Wolfram Computation Meets Knowledge

Get Down to Business with Finite Mathematics in Wolfram Language

Get Down to Business with Finite Mathematics in Wolfram Language

“There is every reason to expect that the various social sciences will serve as incentives for the development of great new branches of mathematics and that some day the theoretical social scientist will have to know more mathematics than the physicist needs to know today.”

John G. Kemeny, first author of the original textbook on finite mathematics and co-inventor of the BASIC programming language

Finite mathematics gives students a mathematical toolkit used in fields as diverse as business, economics, sociology and biology while covering techniques that are logically distinct from calculus.

I am glad to announce the launch of Introduction to Finite Mathematics, a free interactive course that will help open the world of finite mathematics to students from any background. Topics are chosen to align with college courses on finite mathematics and are presented so that you can learn how to use either Wolfram Language or pen and paper to perform calculations.

Click the following to begin your exploration of the interactive course.

Go to free course


The course introduces a range of topics, including matrices, linear systems, linear optimization, the mathematics of finance, probability, Markov chains and game theory. The presentation of these topics will give students a solid foundation for applying the math that they know to real problems that arise in business and decision making.

Here is a sneak peek of what the course contents look like:

Course framework

This course on finite mathematics has 30 lessons. You can watch the video component of the course in under seven hours; however, I recommend you spend approximately twice this long reading the full lesson text, attempting the ungraded exercises and trying the quiz questions to build your understanding of the material.

This course is designed on the assumption that most students will have some background in elementary algebra. However, the design also assumes these students may want a refresher or at least a fresh take on those topics before proceeding. New topics are presented in a way that builds on the foundational skills but also shows how Wolfram Language functions can be used to perform specialized calculations without needing to think about each algebraic step.

Let’s dive deeper into the structure of the course.


The course is organized into 30 lessons, each with a video recording of the content. Each lesson also has a notebook version containing the full lesson text. The downloadable notebook for each lesson will sometimes have additional explanations and examples that were cut from the video recordings to keep them concise. The lesson text also has helpful sections for overview, as well as key terms that summarize the key results of each lesson.

Since the lessons are written in Wolfram Notebooks, important concepts can be easily visualized and explored computationally.

See the Nash equilibrium when choice of strategies is not strictly determined:

Nash equilibrium

Illustrate Bayes’s theorem as applied to screening tests:

Bayes's theorem

Show the distribution vector associated with a discrete Markov process evolving over time:

Distribution vector with discrete Markov process

Visualize the simplex method as a search algorithm:

Simplex method


Aside from the worked examples you will find in the lessons, each lesson also has a set of ungraded exercises along with solutions. The ungraded exercises are a great way for you to solidify your understanding of the material and gain confidence for the assessments.

Sample exercise

Each exercise is designed so that it can be solved using pen and paper for students who need that as a learning outcome, but each can also be solved by writing and running code in the Wolfram Cloud.


Each section of the course ends with a multiple-choice quiz of 10 questions. These questions are a way for students to check that they understand the concepts from the lessons. Students who have completed the ungraded exercises with confidence will be well prepared to pass the quizzes:

Sample quiz

Quiz question responses receive instant feedback, and any question can be solved either by hand or with assistance from Wolfram Language.

Course Certificate

Completing the course, including all 30 video lessons and eight quizzes, will allow the student to receive a certificate of completion. This certificate represents that a student has studied the fundamental concepts in finite mathematics, and makes a great addition to either social media profiles or résumés:

Course certificate

In addition to the certificate of completion, students can take an optional final exam. Students who can confidently answer the quiz questions and who have studied the lesson materials will be in a good position to pass the final exam. Students who do pass this exam will receive an additional certificate indicating their proficiency in the course material.

Daily Study Group Preview

Wolfram U offered a preview version of the course to Daily Study Group participants in November, and we received some valuable feedback. Here is what participants said:

  • “I really like that this course shows important applications.”
  • “The lectures on finance-related concepts were very useful.”
  • “By far, the Wolfram courses have been the smoothest and most timely experiences I’ve had (and I take courses for fun quite a lot). Don’t change a thing!”
  • “Very good course.”
  • “The main lecturer is pedagogically quite gifted as a presenter! Perhaps the best I have experienced—certainly in mathematics.”
  • “Previously, I thought game theory would be boring, but I found the patterns intriguing. In particular, I enjoyed seeing graphs employed in Markov chains and would like to delve deeper into that. Thank you for sparking my interest! And thank you for the reasonable length of the final. REALLY, THANKS!”

A Building Block for Success

“Such experience in writing and debugging their own computer programs both provides students with greater mathematical power and helps to reinforce the understanding of fundamental concepts.”

— John G. Kemeny, from the preface to the third edition of his original Introduction to Finite Mathematics

Students often wonder how the mathematics they are learning can be applied to real situations. This can be particularly true of students in business, economics and the social sciences. Kemeny identified this as a unique educational challenge. Finite mathematics was conceived to provide a foundation for mathematical analysis of problems that arise in everyday decisions. Introduction to Finite Mathematics will provide students with an overview of important methods and the foundation they need to pursue future courses of mathematical study.


This course is the result of the work of the Wolfram U, Algorithms R&D and Academic Innovation teams. I would like to thank Devendra Kapadia, Mads Bahrami, Anisha Basil, Abrita Chakravarty, Cassidy Hinkle, Jamie Peterson, Joyce Tracewell, Laura Crawford, Bob Owens, Matt Coleman, Ryan Domier, Luke Titus and Mariah Laugesen for all the work they put into getting this course up and running.

Register for one of Wolfram U’s Daily Study Groups.


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