The median and the mode walked into a bar.
The bartender asks, “Where’s your other friend?”
The median says, “We don’t like him anymore. He’s mean.”
What is Mathematics, Statistics, and Finance?
The EngSci Mathematics, Statistics, and Finance major (MSF) teaches the theory behind the financial instruments and markets that impact our global economy, giving students a strong background in using engineering mathematics to tackle problems in any domain. The first of its kind in Canada, MSF provides students with the mathematical, statistical, and engineering tools they need to be successful in many industries. These include consulting engineering, finance, the public sector, energy, mining, insurance, banking, aerospace, supply chain management, risk management, manufacturing, and more.
Course themes include mathematics and statistics (including probability, stochastic processes, statistical computation, and econometrics), finance and financial engineering (including economics, option pricing, portfolio optimization, and real options), and computation (including numerical methods, optimization, Monte Carlo methods, and partial differential equations). MSF courses are taught by professors in U of T’s Departments of Mechanical & Industrial Engineering and Chemical Engineering & Applied Chemistry in cooperation with the Department of Statistics, the Department of Mathematics, and the Rotman School of Management.
Why Choose MSF?
Why Choose This Major?
You’re interested in:
- Math and statistics. Of course, you can’t escape math in engineering, but students who are particularly passionate about math might lean towards MSF (or Engineering Physics). The math in MSF is more related to data, statistics, and optimization.
- Economics or finance. MSF courses cover plenty of economic and financial theory, and techniques to analyze and predict economics. Knowing this theory is especially helpful if you want to study these subjects in graduate school.
- Combining math and programming through data processing, simulation, and computation.
- Generalizing data and modelling to many fields, especially in graduate studies.
- Working in almost any industry. Everyone relies on mathematics, statistics, and finance, so you can put your degree to excellent use.
The program’s location in downtown Toronto, extremely close to Canada’s financial heart, provides students access to professionals, companies, and excellent opportunities in this vibrant sector.
Where Can This Major Take You?
Recent EngSci MSF graduates have pursued graduate studies at top universities such as:
- Columbia University
- Cornell University
- MIT
- Stanford University
- University of Michigan
- University of Toronto
Sample employers for recent MSF graduates include:
- BCG
- BMO Investment Banking
- CPP
- Goldman Sachs
- IBM Consulting
- JP Morgan
- McKinsey & Company
- Yahoo.com
Upper-Year Insights
EngSci MSF 2T3 + 1 + PEY
“Some of the most interesting MSF courses are Financial Engineering (MIE375) and Financial Optimization Models (MIE377), both of which are taught by Roy Kwon [the chair of the MSF major] […] The foundation years give you the ability to understand and work with financial instruments, with a level of technical detail beyond what you can find almost anywhere else.“
“[My] advice when going into MSF is to connect the new content you’ll be learning back to the foundation years. MSF, more than most majors, will look and feel entirely different from [the foundation years]. The foundation will still be useful for everything in years 3 and 4, but you’ll have to apply it to contexts that you’ve never seen before. […] In [courses] taught through the Department of Mathematics, you’ll see similar concepts to the math and stats you’ve done before, but with different philosophies and styles behind how they’re studied and used. Similarly, in courses such as MIE375 and MIE377, you’ll be using the same math that you’ve learned in Ordinary Differential Equations (MAT292) and Calculus II (ESC195), but now applied to the world of financial instruments. The [key is to] relate the content back to what you’ve learned, rather than trying to start from scratch and understand everything all over again.”
Courses in Year 1 and Year 2 That Relate to Mathematics, Statistics, and Finance
Year 1
ESC103 will give you the basics of computer-assisted computation. The lab portion of this course introduces you to MATLAB, one of the world’s most popular programming languages for computation. You will also be introduced to a fundamental domain of math: linear algebra! MAT185 will give you a more rigorous, pure mathematical perspective to linear algebra.
