# Departmental Syllabus for Finite Mathematics with Application

**Textbook: **Mathematics - An Applied Approach, 8^{th}
Edition, by Sullivan & Mizrahi

**Prerequisites:** MATH 15 or MATH 1530 or a
mathematics proficiency level of 15 or

above.

**Calculators: **Scientific calculator required. (NOTE: On occasion, individual
instructors

may restrict the use of any type of calculator.)

**Course Description:**

Part I Linear Algebra: coordinate systems and graphs, linear systems, matrices,
linear

programming (geometric and simplex methods).

Part II Probability: set theory, counting techniques, probability.

Extensive use is made of applications in the fields of business and economics.

**Topics and sections to be covered:**

**Part I Linear Algebra
**1.1 Rectangular Coordinates; Lines

1.2 Pairs of Lines

1.3 Applications: Prediction; Break-Even Point; Mixture Problems; Economics

2.1 Systems of Linear Equations: Substitution; Elimination

2.2 Systems of Linear Equations: Matrix Method

2.3 Systems of m Linear Equations Containing n Variables

2.4 Matrix Algebra

2.5 Multiplication of Matrices

2.6 The Inverse of a Matrix

2.7 Applications: Leontief Model (and as time permits, Cryptography;

Accounting; The Method of Least Squares)

3.1 Systems of Linear Inequalities

3.2 A Geometric Approach to Linear Programming Problems

3.3 Applications

4.1 The Simplex Tableau; Pivoting

4.2 The Simplex Method: Solving Maximum Problems in Standard Form

** The instructor should choose one of the following two sections.

4.3 Solving Minimum Problems in Standard Form Using the Duality Principle

4.4 The Simplex Method with Mixed Constraints

**Part II Probability
**6.1 Sets

6.2 The Number of Elements in a Set

6.3 The Multiplication Principle

6.4 Permutations

6.5 Combinations

6.6 The Binomial Theorem (as time permits)

7.1 Sample Spaces and the Assignment of Probabilities

7.2 Properties of the Probability of an Event

7.3 Probability Problems Using Counting Techniques

7.4 Conditional Probability

7.5 Independent Events

8.1 Bayes’ Formula