In this article, I compiled 120 free online courses offered by the 60 best universities in the world for studying math in 2023.

I did so by combining popular university rankings to identify the best institutions, and then I used the Class Central database to find all their math online courses.

If you’d like to jump to the course list, you can jump directly to the course list. If you’d like to know how I built the list, or if you’d like to look at the raw data or Jupyter Notebook, keep reading.

**Methodology**

I built the list following the same data-driven approach I used to build my list of computer science courses from the top CS universities.

**First**, I identified the leading world university rankings. Since I was specifically interested in math, I looked at their latest rankings of the best universities for studying math (or closest superset). Here are the rankings I ended up using:

- QS: World University Ranking 2023 — Mathematics
- Times Higher Education: World University Ranking 2023 — Physical Sciences
- Shanghai Ranking: Academic Ranking of World Universities 2022 — Mathematics

**Second**, I scraped each ranking. In the simplest cases, this involved finding the underlying API, allowing me to directly request the ranking data in JSON format using Scrapy. In the most complex case, this involved crawling the ranking page by page using Playwright.

You can find the implementation details and raw data in my GitHub repo.

**Third**, I used JupyterLab to process the data. In essence, this involved cleaning the raw data, normalizing the university names across the rankings, and combining the three rankings into one by averaging the position of each institution across each ranking.

As you can see in the image above, I found that the top three math institutions are:

You can also find the data processing details and full ranking in my GitHub repo.

**Fourth**, I used the Class Central database, with its over 150K online courses, to find all the math courses offered by the universities in the ranking.

The end result is a list of 120 online courses offered by 60 of the best universities in the world for studying math in 2023.

While processing the data, I noticed something interesting: 59 of the top 60 universities offer online courses, a lot more than I would have guessed. The world’s top institutions are very prolific creators of online courses.

**Online Math Courses**

The full list is split into subjects. Click on a subject below to go to the relevant section.

With 120 courses to pick from, I hope you find something you like. But if these aren’t enough, check out the Class Central catalog, which has over 150K online courses, many of them free or free-to-audit.

# Mathematics Online Courses (30)

- Introduction to Mathematical Thinking from
*Stanford University*★★★★☆(53) - Effective Thinking Through Mathematics from
*The University of Texas at Austin*★★★★★(14) - How to Learn Math: For Students from
*Stanford University*★★★★☆(17) - Convex Optimization from
*Stanford University*★★★★★(8) - Mathematical Thinking in Computer Science from
*University of California, San Diego*★★★★★(2) - A-level Mathematics for Year 12 - Course 1: Algebraic Methods, Graphs and Applied Mathematics Methods from
*Imperial College London*★★★★★(2) - Fun with Prime Numbers: The Mysterious World of Mathematics from
*Kyoto University*★★★★☆(2) - Cómo Aprender Matemáticas - Para Estudiantes from
*Stanford University* - Transfer Functions and the Laplace Transform from
*Massachusetts Institute of Technology* - Delivery Problem from
*University of California, San Diego* - Analyse I (partie 1) : Prélude, notions de base, les nombres réels from
*École Polytechnique Fédérale de Lausanne* - Analyse I (partie 2) : Introduction aux nombres complexes from
*École Polytechnique Fédérale de Lausanne* - Analyse I (partie 3) : Suites de nombres réels I et II from
*École Polytechnique Fédérale de Lausanne* - Analyse I (partie 4) : Limite d'une fonction, fonctions continues from
*École Polytechnique Fédérale de Lausanne* - Analyse I (partie 5) : Fonctions continues et fonctions dérivables, la fonction dérivée from
*École Polytechnique Fédérale de Lausanne* - Analyse I (partie 6) : Etudes des fonctions, développements limités from
*École Polytechnique Fédérale de Lausanne* - Analyse I (partie 7) : Intégrales indéfinies et définies, intégration (chapitres choisis) from
*École Polytechnique Fédérale de Lausanne* - A-level Further Mathematics for Year 12 - Course 1: Complex Numbers, Matrices, Roots of Polynomial Equations and Vectors from
*Imperial College London* - A-level Further Mathematics for Year 13 - Course 1: Differential Equations, Further Integration, Curve Sketching, Complex Numbers, the Vector Product and Further Matrices from
*Imperial College London* - Further Mathematics Year 13 course 2: Applications of Differential Equations, Momentum, Work, Energy & Power, The Poisson Distribution, The Central Limit Theorem, Chi Squared Tests, Type I and II Errors from
*Imperial College London* - 离散数学 from
*Shanghai Jiao Tong University* - More Fun with Prime Numbers from
*Kyoto University* - Introduction to Complexity Science from
*Nanyang Technological University* - Introduction to Graph Theory from
*University of California, San Diego*★★★★☆(1) - Graph Theory and Additive Combinatorics (Fall 2019) from
*Massachusetts Institute of Technology* - Cours préparatoire: Fonctions Trigonométriques, Logarithmiques et Exponentielles from
*École Polytechnique Fédérale de Lausanne*★★★★☆(1) - 离散数学概论 Discrete Mathematics Generality from
*Peking University* - Discrete Mathematics from
*Shanghai Jiao Tong University*

