Learn Advanced Mathematics The internet is a great place to share information, but it might be overwhelming. This page is for you when you would like to learn and build on mathematical intuition, either starting from scratch or to recap what you might have forgotten.

Get yourself familiar with the basics of algebra, geometry, trigonometry, differential and integral calculus, and some linear algebra. The courses given during secondary school or highschool are mainly mechanical in nature. However, during the advanced courses you will notice that the mathematics will become more formal, with an emphasise on proof writing.

For motivation to get started or to keep going, check out this short course from Stanford.

• Foundations

  • Khanacademy. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Brilliant. [Videos: No; Notes: Yes; Exercise: Yes]
  • ExamSolutions. [Videos: No; Notes: Yes; Exercise: Yes]

• Number theory

  • Keith Devlin, Stanford University, Coursera. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Abhinav Kumar, MIT OCW. [Videos: No; Notes: Yes; Exercise: Yes]
  • Tom Leighton, MIT OCW. [Videos: Yes; Notes: Yes; Exercise: Yes]

• Set Theory

  • Burak Kaya. [Videos: Yes; Notes: No; Exercise: No]
  • PocketPrep. [Videos: Yes; Notes: No; Exercise: No]

• Group Theory

  • Ladislau Fernandes. [Videos: Yes; Notes: No; Exercise: No]
  • Indian Institute of Technology Bombay. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • J.S. Milne. [Videos: No; Notes: Yes; Exercise: Yes]
  • Jonathan Evans. [Videos: Yes; Notes: No; Exercise: No]
  • Brilliant. [Videos: No; Notes: Yes; Exercise: Yes]

• Linear Algebra

  • Gilbert Strang, MIT OCW. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Gilbert Strang, MatLab course. [Videos: Yes; Notes: No; Exercise: Yes]
  • Adrian Banner, Princeton University. [Videos: Yes; Notes: No; Exercise: No]
  • 3Blue1Brown. [Videos: Yes; Notes: No; Exercise: No]
  • Brilliant. [Videos: No; Notes: Yes; Exercise: Yes]

• Abstract Algebra

  • Gross, Harvard University. [Videos: Yes; Notes: No; Exercise: No]
  • Lother Gottsche. [Videos: Yes; Notes: No; Exercise: No]

• Topology & Metric Spaces

  • James Munkres, MIT OCW. [Videos: No; Notes: Yes; Exercise: No]
  • J. Rasmussen, Tripos Cambridge. [Videos: No; Notes: Yes; Exercise: No]
  • Daniel Chan. [Videos: Yes; Notes: No; Exercise: No]
  • Eliott724, Metric Spaces. [Videos: Yes; Notes: No; Exercise: No]
  • Eliott724, Topology. [Videos: Yes; Notes: No; Exercise: No]
  • Topology spaces: part 1part 2.
  • Topological subspaces: part 1part 2.
  • Continuous functions: part 1part 2part 3.
  • Homeomorphisms: part 1part 2.
  • Standard topology: part 1part 2.
  • Topological manifolds: part 1part 2part 3.
  • E-Academy. [Videos: Yes; Notes: No; Exercise: No]
  • Tadashi Tokieda. [Videos: Yes; Notes: No; Exercise: No]
  • Jonathan Evans. [Videos: Yes; Notes: No; Exercise: No]
  • Bruno Zimmerman. [Videos: Yes; Notes: No; Exercise: No]

• Algebraic Topology

  • N.J. Wildberger, UNSW. [Videos: Yes; Notes: No; Exercise: No]
  • Pierre Albin, Illinois. [Videos: Yes; Notes: No; Exercise: No]
  • Fernando Rodriguez Villegas. [Videos: Yes; Notes: No; Exercise: No]
  • Haynes Miller, MIT OCW. [Videos: No; Notes: Yes; Exercise: Yes]
  • Isabel Darcy, University of Iowa. [Videos: Yes; Notes: Yes; Exercise: No]

• Euclidean Geometry

  • Rich Cochrane & Andrew McGettigan . [Videos: No; Notes: Yes; Exercise: No]

• Algebraic Geometry

  • Lothar Gottsche. [Videos: Yes; Notes: No; Exercise: No]
  • Kiran Kedlaya, MIT OCW. [Videos: No; Notes: Yes; Exercise: Yes]
  • Ravi Vakil, MIT. [Videos: No; Notes: Yes; Exercise: No]
  • Tadashi Tokieda. [Videos: Yes; Notes: No; Exercise: No]

