Curriculum

Core Courses

The following core courses are required for the Quant program. Course sequence and specific requirements vary by cohort for both the freestanding and AMDP tracks. For details on the freestanding program, see the Academics page. AMDP requirements by cohort are available on the AMDP page.

Semester 1

MATH 472 (3 credits)

Numerical Methods with Financial Applications

This is a survey course of basic numerical methods used to solve scientific problems. The emphasis is divided between the analysis of the methods, their practical applications, and getting comfortable using a computer language for implementation. Topics intended to be covered are: root finding methods; system of linear equations; interpolation and polynomial approximation; numerical differentiation and integration; numerical methods for ordinary differential equations; basic Monte-Carlo simulations and financial applications. A part of the coursework requires programming in a high-level language.

MATH 526 (3 credits)

Discrete State Stochastic Processes

This is an introductory course in the Theory of Stochastic Processes. The topics covered include Markov and Poisson processes, basic Martingale Theory, and introduction to Brownian Motion. The mathematical theory is illustrated with many relevant examples from Economics and Finance, showing how mathematical (probabilistic) methods can be used in these fields. 

MATH 573 (3 credits)

Advanced Financial Mathematics I

This is an introductory course in Financial Mathematics. This course starts with the basic version of Mathematical Theory of Asset Pricing and Hedging (Fundamental Theorem of Asset Pricing in discrete time and discrete space). This theory is applied to problems of Pricing and Hedging of simple Financial Derivatives. Finally, the continuous time version of the proposed methods is presented, culminating with the Black-Scholes model. A part of the course is devoted to the problems of Optimal Investment in discrete time (including Markowitz Theory and CAPM) and Risk Management (VaR and its extensions). This course shows how one can formulate and solve relevant problems of financial industry via mathematical (in particular, probabilistic) methods. 

STATS 500 (3 credits)

Applied Statistics I / Statistical Learning I: Regression

This course introduces the essentials of linear models. Topics include linear models, model fitting, identifiability, collinearity, Gauss-Markov theorem, variable selection, transformation, diagnostics, outliers and influential observations, ANOVA and ANCOVA, and common designs. Applications and real data analysis are emphasized, with students using the computer to perform statistical analyses.

Semester 2

MATH 574 (3 credits)

Advanced Financial Mathematics II

This is a continuation of MATH 573. This course discusses Mathematical Theory of Continuous-time Finance. The course starts with the general Theory of Asset Pricing and Hedging in continuous time and then proceeds to specific problems of Mathematical Modeling in Continuous-time Finance. These problems include pricing and hedging of (basic and exotic) Derivatives in Equity, Foreign Exchange, Fixed Income and Credit Risk markets. In addition, this course discusses Optimal Investment in Continuous time (Merton’s problem), High-frequency Trading (Optimal Execution), and Risk Management (e.g. Credit Value Adjustment). Although Math 506 is not a prerequisite for Math 574, it is strongly recommended that either these courses are taken in parallel, or Math 506 precedes Math 574.

MATH 506 (3 credits)

Stochastic Analysis of Finance

This is a continuation of MATH 526. This course covers such topics as: Stochastic Integration and Stochastic Differential Equations, Change of Measure, advanced Martingale Theory and Brownian Motion, Levy processes, and Stochastic Control. A strong emphasis is made on applications of the developed methods to the problems of Mathematical Modeling in Finance. In particular, it shows how Stochastic Analysis is applied to problems arising in Equity Derivatives, Foreign Exchange, Fixed Income and Credit Risk markets. This course also demonstrates the use of Stochastic Control in the problems of Optimal Investment and Optimal Execution. This is a good complement to MATH 574, or MATH 506 precedes MATH 574.

STATS 509 (3 credits)

Statistical Analysis of Financial Data

This course will cover basic topics involved in modeling and analysis of financial data. These include linear and non-linear regression, nonparametric and semi-parametric regression, selected topics on the analysis of multivariate data and dimension-reduction, and time series analysis. Examples and data from financial applications will be used to motivate and illustrate the methods.