# Statistics & Probability Online Courses (38)

- Intro to Statistics from
*Stanford University*★★★★☆(39) - Probability - The Science of Uncertainty and Data from
*Massachusetts Institute of Technology*★★★★★(34) - Statistical Learning from
*Stanford University*★★★★☆(28) - Bayesian Statistics from
*Duke University*★★★☆☆(12) - Fundamentals of Statistics from
*Massachusetts Institute of Technology*★★★★☆(10) - Introduction to Probability and Data with R from
*Duke University*★★★★☆(6) - Fat Chance: Probability from the Ground Up from
*Harvard University*★★★★★(5) - Statistical Inference and Modeling for High-throughput Experiments from
*Harvard University*★★★★★(4) - Computational Probability and Inference from
*Massachusetts Institute of Technology*★★★★★(3) - Introduction to Statistics from
*Stanford University*★★★★★(2) - Statistics: Unlocking the World of Data from
*University of Edinburgh*★★★★☆(2) - Introduction to Probability from
*Harvard University*★★★★★(1) - Statistics for Applications (Fall 2016) from
*Massachusetts Institute of Technology*★★★★★(1) - A Crash Course in Causality: Inferring Causal Effects from Observational Data from
*University of Pennsylvania*★★★★☆(1) - Hypothesis Testing in Public Health from
*Johns Hopkins University*★★★★★(1) - Summary Statistics in Public Health from
*Johns Hopkins University*★★★★★(1) - Multiple Regression Analysis in Public Health from
*Johns Hopkins University*★★★★★(1) - Introduction to Statistics & Data Analysis in Public Health from
*Imperial College London*★★★★★(1) - Introduction to Probability Management from
*Stanford University* - Probabilistic Systems Analysis and Applied Probability (Fall 2010) from
*Massachusetts Institute of Technology* - Probabilistic Systems Analysis and Applied Probability (Fall 2013) from
*Massachusetts Institute of Technology* - Introduction to Probability: Part II – Inference & Processes from
*Massachusetts Institute of Technology* - What are the Chances? Probability and Uncertainty in Statistics from
*Johns Hopkins University* - Causal Inference 2 from
*Columbia University* - Causal Inference from
*Columbia University* - R을 사용한 확률 및 데이터 소개 from
*Duke University* - Inferenzstatistik from
*Duke University* - Inferential Statistics from
*Duke University* - Probability and Statistics IV: Confidence Intervals and Hypothesis Tests from
*Georgia Institute of Technology* - Probability and Statistics II: Random Variables – Great Expectations to Bell Curves from
*Georgia Institute of Technology* - Probability and Statistics III: A Gentle Introduction to Statistics from
*Georgia Institute of Technology* - Probability and Statistics I: A Gentle Introduction to Probability from
*Georgia Institute of Technology* - Probability: Basic Concepts & Discrete Random Variables from
*Purdue University* - Probability: Distribution Models & Continuous Random Variables from
*Purdue University* - Selected Topics on Discrete Choice from
*École Polytechnique Fédérale de Lausanne* - Logistic Regression in R for Public Health from
*Imperial College London* - Survival Analysis in R for Public Health from
*Imperial College London* - Statistics Using Python from
*University of Wisconsin–Madison*

