I. Course Description:
This course presents the basics of college algebra. The
material includes solving polynomial expressions , inequalities, exponential and
logarithmic functions , and radicals.
II. Purpose of the Course:
The course concentrates on the mechanics of algebra and
serves as an introduction to elementary functions and coordinate geometry. The
presentation of each topic will include problem solving skills involving
applications from other disciplines.
III. College Learning Outcomes and Objectives:
This course is de signed to help students fulfill the
Quantitative Competence and Critical Thinking Ability Learning Outcomes through
achievement of the fol lowing objectives :
(9a) Students can formulate specific questions from
vague problems, select effective problem-solving strategies, and know which
mathematical operations are appropriate in particular contexts.
(9b) Students can perform mental calculations and estimates with
proficiency, and decide when an exact answer is needed and when an estimate is
more appropriate.
(9c) Students can use a calculator correctly, confidently, and
appropriately and/or use computer software for mathematical tasks.
(9d) Students can use tables, graphs, spreadsheets and statistical
techniques to organize, interpret and present numerical information.
(9e) Students can judge the validity of quantitative results presented by
others.
IV. Course Objectives:
1. Students should be able to solve linear equations
and inequalities. (LO 9a-e)
2. Students should be able to solve quadratic equations over the field of
complex numbers . (LO 9a-e)
3. Students should be able to manipulate and solve equations involving
polynomial expressions. (LO 9a-e)
4. Students should be able to manipulate and solve equations involving
rational expressions. (LO 9a-e)
5. Students should be able to manipulate expressions involving radicals
and exponents. (LO 9a-e)
6. Students should be able to solve systems of linear equations involving
2 or more variables. (LO 9a-e)
7. Students should be able to define a function and perform basic
operations on functions. (LO 9a-e)
8. Students should be able to analyze basic properties of graphs of
functions . (LO 9a-e)
9. Students should be able to perform basic operations involving
exp onential and logarithmic functions. (LO 9a-e)
10. Students should be able to solve basic application problems involving
algebraic expressions. (LO 9a-e)
11. Students should be able to utilize written communication forms that
are appropriate to the mathematical sciences.
V. Topical Outline
A. Linear Equations and Inequalities
1. Overview and review of the real number system
2. Linear equations and inequalities in one and two variables
3. Absolute value equations and inequalities
4. Graphs of linear equations and inequalities
5. Applications of linear equations and inequalities
B. Polynomials
1. Operations on polynomials
2. Factoring methods and equations involving polynomials
C. Rational Expressions
1. Operations on rational expressions (including complex fractions)
2. Equations involving rational expressions
D. Exponents and Complex Numbers
1. Integral and rational exponents
2. Scientific notation
3. Definition, notation and operations on the set of complex numbers
E. Quadratic Equations and Inequalities
1. The quadratic formula
2. Equations in quadratic form
3. Applications involving quadratic equations
4. Nonlinear inequalities
F. Relations and Functions
1. Definitions, notations and operations
2. Constant, linear and quadratic functions
3. Circles , ellipses and hyperbolas
4. Symmetry and other properties of graphs
G. Exponential and Logarithmic Functions
1. Definition and properties of exponentials and logarithmic functions
2. Applications of exponential and logarithmic functions
