Duke - The Fuqua School of Business

Mathematical Foundations


Your course material will often rely on the use of mathematical relationships to represent real-world relationships, so your preparation goal is, first, to be comfortable with that notion. Second, it is often useful (and sometimes necessary) to "do some theory" in order to get to the point at which the application of the theory is clearly understood, allowing you to appreciate insights provided by the analysis. "Doing the theory" may involve an element of abstract thinking that is necessary for success.

A basic knowledge of algebra will be used in many courses, and basic concepts of calculus provide important conceptual foundations. From calculus, you will need an understanding of the basic notions of optimization, rates of change, and areas under curves. Some applications of such concepts are marginal costs (rate of change of total cost), total revenue or probability (represented by areas under curves), and maximizing output subject to a raw material constraint (applying optimization principles). Functional area courses (finance, marketing, and operations) will provide opportunities for applications of the understanding gained in the various tools courses (decisions models, statistics, economics and accounting).

What You Should Know

  • Common math notation (exponents, absolute value, summation notation)
  • Functions (notations, graphing, ability to create graphs and to reason from a graph)
  • Linear models (interpretations of slope)
  • Logarithmic and exponential functions
  • Solving systems of equations and inequalities
  • Understanding the derivative as slope and as a rate of change (the concept of marginal)
  • Using the derivative to find maximum and minimum points, and inflection points 
  • Calculating and interpreting area under the marginal cost (or marginal revenue, etc.) curve
  • Computing the partial derivative and understanding it as a rate of change

If You Want to Review or Preview

Any of the following are recommended:

Choice 1: (for admitted students only)

Pre-Program Math Foundations software   – Modules I and II

All incoming students will receive access to Pre-Program Math Foundations, a collection of short presentations of math concepts and their applications. It is expected that you will work through the entire software before Orientation. 

Pre-Program Math Foundations  is organized around four modules:

  • Module I:   Algebra for Managers
  • Module II:  Calculus
  • Module III: Dealing with Data
  • Module IV: Introduction to Math for Finance (Time Value of Money)


Choice 2:
Soft-bound book: Forgotten Calculus, A Refresher Course with Applications to Economics and Business,3rd Edition by B. Bleau, published by Barron's (ISBN 0-7641-1998-2 ). Obtain via www.amazon.com. This workbook starts with an excellent review of algebra with business applications. Read Units 1-8. Also read the beginning of Units 22 and 23. Units 9-11 and 19 give a review of calculus.

Also, download and read Calculus: What is it? What is it for?  by Sloan and Bernstein. This is a brief introduction for people who have never seen calculus Do this reading before you work through Units 9-11.