With the successful completion of the course, the students should be able to:

• handle mathematical expressions involving real numbers (e.g. radicals, fractions etc)
• solve equations and inequalities of 1st and 2nd degree
• handle functions in Cartesian coordinates, including obtaining their graph
• solve linear systems of equations
• perform matrix operations
• compute the inverse of a matrix
• handle the basic counting principles
• compute conditional probabilities either using the definitions or the Bayes formula and to be able to check independence of events
• work with both discrete and continuous random variables, with emphasis to Binomial and Normal distributions
• work out the Normal approximation to the Binomial Distribution
• understand the notions of mean value and variance and be able to calculate them in specific distributions.

Review of Algebra

Sets of Real Numbers, Some Properties of Real Numbers, Exponents and Radicals, Operations with Algebraic Expressions, Factoring, Fractions, Linear Equations, Quadratic Equations

Applications and More Algebra

Applications of Equations, Linear Inequalities, Applications of Inequalities, Absolute Value, Summation Notation, Sequences

Functions and Graphs

Functions, Special Functions, Combinations of Functions, Inverse Functions, Graphs in Rectangular Coordinates, Symmetry, Translations and Reflections, Functions of Several Variables

Lines, Parabolas, and Systems

Lines, Applications and Linear Functions, Quadratic Functions, Systems of Linear Equations, Nonlinear Systems, Applications of Systems of Equations

Exponential and Logarithmic Functions

Exponential Functions, Logarithmic Functions, Properties of Logarithms, Logarithmic and Exponential Equations

Matrix Algebra

Matrices, Matrix Addition and Scalar Multiplication, Matrix Multiplication, Solving Systems by Gaussian Elimination, Inverses

Linear Programming (optional)

Linear Inequalities in Two Variables, Linear Programming, The Simplex Method, Artificial Variables, Minimization, The Dual Problem

Introduction to Probability and Statistics

Basic Counting Principle and Permutations, Combinations and Other Counting Principles, Sample Spaces and Events, Probability, Conditional Probability and Stochastic Processes, Independent Events, Bayes Formula

Additional Topics in Probability

Discrete Random Variables and Expected Value, The Binomial Distribution, Markov Chains

Limits and Continuity

Limits, Continuity, Continuity Applied to Inequalities

Continuous Random Variables

Continuous Random Variables, The Normal Distribution, The Normal Approximation to the Binomial Distribution