QMA 101: Mathematics for Finance
| Course Code | QMA 101 |
| Course Name | Mathematics for Finance |
| Department | Mathematics |
| Semester Offered | Odd (Term 1) |
| Tuition Hours | 30 hours |
| Course Level | Foundational |
| Pre-requisite | - |
| Co-requisite | FTM 101, TFS 101 |
| Course Objective | Finance looks messy on the surface. Prices move, markets react, people panic. But underneath all of that chaos sits structure. Mathematics is what exposes that structure. This course is about building the numerical and logical backbone of financial thinking. You will learn how money grows, how risk is quantified, and how decisions get modeled. Not as abstract math problems, but as tools you will immediately use while building products and making decisions. You will work through functions, sequences, algebra, calculus, and linear algebra, but always tied to real questions: How does compounding actually behave? What does “optimization” mean when allocating capital? How do portfolios emerge from simple matrix operations? By the end of the course, math should stop feeling like a subject and start feeling like a way to think about money with precision. |
| Course Philosophy | This course emphasizes
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| Course Learning Outcomes | Upon successful completion of this course, students will be able to:
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| Course Author | Sagar Udasi MSc Statistics and Data Science with Computational Finance from The University of Edinburgh. Contact: sagar.l.udasi@gmail.com |
| Course Organiser | TBD |
| No. | Lecture Title | Concepts Covered | Lecture Objective |
|---|---|---|---|
| 01 | Why Money Needs Mathematics | Role of math in finance, modeling reality, deterministic vs uncertain systems | Build respect for math as a decision-making tool, not an academic exercise |
| 02 | Everything Is a Function (Even Your Salary) | Functions, mappings, domain and range, financial relationships | Understand how financial variables depend on each other |
| 03 | The Secret Life of Compounding | Sequences, exponential growth, compound interest | Learn how money actually grows over time and why small rates matter |
| 04 | Discounting: Time Travel for Money | Present value, future value, discount factors | Connect valuation to time and opportunity cost |
| 05 | When Growth Becomes Continuous | Limits, intuition of calculus, continuous compounding | Transition from discrete to continuous thinking in finance |
| 06 | Change Is Everything | Derivatives, rates of change, marginal thinking | Understand sensitivity: how small changes affect outcomes |
| 07 | Optimization: Where Should You Put Your Money? | Maxima, minima, optimization problems | Apply math to real allocation decisions in portfolios and products |
| 08 | Constraints Make Decisions Real | Constrained optimization, Lagrange intuition (informal) | Understand trade-offs in real-world financial decisions |
| 09 | Vectors: The Language of Portfolios | Vectors, representation of assets and returns | Model portfolios as mathematical objects |
| 10 | The Geometry of Risk | Dot product, correlation intuition, projections | Understand diversification and relationships between assets |
| 11 | Matrices: Machines That Transform Data | Matrix operations, transformations, systems of equations | Learn how financial systems scale computations |
| 12 | Solving Real Systems | Linear systems, Gaussian elimination (intuitive) | Solve multi-variable financial problems |
| 13 | From Data to Decisions | Introduction to financial datasets, structuring data mathematically | Bridge math with real financial data used in capstone |
| 14 | When Models Meet Reality | Model limitations, noise, assumptions in finance | Develop skepticism and critical thinking |
| 15 | Building a Simple Financial Model | End-to-end modeling: compounding + optimization | Apply multiple concepts in a unified problem |
| 16 | Portfolio Math in Action | Portfolio returns, weighted averages, simple risk measures | Direct connection to Term 2 investment capstone |
| 17 | Sensitivity and Scenario Thinking | Scenario analysis, stress intuition | Prepare for uncertainty in decision-making |
| 18 | Debugging Your Math | Common mistakes, numerical errors, interpretation issues | Build discipline in mathematical reasoning |
| 19 | From Equations to Code | Translating math into computation (Python-ready thinking) | Prepare for implementation in TFS 102 and beyond |
| 20 | The Math Behind Your Capstone | Integration of all concepts into fintech product thinking | Ensure students can apply math directly to their Term 1 capstone |
| Component | Weightage |
|---|---|
| Problem Sets (3 total) | 30% |
| Applied Financial Modeling Assignment | 30% |
| Final Written Examination (2 hours) | 40% |
| Type | Resource | Provider |
|---|---|---|
| Lecture | Mathematics for Machine Learning | Imperial College London (Coursera) |
| Lecture | Essence of Calculus | Grant Sanderson (3Blue1Brown) |
| Reading | Mathematics for Finance: An Introduction to Financial Engineering | Marek Capinski & Tomasz Zastawniak |
| Tool | Khan Academy (Algebra & Calculus) | Khan Academy |