# Algebra Online Courses (21)

- Linear Algebra - Foundations to Frontiers from
*The University of Texas at Austin*★★★★☆(14) - Introduction to Linear Models and Matrix Algebra from
*Harvard University*★★★★☆(12) - Mathematics for Machine Learning: Linear Algebra from
*Imperial College London*★★★☆☆(8) - Matrix Methods in Data Analysis, Signal Processing, and Machine Learning (Spring 2018) from
*Massachusetts Institute of Technology*★★★★★(2) - Algèbre Linéaire (Partie 1) from
*École Polytechnique Fédérale de Lausanne*★★★★★(2) - Linear Algebra III: Determinants and Eigenvalues from
*Georgia Institute of Technology*★★★★★(1) - Linear Algebra IV: Orthogonality & Symmetric Matrices and the SVD from
*Georgia Institute of Technology*★★★★★(1) - Algèbre Linéaire (Partie 3) from
*École Polytechnique Fédérale de Lausanne*★★★★★(1) - Algèbre Linéaire (Partie 2) from
*École Polytechnique Fédérale de Lausanne*★★★★★(1) - Linear Regression in R for Public Health from
*Imperial College London*★★★★★(1) - Linear Algebra (Fall 2011) from
*Massachusetts Institute of Technology* - Linear Algebra II: Matrix Algebra from
*Georgia Institute of Technology* - Linear Algebra I: Linear Equations from
*Georgia Institute of Technology* - Advanced Linear Algebra: Foundations to Frontiers from
*The University of Texas at Austin* - Data Science: Linear Regression from
*Harvard University* - Linear Regression and Modeling from
*Duke University* - Analytic Combinatorics from
*Princeton University*★★★★☆(3) - Algebra: Elementary to Advanced - Functions & Applications from
*Johns Hopkins University*★★★★☆(1) - Algebra: Elementary to Advanced - Polynomials and Roots from
*Johns Hopkins University* - Algebra: Elementary to Advanced - Equations & Inequalities from
*Johns Hopkins University* - Optimization: principles and algorithms - Linear optimization from
*École Polytechnique Fédérale de Lausanne*

# Calculus Online Courses (29)

- Calculus: Single Variable Part 1 - Functions from
*University of Pennsylvania*★★★★★(8) - Calculus: Single Variable Part 2 - Differentiation from
*University of Pennsylvania*★★★★★(5) - Calculus: Single Variable Part 3 - Integration from
*University of Pennsylvania*★★★★☆(4) - Introduction to Differential Equations from
*Massachusetts Institute of Technology*★★★★★(7) - Differential Equations: 2x2 Systems from
*Massachusetts Institute of Technology*★★★★★(5) - Differential Equations: Fourier Series and Partial Differential Equations from
*Massachusetts Institute of Technology*★★★★★(3) - Calculus: Single Variable Part 4 - Applications from
*University of Pennsylvania*★★★★★(3) - Calculus Applied! from
*Harvard University*★★★★★(2) - Combinatorial Mathematics | 组合数学 from
*Tsinghua University*★★★★☆(2) - Single Variable Calculus (Fall 2006) from
*Massachusetts Institute of Technology*★★★★★(1) - Calculus through Data & Modeling: Differentiation Rules from
*Johns Hopkins University*★★★★☆(1) - Differential Equations: Linear Algebra and NxN Systems of Differential Equations from
*Massachusetts Institute of Technology*★★★★★(2) - Differential Equations (Fall 2011) from
*Massachusetts Institute of Technology*★★★★★(1) - Single Variable Calculus from
*University of Pennsylvania* - Calculus through Data & Modeling: Applying Differentiation from
*Johns Hopkins University* - Calculus through Data & Modeling: Limits & Derivatives from
*Johns Hopkins University* - Calculus through Data & Modeling: Precalculus Review from
*Johns Hopkins University* - Calculus through Data & Modelling: Techniques of Integration from
*Johns Hopkins University* - Calculus through Data & Modelling: Series and Integration from
*Johns Hopkins University* - Applied Calculus with Python from
*Johns Hopkins University* - Calculus through Data & Modelling: Integration Applications from
*Johns Hopkins University* - A-Level Further Mathematics for Year 12 - Course 2: 3 x 3 Matrices, Mathematical Induction, Calculus Methods and Applications, Maclaurin Series, Complex Numbers and Polar Coordinates from
*Imperial College London* - Discovery Precalculus: A Creative and Connected Approach from
*The University of Texas at Austin*★★★★★(3) - Precalculus from
*Modern States*★★★★★(1) - Precalculus: Relations and Functions from
*Johns Hopkins University* - Precalculus: Periodic Functions from
*Johns Hopkins University* - Precalculus: Mathematical Modeling from
*Johns Hopkins University* - Multivariable Calculus (Fall 2007) from
*Massachusetts Institute of Technology*★★★★★(1) - Calculus through Data & Modelling: Vector Calculus from
*Johns Hopkins University*