• Measure Theory

  • Mathematicalmonk. [Videos: Yes; Notes: No; Exercise: No]
  • Jeff Viaclovsky, MIT OCW. [Videos: No; Notes: Yes; Exercise: No]
  • NPTEL. [Videos: Yes; Notes: Yes; Exercise: No]

• Differential Geometry

  • N.J. Wildberger, UNSW Differential Geometry. [Videos: Yes; Notes: No; Exercise: No]
  • Claudio Arezzo. [Videos: Yes; Notes: No; Exercise: No]
  • N.J. Wildberger, UNSW, Universal Hyperbolic Geometry. [Videos: Yes; Notes: No; Exercise: No]

• Real Analysis

  • Francis Su, Harvey Mudd College. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Lectures.
  • Notes.
  • Course website.
  • Joel Feinstein, University of Nottingham. [Videos: Yes; Notes: No; Exercise: No]
  • MIT OCW, Analysis Series. [Videos: No; Notes: Yes; Exercise: Yes]
  • Katrin Wehrheim, Analysis I
  • Paul Seidel, Real Analysis.
  • Victor Guillemin, Analysis II.
  • Arthur Parzygnat, Analysis II. [Videos: Yes; Notes: No; Exercise: No]
  • Art of Problem Solving, Proof Writing [Videos: No; Notes: Yes; Exercise: Yes]
  • Mathforge, The Nature of Proof [Videos: No; Notes: Yes; Exercise: No]

• Complex Analysis

  • Petra Bonfert-Taylor, Wesleyan University, Coursera. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • James Cook, ASU. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Gross, MIT. [Videos: Yes; Notes: No; Exercise: No]
  • Fabio Vlacci. [Videos: Yes; Notes: No; Exercise: No]
  • Alar Toomre, MIT OCW. [Videos: Yes; Notes: No; Exercise: No]
  • R. Rosales, MIT OCW. [Videos: No; Notes: No; Exercise: Yes]

• Numerical Analysis

  • Evgeni Burovski, Coursera. [Videos: Yes; Notes: No; Exercise: No]
  • Justin Solomon, Stanford University. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Laurent Demanet, MIT OCW. [Videos: No; Notes: Yes; Exercise: Yes]
  • stemez.com. [Videos: No; Notes: No; Exercise: Yes]
  • Vivi Andasari, Boston University, using Python. [Videos: No; Notes: Yes; Exercise: Yes]
  • Todd Young & Martin Mohlenkamp, Ohio University, using MatLab. [Videos: No; Notes: Yes; Exercise: Yes]
  • Wikiversity. [Videos: No; Notes: Yes; Exercise: Yes]

• Single-Variable Calculus

  • Robert Ghrist, UPenn, Coursera series. [Videos: Yes; Notes: Yes; Exercise: Yes]:
    • Part 1: Functions
    • Part 2: Differentiation
    • Part 3: Integration
    • Part 4: Applications
    • Part 5: Numerical methods, Convergence, Taylor series
  • Khanacademy, Calculus 1. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Khanacademy, Calculus 2. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • 3Blue1Brown. [Videos: Yes; Notes: No; Exercise: No]
  • Brilliant. [Videos: No; Notes: Yes; Exercise: Yes]

• Multi-Variable Calculus

  • Denis Auroux, MIT OCW. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Math Insight. [Videos: Yes; Notes: Yes; Exercise: No]
  • Khanacademy. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Brilliant. [Videos: Yes; Notes: Yes; Exercise: Yes]

• Differential Equations

  • Arthur Mattuck & Haynes Miller, MIT OCW. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Khanacademy. [Videos: Yes; Notes: Yes; Exercise. Yes]
  • Gilbert Strang, MatLab course. [Videos: Yes; Notes: No; Exercise: Yes]

• Vector Calculus

  • Jeffrey Chasnov, Hong Kong University, Coursera. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Brilliant. [Videos: No; Notes: Yes; Exercise: Yes]

