Expected Outcomes for the Students

Chabot College Fall 2005

Course Outline for Mathematics 40 CONCEPTS OF MATHEMATICS

Catalog Description:

40 – Concepts of Mathematics 3 units

Investigation of the nature of mathematics as a human endeavor and an examination of important concepts of mathematics. Prerequisite: Mathematics 54, 54L, 55, or 55B (completed with a grade of C or higher) or an appropriate skill level demonstrated through the Mathematics Assessment process. 3 hours

Prerequisite Skills:

Before entering the course the student should be able to:

1. solve systems of linear equations and interpret the solutions; 2. graph polynomial, rational, exponential, and logarithmic functions; 3. solve exponential equations; 4. find inverse functions and apply their properties; 5. perform function composition; 6. solve quadratic equations; 7. apply the properties and perform operations with radicals; 8. apply the properties and perform operations with rational exponents; 9. apply the properties and perform operations with logarithms; 10. apply the concepts of exponential functions.

Expected Outcomes for the Students:

Upon completion of the course the student should be able to:

1. apply principles from algebra and elementary number theory to current technology, such as those used in encryption techniques; 2. identify the similarities and differences between Euclidean and non-Euclidean geometries; 3. explore and find certain relationships between geometry and topology; 4. build Platonic solids and describe their properties; 5. determine the cardinality of the set of Platonic solids; 6. apply problem-solving techniques learned in one area to another; 7. measure uncertainty using the principles of probability; 8. systematically count all possible outcomes using permutations and combinations; 9. identify misleading statistics.

Course Content:

1. Geometry a. Non Euclidean b. Three dimensional Euclidean geometry (Platonic solids) 2. Modern Algebra 3. Number theory 4. Probability and Statistics 5. At least two of the following additional topics must be explored (no more than 40% of the course): a. Real and complex numbers b. Dynamical systems c. Topology d. Mathematical systems (groups, rings, and fields) Chabot College Course Outline for Math 40, page 2 Fall 2005

Course Content – continued:

e. Boolean algebra f. Applied mathematics (in biology, physics, business, or other) g. Logic

Methods of Presentation:

1. Lectures/discussions 2. Small and large group work 3. Student presentations 4. Audio-visual presentations 5. Resources available on CD’s or on the Internet

Assignments and Methods of Evaluating Student Progress:

1 1. Typical Assignments a. Journal participation In your journal, construct a Golden Rectangle (using the method we went over in class and as directed in your book on pages 40, 241). Now make a separate paper copy of a Golden Rectangle that is at least 6 inches on its shorter side. In that large Golden Rectangle, find the largest square and move it (cut it off). Measure the dimensions of the remaining rectangle. Record these numbers. In that same remaining rectangle, find the larges square inside and cut that square off. Measure the dimensions of what is left (it should be a rectangle and it should look familiar!) Record these numbers in your journal and state what relationship they have, relevant to the Golden Rectangle. b. Homework problems from the textbook Suppose we start with one pair of baby rabbits, and again they create a new pair every month, but this time let’s suppose that it takes two months before a pair of bunnies is mature enough to reproduce. Make a table for the first 10 months, indicating how many pairs there would be at the end of each month. Do you see a pattern? Describe a general formula for generating the sequence of rabbit-pair counts.

2. Methods of Evaluating Student Progress 2 a. Quizzes b. Student project presentations 3 c. Midterms d. Final examination

Textbook(s) (Typical):

The Heart of Mathematics, Edward B. Burger and Michael Starbird, Key Curriculum Press, 2005

Special Student Matherials:

Toolkit of manipulatives (included with texts such as The Heart of Mathematics) Student journal

Wendy Alexander revised: 09/22/00 CSS revised 09-06-01 AW revised 10-05-04