of appropriate specialized vocabulary; a comprehensive final exam whose structure is similar to that of the unit test; written homework assignments involving problem solving, diagram sketching, and written explanation and/or analysis; and quizzes on which detailed work is demonstrated.
Required Writing, Problem Solving, Skills Demonstration
Writing is required on homework assignments and quizzes
Textbooks Resources
1. Required Sobecki, D.. Math in Our World, 5th ed. New York, NY: MacGraw-Hill Education, 2023 Rationale: -
Other Resources
1. Other appropriate textbooks as chosen by faculty.