Chabot College
Fall 2002
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 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:
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perform basic operations on complex numbers;
solve quadratic equations by factoring, completing the square, and quadratic formula;
find complex roots of a quadratic equation;
sketch the graphs of functions and relations:
a. algebraic, including polynomial and rational
b. logarithmic
c. exponential
d. circles;
find and sketch inverse functions;
perform function composition;
solve exponential and logarithmic equations;
apply the concepts of logarithmic and exponential functions;
solve systems of linear equations in three unknowns using elimination and substitution;
apply the properties of and perform operations with radicals;
apply the properties of and perform operations with rational exponents;
solve equations and inequalities involving absolute values;
solve equations involving radicals;
graph linear inequalities in two variables;
find the distance between two points;
find the midpoint of a line segment.
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. demonstrate a familiarity with the Platonic solids;
5. demonstrate the ability to apply problem-solving techniques learned in one area to another;
6. measure uncertainty using the principles of probability;
7. systematically count all possible outcomes using permutations and combinations;
8. identify misleading statistics.
Chabot College
Course Outline for Mathematics 40, Page 2
Fall Semester 2002
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)
e. Boolean algebra
f. Applied mathematics (in biology, physics, business, or other)
g. Logic
Methods of Presentation:
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Lectures/discussions
Small and large group work
Student presentations
Audio-visual presentations
Resources available on CD’s or on the Internet
Asssignments and Methods of Evaluating Student Progress:
1. Typical Assignments
a. Journal participation
b. Homework
2. Methods of Evaluating Student Progress
a. Quizzes
b. Student project presentations
c. Midterms
d. Final examination
Textbook(s) (Typical):
The Heart of Mathematics, Edward B. Burger and Michael Starbird, Key Curriculum
Press, 2000
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