MTH 1050 - Finite Mathematics

• Solve linear, quadratic, and rational equations algebraically
• Graph and solve linear inequalities
• Find the linear regression equation of a list of data points and make predictions using it
• Perform arithmetic operations on polynomials and rational expressions
• Factor quadratics, expressions with common factors, and some other special polynomials
• Apply laws of exponents and simplify exponential and radical expressions.
• Evaluate logarithmic expressions and apply laws of logarithms
• Solve exponential and logarithmic equations
• Identify the algebraic forms, graphs, and basic properties of polynomial, rational, exponential, and logarithmic functions
• Graph transformations of functions and identify transformations of a basic function from a graph
• Identify vertical and horizontal asymptotes and removable discontinuities of rational functions
• Apply understanding of functions to business applications such as finding the maximum or minimum for quantities which are related quadratically and performing break-even analysis
• Solve systems of linear equations by various methods; identify inconsistent and dependent systems
• Perform arithmetic operations and row operations on matrices
• Use Gauss-Jordan elimination on augmented matrices to solve systems of linear equations
• Compute the inverse of an invertible 2×2 or 3×3 matrix
• Apply understanding of systems of linear equations and matrices to business problems such as inventory, production, and total cost
• Solve systems of linear inequalities
• Set up a linear programming problem, identifying an objective function with constraints, and interpret its solution in the original context
• Use a geometric approach to solve linear programming problems
• Use the simplex method to solve linear programming problems
• Describe sets using set notation
• Determine the cardinality of a set
• Determine whether two sets are equal
• Identify subsets, universal sets, the empty set, and finite and infinite sets
• Determine complements, intersections, and unions of sets
• Use sigma notation to describe and evaluate a finite series
• Solve counting problems using fundamental counting principles
• Compute the numbers of permutations and combinations of a collection of objects
• Determine the sample space of an experiment and identify events
• Calculate probabilities, including conditional probabilities
• Apply understanding of probability to solve business problems and interpret the results
• Identify and create transition matrices for given situations
• Find a stationary matrix for a given transition matrix
• Find absorbing states given a transition matrix
• Determine if a transition matrix is for an absorbing Markov chain
• Find the limiting matrix for an absorbing Markov chain
• Apply understanding of stationary matrices and Markov chains to solve business problems and interpret the results

• High school algebra (solving equations, applying formulas, manipulating expressions involving variables, arithmetic, order of operations)
• Functions and graphs (notation, evaluating, the Cartesian coordinate system, plotting points, sketching plane curves, reading and interpreting graphs)
• Slope, intercepts, and equations of a line

• Linear equations and inequalities
• Linear regression
• Functions and graphs
• Polynomials and rational expressions and functions
• Exponents and radicals
• Quadratic equations and functions
• Transformations of functions
• Exponential and logarithmic expressions and functions
• Systems of linear equations and inequalities
• Matrices, matrix operations, and matrix equations
• Gauss-Jordan elimination
• Inverse of a matrix
• Linear programming
• The simplex method
• Sets
• Counting principles
• Permutations and combinations
• Basic probability
• Conditional probability
• Markov chains