Yuba Community College District

Yuba College Course Outline

### Course Information

Course Number: MATH 10
Full Course Title: Liberal Arts Mathematics
Short Title: Liberal Arts Math
TOP Code: 1701.00 - Mathematics, General
Effective Term: Fall 2012

### Course Standards

Course Type: Credit - Degree Applicable
Units: 3.0
Total class hours: 162.0
Total contact hours in class: 54.0
Lecture hours: 54.0
Hours outside of class: 108.0
Repeatable: No

### Course Description

Designed for students majoring in areas other than science, math, or business to give appreciation and insight into structure and applications of math. Some typical topics, to be chosen by instructor, may include probability and statistics, sequences and series, population growth, graph theory, geometry and topology, number theory, history of math, finance math, voting methods and apportionment. (L,M)

### Conditions of Enrollment

Satisfactory completion of: MATH 52 or (Placement Exam Score)a satisfactory score on the mathematics placement test. -

• Language - recommended eligibility for English 1A
• Mathematics - recommended eligibility for Math 52

### Content

Course Lecture Content

At least four topics (preferably at least five) to be chosen by the instructor. Topics to be chosen from the following list:

1. Probability and statistics.
2. Sequences and series.
3. Population models
4. Finance math
5. Game theory
6. Linear programming
7. Inductive and deductive reasoning, problem-solving strategies, methods of proof.
8. Logic
9. Set theory
10. Graph theory
11. Euclidean plane and solid geometry. The Platonic solids. Euler's characteristic.
12. Non-Euclidean geometry.
13. Iteration functions and fractal geometry.
14. Topology.
15. Voting and apportionment. Fair division
16. History of mathematics
17. Numeration and mathematical systems
18. Number theory
19. Transformational Geometry
20. Growth and form; symmetry and patterns, tilings

### Objectives

1. Demonstrate a good understanding of the topics chosen for the course. For example:

2. Find probabilities and odds; compute mean, median, mode, standard deviation. **Requires Critical Thinking**

3. Find formulas for sequences; make sound conclusions about series.

4. Model populations

5. Amortize loans; compute compound interest; find present values. **Requires Critical Thinking**

6. Find a winning strategy.

7. Use linear programming for optimization problems.

8. Find patterns, reason deductively, formulate proofs. **Requires Critical Thinking**

9. Use truth tables. **Requires Critical Thinking**

10. Find set unions, intersections, complements, use Venn diagrams; count using one-one correspondences.

11. Identify Euler and Hamiltonian circuits. **Requires Critical Thinking**

12. Use straightedge and compasses (constructive geometry); prove geometric theorems (demonstrative geometry); name the Platonic solids. **Requires Critical Thinking**

13. Iterate functions

14. Create Mobius strip and Mobius strip derivative (by cutting).

15. Tally votes and rank; perform fair division.

16. Demonstrate a general knowledge of the history of mathematics

17. Perform calculations using clock arithmetic or modular system.

18. Represent quantities using different numerical systems.

19. Recognize Fibonacci sequence and golden ratio in patterns

### Student Learning Outcomes

1. Critical Thinking –Demonstrate an understanding of a variety of mathematical ideas and systems.

### Methods of Instruction

• Lecture/Discussion
• Other
Group work is recommended.

### Assignments

Writing Assignments
Other Assignments

May include journal, term paper, homework

### Methods of Evaluation

• Homework
• Oral Tests/Class Performance
• Quizzes
• Research Project

### Course Materials

Textbooks:
1. P. Tannenbaum. Excursions in Modern Mathematics, 7th ed. Pearson, 2010, ISBN: 978-0-321-56803-8
Other:
1. Instructor dependent. May include a graphing calculator, straightedge and compasses, paper construction materials.