# MAT-171 Objectives

## MAT-171: Finite Mathematics

### Instructional Objectives

A semester course will consist of all objectives in Units I, II, III, and V and selected topics from Units IV and VI.

Unit I. Coordinate Systems and Graphs

1. Be able to construct a rectangular coordinate system and interpret it as a representation of ordered pairs of real numbers
2. Given an equation in two variables, be able to graph its solution
3. Be able to define, interpret and compute the slope of a line
4. Given a point and slope, be able to find the equation of the line using the slope–intercept and point–slope forms
5. Given two distinct points, be able to find the equation of the line
6. Given a linear equation in two variables, be able to express it in the form: Ax + By = C
7. Given a system of two linear equations in two unknowns, be able to find the solution using graphing, substitution and elimination
8. Be able to solve problems which involve applications of linear equations including simple interest, straight line depreciation, supply and demand, prediction and break–even analysis
9. Given n data points, be able to find the line of best fit using the method of least squares
10. Given linear inequalities in two variables, be able to graph their solution sets

Unit II. Matrices and Linear Systems

1. Given equations in two or more variables, be able to identify linear equations and write them in the form a x + a x + ... + a x = c
2. Given a linear system, be able to find its solution using elementary row operations
3. Given a linear system, be able to write the augmented matrix and use Gauss–Jordan elimination to express it in reduced row echelon form
4. Given an augmented matrix in reduced row echelon form, be able to determine all possible solutions to the system
5. Be able to construct and interpret an m x n matrix and identify its entries using appropriate terminology and notation
6. Given matrices A and B of the same size, be able to determine A+B and A–B
7. Given any matrix A, be able to find the scalar product cA
8. Given any matrices A and B, be able to determine their product AB when it is defined
9. Given a matrix A, be able to write its transpose
10. Be able to write the identity matrix or zero matrix of any specified size
11. Given an n x n invertible matrix, be able to find its inverse
12. Be able to solve a linear system by using the inverse of the coefficient matrix

Unit III. Linear Programming (Geometric Approach)

1. Given a verbal problem to be solved by linear programming methods, be able to:
• identify the variables
• construct a table organizing the information given
• state the objective function
• list all constraints
2. Given a linear programming problem, be able to:
• graph the set of feasible solutions
• determine the corner points of the set
• compute the value of the objective function at each corner point
• determine the optimal solution to the problem

Unit IV. Linear Programming (Algebraic Approach)

1. Given a standard linear programming problem, be able to state it as a problem involving a system of equations using slack variables
2. Given a standard linear programming problem, be able to find its solution using the simplex method

Unit V. Set Theory

1. Given any of the following (set, element, equal sets, empty set, disjoint sets, universal sets, complement of a set, subset, union, intersection, cartesian product) be able to define, identify and give an appropriate example
2. Given any of terms in #1, be able to use and read the corresponding set notation 3.Given any of terms in #1, be able to illustrate relationships using Venn diagrams

Unit VI. Counting, Permutations, Combinations and Probability

1. Given sufficient information, be able to determine the number of elements in two or more sets, be able to determine the number of elements in their Cartesian product
• a named set
• the union of specified sets
• the intersection of specified sets
2. Be able to state the Multiplication Principle (Basic Principle of Counting) and be able to solve problems requiring its application
3. Be able to show the permutations of the elements of a given set and solve problems involving permutations
4. Be able to show the combinations of the elements of a given set and solve problems involving combinations
5. Be able to define sample space, sample point and event and identify them in a given problem situation
6. Given an experiment in a finite sample space having equally likely outcomes, be able to determine the probability of a specified event