Mathematics Primer
Build the algebra, calculus, linear algebra and probability foundations used throughout quantitative finance.
Why study Mathematics Primer?
A pricing formula is useful only when you can read it, rearrange it and understand how its inputs change the result. This primer builds that fluency before notation becomes a barrier to studying returns, risk or derivatives.
Who this is for
Start here if algebra, calculus or matrix notation feels rusty. You do not need a finance background.
What you should be able to do
- Manipulate functions, exponentials and logarithms.
- Use differentiation, integration, vectors and matrices.
- Interpret probability, expectation, variance and regression.
An example of the work this prepares you for
An annotated financial calculation that explains compounding, a rate of change and a weighted portfolio in your own words.
Before you start
You can begin without prior quant-finance study. Use the resources below to refresh the basics as you work through the material.
A preview of the learning journey
The lessons build towards these kinds of reasoning and practical work.
Read financial formulas
Move comfortably between symbols, graphs and numerical examples.
Understand change
Recognise how a small input change affects a financial quantity.
Reason about uncertainty
Interpret averages, variability and simple dependence before using a model.
Members work through the detailed lessons, derivations, worked examples and solutions inside the learning dashboard.
Explore lesson previews by topic
Open a topic preview to see its introduction, learning objectives and prerequisites. Previous and next links let you explore the lessons in study order. Full lessons are available in the member dashboard; selected samples are free to read in full.
Free resources to start learning
Use these alongside the programme or to prepare independently. Start with the introductory material, work through an example, then return to the research papers when the underlying ideas are familiar.
Single Variable Calculus
MIT OpenCourseWare · David Jerison
Use the worked examples and problem sets to practise differentiation and integration.
Introduction to Applied Linear Algebra
Stephen Boyd and Lieven Vandenberghe
Read the opening chapters for vectors, weighted sums and matrix notation.
Statistics 110: Probability on YouTube
Harvard · Joe Blitzstein
Watch the early lectures to build intuition for uncertainty.
Links reviewed 14 October 2026. Free refers to the linked reading, notes or videos; printed books and certificates may cost extra.
Find more papers and learning materials in the SelfMadeQuant Directory.
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