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Mathematical Methods for Quantitative Finance

Mathematical Methods for Quantitative Finance covers topics from calculus and linear algebra that are fundamental for the study of mathematical finance. Students successfully completing this course will be mathematically well prepared to study quantitative finance at the graduate level.


Course at a Glance

About the Course

The Mathematical Methods for Quantitative Finance course reviews the mathematical methods fundamental for the study of quantitative and computational finance. The areas of focus include calculus and multivariable calculus, constrained and unconstrained optimization, and linear algebra.

Topics covered include the following:

  • Functions and inverse functions
  • Limits, derivatives, partial derivatives, and chain rule
  • Integrals and multiple integrals, changing the order of differentiation and integration
  • Taylor series approximations
  • Newton’s method
  • Lagrange multiplier method
  • Vector and matrix arithmetic, determinants, eigenvalue-eigenvector decomposition, singular value decomposition
  • Numerical methods for optimization
Course goal:
Upon completion of the course students will know the fundamental mathematical concepts needed to effectively study quantitative finance areas such as fixed income, options and derivatives, portfolio optimization, and quantitative risk management.

Course Objectives

Upon completion of the course students will:

  1. Understand the concept of a limit, differentiation, and integration;
  2. Be able to compute partial derivatives and multiple integrals;
  3. Understand the utility of matrix decompositions;
  4. Be able to use Lagrange multipliers to solve constrained optimization problems; and
  5. Apply the above methods to problems arising in finance.

Recommended Background

Students should have completed entry-level college calculus courses that include an introduction to multivariable differential calculus; additional introductory mathematics and statistics coursework is desirable.

Suggested Readings

Stefanica, D. (2011). A primer for the mathematics of financial engineering. (2nd ed.). New York, NY: Financial Engineering Press. Retrieved from

Course Format

The class will consist of lecture videos, which are between 8 and 12 minutes in length and there is a short quiz at the end of each video. Additionally, there is a homework assignment accompanying each set of 8-10 videos.


Is there a statement of completion or certificate issued for this course?

  • No, sorry there is not a credential awarded for this course.
Can I access the course and contents after it ends?
  • All quizzes and homework assignments need to be completed by the listed due dates. After this date, currently enrolled students can continue to access this course session via a “View class archive” button on the Coursera landing page for the course. As this course may be run in the future, students may choose to enroll in and attend a new session of the course if they wish.