• Partial Differential Equations

  • Steven G. Johnson, MIT OCW. [Videos: No; Notes: Yes; Exercise: Yes]
  • Jared Speck, MIT OCW. [Videos: No; Notes: Yes; Exercise: No]
  • Matthew Hancock, MIT OCW. [Videos: No; Notes: Yes; Exercise: Yes]
  • Lawrence Guth, MIT OCW. [Videos: No; Notes: Yes; Exercise: Yes]
  • Giovanni Bellettini. [Videos: Yes; Notes: No; Exercise: No]
  • Faculty of Khan. [Videos: Yes; Notes: No; Exercise: No]
  • Christopher Lum. [Videos: Yes; Notes: No; Exercise: No]
  • Commutant. [Videos: Yes; Notes: No; Exercise: No]
  • Saylor.org. [Videos: No; Notes: Yes; Exercise: No]
  • Philippe Trinh, University of Bath. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Lamar University. [Videos: Yes; Notes: Yes; Exercise: Yes]

• Dynamics & Chaos

  • Steven Strogatz, Cornell University. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • David Feldman, Santa Fe Institute. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Math Insight. [Videos: Yes; Notes: No; Exercise: No]
  • Rodolfo Rosales, MIT OCW. [Videos: No; Notes: Yes; Exercise: Yes]
  • George Datseris, Max Planck Institute, using Julia. [Videos: Yes; Notes: No; Exercise: No]

• Stochastic Differential Equations

  • Vladimir Panov, Coursera. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Robert Gallager, MIT OCW. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • MathWorks. [Videos: No; Notes: Yes; Exercise: Yes]
  • Bill Bialek. [Videos: No; Notes: Yes; Exercise: Yes]
  • University of Chicago, Brownian Motion. [Videos: No; Notes: Yes; Exercise: No]
  • Quantpie. [Videos: Yes; Notes: No; Exercise: Yes]
  • Stochastic Lifestyle, using Julia: [Videos: No; Notes: Yes; Exercise: Yes]
  • Jeff Gore, MIT OCW, part of Systems Biology. [Videos: Yes; Notes: No; Exercise: No]

• Probability

  • Jeremy Orloff, MIT OCW. [Videos: No; Notes: Yes; Exercise: Yes]
  • Khanacademy.[Videos: Yes; Notes: Yes; Exercise: Yes]
  • Duke University, Coursera. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Arkady Etkin. [Videos: Yes; Notes: No; Exercise: No]
  • Brilliant.[Videos: No; Notes: Yes; Exercise: Yes]

• Statistics

  • Jeremy Orloff, MIT OCW. [Videos: No; Notes: Yes; Exercise: Yes]
  • Philippe Rigollet, MIT OCW. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Khanacademy. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Mine Çetinkaya-Rundel, Duke University. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Brilliant. [Videos: No; Notes: Yes; Exercise: Yes]

• Perturbation Theory

  • Nitin Upadhyaya. [Videos: Yes; Notes: No; Exercise: No]
  • John Hunter. [Videos: No; Notes: Yes; Exercise: No]
  • Erika May. [Videos: No; Notes: Yes; Exercise: No]
  • Christopher Jones. [Videos: No; Notes: Yes; Exercise: No]

• Fluid Dynamics

  • Matthew Juniper, University of Cambridge. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Kripa Varanasi, MIT OCW. [Videos: No; Notes: Yes; Exercise: Yes]

• Quantum Mechanics

  • Allan Adams, MIT OCW. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Brant Carlson. [Videos: Yes; Notes: No; Exercise: No]

• Algorithms

  • Robert Sedgewick, Princeton University, Coursera. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Kevin Wayne & Robert Sedgewick, Princeton University, Coursera, Algorithms I. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Kevin Wayne & Robert Sedgewick, Princeton University, Coursera, Algorithms II. [Videos: Yes; Notes: Yes; Exercise: Yes]

• Optimisation

  • NPTEL. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Bukin, Coursera, for Economics. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Hentenryck, Coursera, Discrete Optimization. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Lee, Coursera, Solving Algorithms for Discrete Optimization. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Stuckey, Coursera, Basic Modeling for Discrete Optimization. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Lee, Coursera, Advanced Modeling for Discrete Optimization. [Videos: Yes; Notes: Yes; Exercise: Yes]

• Game Theory

  • Ben Polak, Yale University. [Videos: Yes; Notes: Yes; Exercise: No]
  • Matthew Jackson & Kevin Leyton-Brown & Yoav Shoham, Coursera, Game Theory I. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Matthew Jackson & Kevin Leyton-Brown & Yoav Shoham, Coursera, Game Theory II. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Justin Grana, Complex Explorer, Game Theory I. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Justin Grana, Complex Explorer, Game Theory II. [Videos: Yes; Notes: Yes; Exercise: Yes]

• Information Theory

  • Seth Lloyd, MIT. [Videos: Yes; Notes: No; Exercise: Yes]

• Methods for Engineers

  • Gilbert Strang, MIT OCW. [Videos: Yes; Notes: No; Exercise: No]

• Signals and Systems

  • Gadre, edX. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Freeman, MIT OCW. [Videos: Yes; Notes: Yes; Exercise: Yes]

• Dynamic Systems and Control

  • Emilio Frazzoli, MIT OCW. [Videos: No; Notes: Yes; Exercise: Yes].

