COURSE OUTLINE
MIDLANDS TECHNICAL COLLEGE
MAT 122 FINITE COLLEGE MATHEMATICS
3.0 Credit Hours
COURSE DESCRIPTION: This course includes the following topics: logic; sets; Venn diagrams; counting problems; probability; matrices; systems of equations; linear programming, including the simplex method and applications; graphs; and networks.
PREREQUISITE: MAT 102
TEXT: Finite Mathematics, Sixth
Edition
by Howard L. Rolf
Brooks/Cole, 2005
EQUIPMENT: Graphing Calculator required; TI-83 or TI-83+ recommended
GRADING SCALE:
A 90 - 100 B 80 - 89 C 70 - 79 D 60 - 69 F Below 60
MATHEMATICS DEPARTMENT ATTENDANCE REQUIREMENTS
DEFINITIONS:
ABSENCE - Failure to be present for a scheduled meeting of class or arriving for the class more than ten minutes after the scheduled time for the class to begin.
TARDY --- Arrival to class after the instructor has called the roll and before ten minutes past the scheduled time for the class to begin.
I. Absences are counted from the first day of classes.
II. Five absences are allowed for a class that meets three times per week and three absences are allowed for a class that meets twice a week.
III. Three tardies are considered as one absence. The student must meet with the instructor at the end of the class to which he has been late to have an absence changed to a tardy.
IV. There are no "excused" absences. All absences are counted regardless of the reason for the absence.
V. A student missing class time by leaving early will also be counted absent.
Please note:
You are responsible for all material and announcements presented, whether you are present or absent.Mathematics Department
MAT 122 COURSE OBJECTIVES
Students should be able to:
1. Solve/analyze systems of equations/inequalities using geometric and analytical techniques (including but not limited to matrix and computer methods).
2. Solve counting problems; work problems of basic probability; demonstrate a working knowledge of the terminoloy of sets, counting and probability; solve probability problems utilizing the binomial distribution.
3. Apply probability and matrices of Markov Chain processes.
4. Demonstrate a working knowledge of the language of symbolic logic, produce truth tables, assess the validity of arguments, and apply symbolic logic to circuits.
5. Demonstrate a working knowledge of graph theory and its applications, including paths, circuits and trees.
6. Solve problems by identifying what information is available and relevant to the problem; by selecting or developing appropriate procedures and relationships; by correctly applying the methods selected to the information available; and by verifying the validity and appropriateness of the solution.
Note: This outline is given for the regular Fall/Spring fourteen week semesters. The same material is covered in the summer term and the sessions classes, but in the appropriate fewer number of weeks: ten weeks for summer term, seven weeks for fall and spring sessions classes, and five weeks for summer session classes.
| WEEK | TOPIC | SECTION |
| 1 | Functions and Lines | |
| Functions | 1.1 | |
| Graphs and Lines | 1.2 | |
| Mathematical Models and Applications of Linear Functions | 1.3 | |
| 2 | Linear Systems | |
| Systems of Two Equations | 2.1 | |
| Systems with Three Variables: An Introduction to a Matrix Representation of a Linear System of Equations | 2.2 | |
| 3 | Gauss-Jordan Method for General Systems of Equations | 2.3 |
| Matrix Operations | 2.4 | |
| Multiplication of Matrices | 2.5 | |
| 4 | The Inverse of a Matrix | 2.6 |
| TEST 1 | ||
| Linear Programming | ||
| Linear Inequalities in Two Variables | 3.1 | |
| Solutions of Systems of Inequalities: A Geometric Picture | 3.2 | |
| 5 | Linear Programming: A Geometric Approach | 3.3 |
| Applications | 3.4 | |
| Linear Programming: The Simplex Method | ||
| Setting Up the Simplex Method | 4.1 | |
| 6 | The Simplex Method | 4.2 |
| The Standard Minimum Problem: Duality | 4.3 | |
| 7 | TEST 2 | |
| Sets and Counting | ||
| Sets | 6.1 | |
| 8 | Counting Elements in a Subset Using a Venn Diagram | 6.2 |
| Basic Counting Principles | 6.3 | |
| Permutations | 6.4 | |
| 9 | Combinations | 6.5 |
| A Mixture of Problems | 6.6 | |
| TEST 3 | ||
| 10 | Probability | |
| Introduction to Probability | 7.1 | |
| Equally Likely Events | 7.2 | |
| Compound Events: Union, Intersection, and Complement | 7.3 | |
| 11 | Conditional Probability | 7.4 |
| Independent Events | 7.5 | |
| Bayes' Rule | 7.6 | |
| 12 | Markov Chains | 7.7 |
| TEST 4 | ||
| Logic | ||
| Statements | 10.1 | |
| 13 | Conditional Statements | 10.2 |
| Equivalent Statements | 10.3 | |
| Valid Arguments | 10.4 | |
| 14 | The Nature of Networks and Graph Theory | |
| (The Nature of Problem Solving in Algebra, Karl Smith) | ||
| Euler Circuits | 9.1 | |
| Trees and Minimum Spanning Trees | 9.2 | |
| TEST 5 | ||