Semester 3

MATH 623 (3 credits)

Computational Finance

This is a continuation of MATH 472. This course starts with the introduction to numerical methods for solving differential equations of evolution, including the Partial Differential Equations (PDEs) of parabolic type. Convergence and stability of explicit and implicit numerical schemes is analyzed. Examples include the generalized Black- Scholes PDE for pricing European, American and Asian options. Another part of the course is concerned with the Monte Carlo methods. This includes the pseudo random number generators (with applications to option pricing) and numerical methods for solving stochastic differential equations (with applications to Stochastic Volatility models). Finally, the students are introduced to the idea of calibration, which allows one to determine the unknown model parameters from observed quantities (typically, prices of financial products). The calibration is first formulated as a general inverse problem, then, the solution methods are presented in several specific settings. The theory is accompanied by applications of proposed numerical methods in particular models of Stochastic Volatility and Interest Rate models. This includes an in-depth study of numerical methods for pricing, hedging and calibration in the Hull-White and Black-Derman-Toy models. A part of the coursework requires programming in a high-level language.

MATH 507 (3 credits)

Mathematical Methods for Algorithmic Trading

This course focuses on using tools of stochastic optimal control for designing trading strategies. The aim is to teach the relevant techniques from Probability, Statistics, PDEs, and Optimization, as well as to introduce students to the wide range of specific problems and existing models related to price impact and algorithmic trading.

Electives

Quant students will choose from a range of approved electives offered across the university. This flexibility allows students to tailor their academic path to align with their specific interests, such as programming, data science, finance, or advanced mathematics. In addition to the approved elective courses listed below, students may propose other courses for consideration, subject to approval by the Quant program. Requests for approval should be emailed to [email protected].

It is strongly recommended to enroll in MATH 628/629 – Machine Learning for Finance I/II (2 + 2 credits, offered in Fall/Winter) as part of your elective courses. This sequence offers valuable insights into the intersection of machine learning and finance.

Students should verify course credits, semester offerings, and any requisites or permissions with the respective departments, either through Wolverine Access or by contacting the department directly. We cannot enroll students in elective courses or adjust their position on a waitlist; enrollment in these courses is at the discretion of the instructor or department. Listing a course as an approved elective below simply means it can count toward your degree, but students must still meet any department-specific requirements. Explore the pre-approved elective options by clicking on each dropdown below.

Mathematics Courses (MATH)

  • MATH 520: Life Contingencies I (3 credits)
  • MATH 521: Life Contingencies II ( 3 credits)
  • MATH 523: Loss Models I (3 credits)
  • MATH 524: Loss Models II (3 credits)
  • MATH 547: Mathematics of Data (3 credits)
  • MATH 551: Introduction to Real Analysis (3 credits)
  • MATH 556: Applied Functional Analysis (3 credits)
  • MATH 561/IOE 510: Linear Programming (3 credits)
  • MATH 562/IOE 511: Continuous Optimization Methods (3 credits)
  • MATH 571: Numerical Linear Algebra (3 credits)
  • MATH 572: Numerical Methods for Differential Equations (3 credits)
  • MATH 597: Analysis II (3 credits)
  • MATH 602: Real Analysis II (3 credits)
  • MATH 625: Probability and Random Processes I (3 credits)
  • MATH 626:Probability and Random Processes II
  • MATH 628/629: Machine Learning for Finance I/II (2 + 2 credits)
  • MATH 657: Linear and Nonlinear Patrial Diff Equations (3 credits)
  • MATH 663/IOE 611: Nonlinear Programming (3 credits)
  • MATH 929: Internship (3 credits)

Statistics Courses (STATS)

  • STATS 415: Data Mining (4 credits)
  • STATS 503: Statistical Learning II: Multivariate Analysis (3 credits)
  • STATS 504: Statistical Consulting (3 credits)
  • STATS 507: Data Science and Analytics Using Python (3 credits)
  • STATS 511: Stat Inference (3 credits)
  • STATS 531: Analysis of Time Series (3 credits)
  • STATS 535: Reliability (3 credits)
    STATS 551: Bayesian Modeling (3 credits)
  • STATS 600: Linear Models (3 credits)
  • STATS 601: Statistical Learning (4 credits)
  • STATS 607: Programming and Numerical Methods in Statistics (1.5 credits)
  • STATS 608: Monte Carlo Methods in Statistics (3 credits)

Finance Courses (FIN)

