Applied Finite Mathematics

Straight lines and linear functions: the Cartesian coordinate system; straight lines; linear functions and mathematical models; intersection of straight lines; the method of least squares. Systems of linear equations and matrices: systems of linear equations - introduction; solving systems of linear equations I; solving systems of linear equations II; matrices; multiplication of matrices; the inverse of A square matrix; Leontief input-output model. Part 3 Linear programming - a geometric approach: graphing systems of linear inequalities in two variables; linear programming problems; graphical solution of linear programming problems. Part 4 Linear programming: an algebraic approach: the simplex method - standard maximization problems; the simplex method - standard minimization problems; the simplex method - nonstandard problems. Part 5 Mathematics of finance: compound interest; annuities; amortization and sinking funds; arithmetic and geometric progressions. Part 6 Sets and counting: sets and set operations; the number of elements in a finite set; the multiplication principle; permutations and combinations. Part 7 Probability: experiments, sample spaces, and events; definition of probability; rules of probability; use of counting techniques in probability; conditional probability and independent events; Bayes' theorem. Part 8 Probability distributions and statistics: distributions of random variables; expected value; variance and standard deviation; the binomial distribution; the normal distribution; applications of the normal distribution. Part 9 Markov chains and the theory of games: Markov chains; regular Markov chains; absorbing Markov chains; game theory and strictly determined games; games with mixed strategies. Appendices: logic - propositions and connectives; truth tables; the conditional and the biconditional connectives; laws of logic; arguments; applications of logic to switching networks; the system of real numbers.