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
- Be able to construct a rectangular coordinate system and interpret it as a representation of ordered pairs of real numbers
- Given an equation in two variables, be able to graph its solution
- Be able to define, interpret and compute the slope of a line
- Given a point and slope, be able to find the equation of the line using the slope–intercept and point–slope forms
- Given two distinct points, be able to find the equation of the line
- Given a linear equation in two variables, be able to express it in the form: Ax + By = C
- Given a system of two linear equations in two unknowns, be able to find the solution using graphing, substitution and elimination
- 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
- Given n data points, be able to find the line of best fit using the method of least squares
- Given linear inequalities in two variables, be able to graph their solution sets
Unit II. Matrices and Linear Systems
- 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
- Given a linear system, be able to find its solution using elementary row operations
- Given a linear system, be able to write the augmented matrix and use Gauss–Jordan elimination to express it in reduced row echelon form
- Given an augmented matrix in reduced row echelon form, be able to determine all possible solutions to the system
- Be able to construct and interpret an m x n matrix and identify its entries using appropriate terminology and notation
- Given matrices A and B of the same size, be able to determine A+B and A–B
- Given any matrix A, be able to find the scalar product cA
- Given any matrices A and B, be able to determine their product AB when it is defined
- Given a matrix A, be able to write its transpose
- Be able to write the identity matrix or zero matrix of any specified size
- Given an n x n invertible matrix, be able to find its inverse
- Be able to solve a linear system by using the inverse of the coefficient matrix
Unit III. Linear Programming (Geometric Approach)
- 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
- 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)
- Given a standard linear programming problem, be able to state it as a problem involving a system of equations using slack variables
- Given a standard linear programming problem, be able to find its solution using the simplex method
Unit V. Set Theory
- 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
- 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
- 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
- Be able to state the Multiplication Principle (Basic Principle of Counting) and be able to solve problems requiring its application
- Be able to show the permutations of the elements of a given set and solve problems involving permutations
- Be able to show the combinations of the elements of a given set and solve problems involving combinations
- Be able to define sample space, sample point and event and identify them in a given problem situation
- Given an experiment in a finite sample space having equally likely outcomes, be able to determine the probability of a specified event