ESC180 will introduce you to computer programming, an essential tool in computation and modelling. ESC190 will teach you how to implement algorithms, such as searching, sorting, and optimizing, as well as data structures, which are objects or systems in computers that store data in a useful way. With modern finance being so dependent on data and computers, the skills you will gain from these courses are indispensable.
ESC101 and ESC102 will involve a lot of stakeholder communication, risk management, and collaboration as you and your team solve a real-world engineering opportunity. You might need to consider factors such as budget, and the management, project planning, and project execution skills you will develop during these courses will be essential for a career in MSF (or any field, for that matter).
Year 2
MAT292 will build upon the differential equations you learned in Calculus I. There are only a few types of differential equations for which we can produce exact answers using mathematical techniques. We can find an approximate solution for the rest using a computer. Differential equations are extremely important to the finance field. A derivative (the main part of a differential equation) is really just the trend of a function at any point. A trend gives us some hints about what’s going to happen next. On a simplified level, when we make predictions in finance, we’re analyzing these trends/derivatives to make a prediction.
MIE286 will cover the basics of probability and statistics. You’ll apply the techniques of these courses in MSF to gain powerful analytical and predictive tools.
ESC203 teaches you about the global implications of engineering. Since markets impact and are impacted by global events, it is crucial to be knowledgeable about world events, policy, and sustainability throughout your engineering career.
Interesting Courses in This Major
MIE375: Financial Engineering
This course will cover the fundamentals of financial engineering through interest rate theory, fixed income securities, bond portfolio construction, term structure of interest rates, mean-variance optimization theory, the capital asset pricing model, arbitrage pricing theory, forwards and futures, and an introduction to option pricing and structured finance.
MIE377: Financial Optimization Models
In this course, you will learn how to create optimization models for the design and selection of an optimal investment portfolio through risk management, mean variance analysis, models for fixed income, scenario optimization, dynamic portfolio optimization with stochastic programming, index funds, designing financial products, and scenario generation. Applications of these topics include international asset allocation, corporate bond portfolios, and insurance policies with guarantees.
MIE424: Optimization in Machine Learning
This course is about applying machine learning into optimization problems within finance and marketing, such as stock return forecasting, portfolio management, fraud detection, and customer segmentation.
CHE471: Modelling in Biological and Chemical Systems
This course applies differential equations into problem-solving within biological contexts such as environmental issues, chemical and biochemical processes, and biomedical systems. Topics include physical laws, compartmental and distributed models, conservation laws for discrete and continuous systems, and more.
See the full course listing for each EngSci major in the academic calendar.
Beyond First Year?
University of Toronto Engineering Finance Association (UTEFA)
UTEFA aims to teach students about the financial industry through engaging investment activities. UTEFA hosts weekly meetings where you can learn about capital markets, compete in stock pitches, network and learn from experienced industry professionals, and more. To learn about their upcoming events, check out their schedule here.
University of Toronto Sports Analytics Student Group (UTSPAN)
UTSPAN combines many mathematical fields to study and predict the performance of sports teams. The student group’s goals are to connect members who share a passion for sports analytics, organize and conduct research, and connect members to industry leaders in the field. UTSPAN is always working on cool projects, including working with Canada’s national basketball team. If you want to combine programming, math, and sports, you can’t go wrong with this club. Fun fact: they consistently place highly in the NFL’s annual Big Data Bowl, and even earned first place in 2023! Here is a link to their Big Data Bowl report in the past year: 2024 NFL Big Data Bowl Projects by UTSPAN
Clubs at the Rotman School of Management
The Rotman School of Management, much like our own Faculty of Applied Science and Engineering, has many associated clubs through which you can connect with industry leaders, conduct research, and engage in community and university events. The clubs cover a variety of topics related to MSF such as asset management, venture capital, finance, and more.
Visit the Skule Clubs and Design Teams pages to find more extracurriculars.
Check out the EngSci majors website here for more info: