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Course Outline for Mathematics 33
Fall 2003
Chabot College Fall 2003
Course Outline for Math 33
FINITE MATHEMATICS
Catalog Description:
Math 33 – Finite Mathematics 4 units
Straight lines, systems of linear equations, matrices, systems of linear inequalities, linear programming, mathematics of finance, sets and Venn diagrams, combinatorial techniques and an introduction to probability. Prerequisite: Mathematics 55 or Mathematics 55B (completed with a grade of “C” or higher) or an appropriate skill level demonstrated through the mathematics assessment process. 4 hours. 0-1 hours laboratory.
Prerequisite Skills:
Before entering the course the student should be able to:
1. perform basic operations on complex numbers;
2. solve quadratic equations by factoring, completing the square, and quadratic formula;
3. find complex roots of a quadratic equation;
4. sketch the graphs of functions and relations:
a. algebraic, including polynomial and rational
b. logarithmic
c. exponential
d. circles;
5. find and sketch inverse functions;
6. perform function composition;
7. solve exponential and logarithmic equations;
8. apply the concepts of logarithmic and exponential functions;
9. solve systems of linear equations in three unknowns using elimination and substitiution;
10. apply the properties of and perform operations with radicals;
11. apply the properties of and perform operations with rational exponents;
12. solve equations and inequalities involving absolute values;
13. solve equations involving radicals;
14. graph linear inequalities in two variables;
15. find the distance between two points;
16. find the midpoint of a line segment.
Expected Outcomes for Students:
Upon completion of the course the student should be able to:
1. interpret graphs of linear equations;
2. identify the three types of solutions of a linear system;
3. use Gauss-Jordan elimination to put a matrix into reduced row echelon form;
4. write a system of linear equations to solve an applied problem;
5. perform operations with data matrices and interpret the result;
6. solve a system of linear equations and interpret the result;
7. find the inverse of a square matrix;
8. use the inverse to solve a system of linear equations;
9. determine graphically the solution of a system of linear inequalities;
10. formulate the solution to a linear programming problem in two or three variables;
11. use graphical methods to solve a linear programming problem in two variables;
12. find unions, intersections and complements of sets;
Expected Outcomes for Students: continued
13. use Venn diagrams to solve problems;
14. apply basic combinatorial principles to enumeration problems;
15. demonstrate an understanding of the basic definitions of elementary probability;
16. determine the probability distribution for a sample space (uniform or nonuniform);
17. determine the probability that a specified event will occur;
18. find the conditional probability of an event;
19. solve applied problems involving simple and compound interest;
20. solve applied problems involving annuities, sinking funds and amortization.
Course Content:
1. Review linear equations and functions, intersection of straight lines
a. Graphing linear functions with a calculator
2. Applications of linear functions to economics
a. Cost, revenue and profit functions
b. Supply and demand equations
c. Break-even point
d. Market equilibrium
e. Estimating intersection points with a calculator
3. Systems of linear equations
a. Graphing , substitution and elimination
b. Types of solutions
c. Applications
4. Matrices
a. Gauss-Jordan elimination and reduced-row echelon form
i. Reducing a matrix without using matrix functions on a calculator
ii. Using a calculator to reduce a matrix
b. Matrix algebra
i. Addition and multiplication of matrices by hand calculations
ii. Using a calculator to add and multiply matrices
c. Inverse matrix method for solving systems of linear equations
i. Finding the inverse by hand calculations
ii. Using a calculator to find the inverse
d. Applications
5. Linear programming
a. Graphical solution of a system of linear inequalities
b. Formulation of a linear program in two variables (optional: formulation of a linear program in three variables)
c. Graphical solution of linear programming problems in two variables
6. Math of finance
a. Simple and compound interest
b. Future amount and present value
c. Annuities, sinking funds and amortization
d. Using the calculator to evaluate complex formulas
7. Sets
a. Subsets, set equality, union, intersection and complement
b. Set builder notation
c. DeMorgan’s Laws
d. Venn diagrams
8. Combinatorics
a. Number of elements in a finite set
b. Number of elements in the union o f two or three sets
Expected Outcomes for Students: continued
8. Combinatorics continued
c. Sum and product rules
d. Permutation and combination
e. Combinatorial functions on the calculator
9. Probability
a. Basic definitions of probability theory
b. Probability distributions
c. Finding the probability of an event, given the probabilities of the simple events in a sample space
d. Use of combinatorial principles to determine the probability of an event
e. Conditional probability
f. Independence of two events
g. Bayes Theorem (optional)
Methods of Presentation:
1. Lectures
2. Problem Solving
3. Discussions
Assignments and Methods of Evaluating Student Progress:
1. Typical Assignments
a. The Coffee Shoppe sells a coffee blend made from two coffees, one costing $2.50/lb. If the blended
coffee sells for $2.80/lb, find how much of each coffee is used to obtain the desired blend. (Assume
the weight of the blended coffee is 100lb.)
b. Find how much money should be deposited in a bank paying interest at the rate of 8.5% per year
compounded quarterly so that at the end of five years the accumulated amount will be $40,000.
c. A member of a book club wishes to purchase two books from a selection of eight books
recommended for a certain month. In how many ways can she choose them?
2. Methods of Evaluating Student Progress
a. Homework
b. Quizzes
c. Exams
d. Final Examination
Textbook(s) (Typical):
Applied Mathematics for Business, Economics, Life Sciences and Social Sciences, Barnett/Ziegler/Byleen, Prentice Hall, 2003
Special Student Materials:
Scientific or graphing calculator
Prior: Dec 1998
Revised: Math 33 Course Outline Fall 2003
3-10-03 CSS