## Course Coordinator

Alejandro Andreotti

aleand@iastate.edu

515-294-5128

## Catalog description

**MATH 1500: Discrete Mathematics for Business and Social Sciences**

(2-1) Cr. 3. F.S.SS.

*Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of high school geometry*

Linear equations and inequalities, matrix algebra, linear programming, discrete probability. Either MATH 1040 or MATH 1500 may be counted toward graduation, but not both.

## Textbook

**Finite Mathematics
**Barnett

ISU Custom Edition, bundled with MyMathLab Plus access code

ISB3: 9781256310082

## Syllabus

Times are suggested based on a 15-week semester, allowing 4 weeks for days for catch-up, review and exams.

All exams (including the final exam) are done online in a computer lab. They can be taken any time before the given deadline, at the students’ convenience.

**Appendix A – Basic Algebra Review (1 week)**

- A1, A2, A5, A6, A7

**Chapter 1 – Linear Equations and Graphs (0.5 weeks)**

- 1.1, 1.2

**Chapter 2 – Functions and Graphs (1.5 weeks)**

- 2.1 – 2.5

**Chapter 3 – Mathematics of Finance (1 week)**

- 3.1, 3.2

**Chapter 4 – Systems of Linear Equations; Matrices (2 weeks)**

- 4.1 – 4.6

**Chapter 5 – Linear Inequalities and Linear Programming (1 week)**

- 5.1 – 5.3

**Chapter 6 – Linear Programming: Simplex Method (1 week)**

- 6.1 – 6.3

**Chapter 7 – Logic, Sets, and Counting (0.5 weeks)**

- 7.2 – 7.4

**Chapter 8 – Probability (1.5 weeks)**

- 8.1 – 8.5

**Chapter 11 – Data Description and Probability Distributions (1 week)**

- 11.1-3

## Objectives

**Review of Some Algebra (Appendix A)**

- Sets: Set notation, union, intersection, complement
- Fraction Properties: Add/subtract/multiply/divide fractions
- Polynomials: Add, subtract, multiply, expand and combine terms
- Integer Exponents and Scientific Notation: Rules of working with integer powers; convert from standard to scientific notation and back
- nth Roots of Real Numbers and Rational Exponents and Radicals: Converting between root notation and fractional power notation; practice the rules of working with powers
- Quadratic Formula: How to solve a quadratic equation numerically

**Functions and Graphs**

- Concept of a function, graph of a function, domain and range
- Graphs and Transformations: What do the graphs of some elementary functions look like [straight lines, absolute value function, simple powers and roots]; horizontal and vertical shifts, contractions or dilations, reflection in x-axis or y-axis; piecewise defined functions
- Lines: Slope, intercept, point-slope form, slope-intercept form, finding line through two points, applications
- Quadratic Functions: Find vertex and intercepts
- Polynomial and Rational Functions: For polynomials, the possible shapes of the graph, specifically the number of intercepts and turning points it can have. For rational functions, the domain and vertical and horizontal asymptotes.
- Exponential Functions: Properties and graphs, natural exponential function ex, application to compound interest
- Logarithmic Functions: Definition, properties, applications on investment

**Applications of Exponential Functions and Logarithmic Functions**

- Simple Interest
- Compound Interest
- Continuous Compound Interest

**Systems of Linear Equations**

- Graphical method
- Substitution method
- Elimination method
- Augmented Matrix method
- Inverse Matrix method: Definition of matrix, matrix addition, subtraction, multiplication,inverse matrix

**Linear Programming**

- Inequalities: Properties, interval notation, solving linear inequalities
- The Simplex Method
- Dual Problems

**Elementary Probability and Statistics**

- Basic Counting Principles
- Permutations and Combinations
- Sample Spaces, Events, and Probability
- Union, Intersection, and Complement of Events
- Conditional Probability, Intersection, and Independence
- Bayes’ Formula
- Random Variable, Probability Distribution, and Expected Value

**Data Description and Probability Distributions**

- Graphing Data
- Measures of Central Tendency
- Measures of Dispersion