Chabot College
Fall 2013
Course Outline for Mathematics 33
FINITE MATHEMATICS
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Catalog Description:
MTH 33 - Finite Mathematics
4.00 units
• Straight lines, systems of linear equations, matrices, systems of linear inequalities, linear programming,
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mathematics of finance, sets and Venn diagrams, combinatorial techniques and an introduction to
probability. Applications in business, economics and the social sciences.
Prerequisite: MTH 55 , MTH 55L or , MTH 55B (completed with a grade of "C" or higher) or an appropriate
skill level demonstrated through the mathematics assessment process.
Units
(Min)
Units
(Max)
Contact Hours
Week
(Min)
4.00
Lecture
Laboratory
Clinical
Total
•
4.00
Week
(Max)
Term
(Min)
Term
(Max)
4.00
4.00
4.00
0.00
0.00
4.00
4.00
1.00
0.00
5.00
70.00
0.00
0.00
70.00
70.00
17.50
0.00
87.50
Prerequisite Skills:
Before entry into this course, the student should be able to:
1.
2.
3.
4.
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;
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 substitution;
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.
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Expected Outcomes for Students:
Upon completion of this 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;
13. use Venn diagrams to solve problems;
14. apply basic combinatorial principles to counting problems;
15. demonstrate an understanding of the basic definitions of elementary probability;
16. determine the probability of a simple or compound event using combinatorics and basic probability
theorems;
17. determine whether events are independent;
18. use conditional probability to find the probability of compound events;
19. use Bayes’ theorem to find probabilities;
20. determine the probability distribution and Expected Value of a Random Variable;
21. solve applied problems involving simple and compound interest;
22. solve applied problems involving annuities, sinking funds and amortization;
23. be able to use calculator and/or computer technology to solve complex finite math problems.
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Course Content:
1. Review linear equations and functions, intersection of straight lines
A. Graphing linear functions using intercepts and/or slope
B. Finding linear equations from data
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
3. Systems of linear equations
A. Graphing , substitution and elimination
B. Types of solutions, unique and non-unique solutions and inconsistent systems
C. Applications to business and social science
4. Matrices and Matrix methods for solving systems of equations
A. Gauss-Jordan elimination and reduced-row echelon form
B. Matrix algebra
C. Inverse matrix method for solving systems of linear equations
D. Applications to business and social science
5. Linear programming
A. Graphical solution of a system of linear inequalities
B. Formulation of a linear programming problems in two and three variables
C. Graphical solution methods of linear programming problems in two variables
D. Applications to business and social science
6. Math of finance
A. Simple and compound interest
B. Future amount and present value
C. Annuities, sinking funds and amortization
7. Sets and counting
A. Subsets, set equality, union, intersection and complement
B. Set builder notation and Venn diagrams
C. DeMorgan’s Laws
D. Counting elements in a set using Venn diagrams and/or formulas
E. Multiplication rule
F. Permutations and combinations
G. Applications to business and social science
8. Probability
A. Basic definitions, principles and theorems of probability theory
B. Probability distributions and expected value
C. Use of combinatorial principles to determine the probability of an event
D. Finding the probability of a compound event
E. Conditional probability
F. Independence of two events
G. Bayes Theorem
H. applications to business and social science
9. Use of technology
A. Use of calculator or computer technology to supplement manual calculation methods.
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Methods of Presentation
1. Lecture/Discussion
2. Problem Solving
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Assignments and Methods of Evaluating Student Progress
1. Typical Assignments
A. A company makes widgets and gadgets. Widgets are comprised of 10 units canvas, 5
units nylon. Gadgets are comprised of 8 units canvas, 9 units nylon. The company has
1000 units of canvas and 800 units of nylon available. A widget returns $12 profit and a
gadget returns $15 profit. How many widgets and how many gadgets should be
manufactured to maximize profit.
B. Using an interest rate of 7% per year, set up the formula to determine how much someone
should pay now (the present value) for an annuity that would pay the purchaser $200 per
month for the next 10 years.
C. If a committee of 3 people is chosen at random from a group of 20 men and 25 women,
what is the probability that 2 out of the 3 would be men?
2. Methods of Evaluating Student Progress
A.
B.
C.
D.
E.
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Exams/Tests
Quizzes
Projects
Home Work
Final Examination
Textbook (Typical):
1. Lial (2011). Finite Mathematics with Applications (10th/e). Pearson.
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Special Student Materials
1. May require scientific or graphing calculator and/or computer lab fee.