Math 1500 – Discrete Mathematics for Business and Social Sciences

Course Coordinator

Alejandro Andreotti

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.


Finite Mathematics
ISU Custom Edition, bundled with MyMathLab Plus access code
ISB3: 9781256310082


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


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

Free expression statement

Iowa State University supports and upholds the First Amendment protection of freedom of speech and the principle of academic freedom in order to foster a learning environment where open inquiry and the vigorous debate of a diversity of ideas are encouraged. Students will not be penalized for the content or viewpoints of their speech as long as student expression in a class context is germane to the subject matter of the class and conveyed in an appropriate manner.

Students with disabilities

Iowa State University is committed to assuring that all educational activities are free from discrimination and harassment based on disability status. Students requesting accommodations for a documented disability are required to work directly with staff in Student Accessibility Services (SAS) to establish eligibility and learn about related processes before accommodations will be identified. After eligibility is established, SAS staff will create and issue a Notification Letter for each course listing approved reasonable accommodations. This document will be made available to the student and instructor either electronically or in hard-copy every semester. Students and instructors are encouraged to review contents of the Notification Letters as early in the semester as possible to identify a specific, timely plan to deliver/receive the indicated accommodations. Reasonable accommodations are not retroactive in nature and are not intended to be an unfair advantage. Additional information or assistance is available online at, by contacting SAS staff by email at, or by calling 515-294-7220. Student Accessibility Services is a unit in the Dean of Students Office located at 1076 Student Services Building.

More information about disability resources in the Mathematics Department can be found at