  • FIN 466: Real Estate investment (3 credits)
  • FIN 551: Financial Management and Policy (3 credits)
  • FIN 575: Financial Modeling (1.5 credits)
  • FIN 580: Financial Derivatives in Corporate Finance (2.25 credits)
  • FIN 608: Capital Markets & Investment Strategies (2.25 credits)
  • FIN 609: Fixed Income Securities and Markets (2.25 credits)
  • FIN 612: International Finance Management I (2.25 credits)
  • FIN 614: International Finance Management II (2.25, credits)
  • FIN 621: Corporate Financial Policy (2.25 credits)
  • FIN 623: Venture Capital Finance (2.25 credits)
  • FIN 631: Risk Management in Banks and Financial Institutions (2.25 credits)
  • FIN 640: Financial Trading (1.5 credits)
  • FIN 645: Real Options in Valuation (2.25 credits)
  • FIN 725: Maize and Blue Fund (1.5 credits)
  • FIN 726: Maize and Blue Fund (1.5 credits)

Computer Science Courses (EECS)

  • EECS 402: Programming for Scientists and Engineers (4 credits)
  • EECS 445: Introduction to Machine Learning (4 credits)
  • EECS 453: Principles of Machine Learning (4 credits)
  • EECS 477: Intro to Algorithms (4 credits)
  • EECS 482: Introduction to Operating Systems (4 credits)
  • EECS 484: Database Management (4 credits)
  • EECS 498: Special Topics (select sections)
  • EECS 492: Introduction to Artificial Intelligence (4 credits)
  • EECS 505: Computational Data Science and Machine (4 credits)
  • EECS 545: Machine Learning (3 credits)
  • EECS 547: Electronic Commerce (3 credits)
  • EECS 551: Matrix Methods for Signal Processing, Data Analysis and Machine Learning (4 credits)
  • EECS 553: Machine Learn (ECE) (3 credits)
  • EECS 586: Design and Analysis of Algorithms (4 credits)
  • EECS 592: Foundations of Artificial Intelligence (4 credits)
  • EECS 595: Natural Language Processing (3 credits)
  • EECS 597: Language and Information (3 credits)
  • EECS 498: Reinforcement Learning Theory (Special Topics) (3 credits)
  • EECS 605: Data Science and Machine Learning Design (4 credits)

Economics Courses (ECON)

  • ECON 411: Monetary and Financial Theory (3 credits)
  • ECON 441: International Trade Theory (3 credits)
  • ECON 442: International Finance (3 credits)
  • ECON 454: Advanced Intro to Statistics and Econometrics II (3 to 4 credits)
  • ECON 501: Microeconomics (3 credits)
  • ECON 502: Macroeconomics (3 credits)
  • ECON 601: Microecon Theory I (1.5 credits)

Other Elective Courses

  • BIOSTAT 615: Statistical Computing (3 credits)
  • BIOSTAT 650: Applied Statics I: Linear Regression (4 credits)
  • BIOSTAT 801: Advanced Inference I (3 credits)
  • ENGR 599: Special Topics in Engineering – Multidisciplinary Design Projects (1-4 credits)
  • HS 650: Predictive Analytics (4 credits)
  • SI 506: Programming I (3 credits)
  • SI 507: Intermediate Programming (3 credits)
  • SI 561: Natural Language Processing (3 credits)
  • SI 618: Data Manipulation and Analysis (3 credits)
  • SI 630: Natural Language Processing: Algorithms and People (3 credits)
  • SI 670: Appld Machine Learng (3 credits)
  • TO 513: Spreadsheet Modeling and Applications (1.5 credits)
  • TO 515: Business Application Development with Visual Basic for Excel (2.25 credits)
  • TO 618: Applied Business Analytics and Decisions (3 credits)
  • TO 628: Advanced Big Data Analytics (2.25 credits)
  • TO 638: FinTech: Blockchain, Cryptocurrencies, and Other Technology Innovations In and Out of Finance (3 credits)

It is essential to prioritize the core course requirements within the program. Students are advised that making changes to their core course schedule without prior approval will lead to complications. Therefore, it is crucial to follow the approved course sequences and consult with the program before making any adjustments. For further details, please refer to our Quant Program Core Course Policy.