Business Mathematics

 

COURSE DESCRIPTION

1. System of Linear equations and Matrices:

Systems of linear equations – introduction, Systems of linear equations – unique solutions, Systems of linear equations—Underdetermined and over determined systems, Matrices, Multiplication of matrices, The inverse of a square matrix

2. Linear Programming:

Graphing systems of Linear equations in 2 variables, Linear programming problems,

Graphical solutions to linear programming problems, The simplex method: Standard maximization problems, The simplex method: Standard minimization problems

3. Mathematics of Finance:

Simple and compound interest, effective rate of interest, present value, Review of logarithms and solving exponential equation, Annuities, Amortization, sinking funds, Arithmetic and geometric progressions

4. Sets and Probability:

Sets and set operations, Number of elements in a finite set, Multiplication principle, Permutations and combinations, Experiments, sample spaces, and events , Definition of probability, Rules of probability

5. Additional Topics in Probability:

Use of counting techniques in probability, Conditional probability and independent events,

Bayes’ theorem, Distributions of random variables

COURSE OBJECTIVES

1. To teach students to how to solve basic financial mathematics problems involving simple

and compound interest and annuities.

2. To teach students to how to solve linear systems of equations using matrices and Gaussian

elimination method.

3. To teach students to how to use simplex method to solve standard linear programming

problems.

4. To teach students the elements of sets theory and probability theory.

5. To teach students to how to solve problems involving conditional probability (Bayes’ theorem) and introduce basic statistical concepts such as mean and variance.

6. To teach students to how to use technology in solving business problems.

LEARNING OUTCOMES

By the end of the course, students should acquire the following knowledge and skills:

1. To calculate interest, the present and the future value of an annuity of (equal) payments, to

amortize a loan or to be paid into a sinking fund account.

2. To find the n-th term and the sum of any consequent number of terms of a geometric (or

arithmetic) progression. To determine the progression if sufficient conditions are given.

3. To perform matrix operations and to solve systems of linear equations by both the Gauss- Jordan’s method and by using the inverse of a matrix.

4. To solve linear optimization problems in two variables by graphical method.

5. To apply simplex method to standard linear programming problem. To construct a dual problem to a linear programming problem.

6. To apply basic counting and combinatoric principles to applied business problems.

7. To construct abstract sample spaces and identify subsets of these spaces with events.

8. To solve problems using conditional probability, Bayes formula and independence of events.

9. To understand distributions of random variables and compute mean and standard deviation

for given data.

 

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