Data science uses different methods to understand data. It encompasses a broad range of skills, such as data management, statistics, visualization and computer science.

• Courses

  • John Hopkins University. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • TU Delft. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • John Hopkins University, Toolbox. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • IBM. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Udacity. [Videos: No; Notes: Yes; Exercise: Yes]
  • EdX. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • John Hopkins University, Coursera, using R. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • University of Michigan, Coursera, using Python. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • O'Reilly. [Videos: No; Notes: Yes; Exercise: Yes]

• Podcasts and Channels

  • O'Reilly Data Show, Ben Lorica.
  • Data Stories, Enrico Bertini & Moritz Stefaner.
  • Two Minute Papers, Károly Zsolnai-Fehér.

• Code

  • Oracle Data Science.
  • Codecademy.
  • CodeWars.
  • Joel Grus.
  • O'Reilly.

Machine Learning (ML) is used for making predictions without having someone explicitly telling/coding the rules. In this way, the computer itself needs to find patterns in big data sets in order to make a prediction. There are different approaches in ML, such as Supervised Learning, Unsupervised Learning, and Reinforcement Learning. All these models look for patterns and relationships in data to make predictions. Examples include the suggestions Netflix gives for movies you might like, or predicting the behavioural output of neuron networks.

• Courses

  • Yaser Abu-Mostafa, CalTech. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Andrew Ng, Stanford University, Coursera. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • David Silver. [Videos: Yes; Notes: No; Exercise: No]
  • O'Reilly. [Videos: No; Notes: Yes; Exercise: Yes]
  • Higher School of Economics. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • O'Reilly, Python Cookbook. [Videos: No; Notes: Yes; Exercise: Yes]

• Podcasts

  • Talking Machines, Katherine Gorman & Ryan Adams.
  • Data Skeptic, Kyle & Linh Da.
  • Partially Derivative, Willian Justen.

• Code

  • Python tools.
  • R recipes.

The biologically inspired Artificial Neural Networks (ANN, also known as Deep Learning), is a way to determine how elements are connected. It is based on how our neurons in the brain work. Each neuron is connected to multiple other neurons, and depending on the amount of other neurons signalling to that one neuron, a signal is transported. Think of it how you normally draw a network, with circles and arrows. To make it more interesting, a signal between neurons does not only travel in one direction, such as in Feedforward NN, but can also feedback, such as in Recurrent NN.

• Courses

  • 3Blue1Brown. [Videos: Yes; Notes: No; Exercise: No]
  • Andrew Ng. [Videos: No; Notes: Yes; Exercise: Yes]
  • Coursera. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Google. [Videos: Yes; Notes: Yes; Exercise: Yes]
  • Michael Nielsen. [Videos: No; Notes: Yes; Exercise: Yes]
  • The Asimov Institute. [Videos: No; Notes: Yes; Exercise: No]
  • Brilliant. [Videos: No; Notes: Yes; Exercise: Yes]

• Podcasts

  • Neural Networks, Richard Golden.
  • CBC Player, Geoffrey Hinton.

• Code

  • Fast Artificial Neural Network Library, using C.
  • Keras, using Python.
  • TensorFlow.

For further study and motivation.

• Books

  • Cambridge mathematical reading list.
  • Books for learning math, John Baez.
  • Tibees book recommendations.

• Practice

  • Project Euler
  • Brilliant

• Channels

  • 3Blue1Brown
  • Reddit: r/math
  • Reddit: r/mathematics
  • Tibees
  • Mathbff
  • Professor Leonard
  • Numberphile
  • SocraticaStudios
  • Crash Course
  • LeiosOS
  • Prof. N.J. Wildberger
  • N.J. Wildberger blogs
  • Decaf-Math

• Inspiration

  • Stanford:learning maths
  • Emmy Noether
  • Katherine Johnson
  • Mary Cartwright
  • Vladimir Voevodsky
  • Sheila Scott Macintyre
  • Stephen Smale
  • Persi Diaconis
  • Joan Briman