Free online math courses with certificate: the short list
Across the 30 courses on this page, the certificate picture is lopsided. A single freeCodeCamp course issues a free certificate, the university courses on edX and MITx Online sell one on top of a free audit track, and everything from Khan Academy, MIT OpenCourseWare, Stanford Engineering Everywhere, Open Yale Courses and Princeton on Coursera issues nothing at all.
Free certificate: College Algebra with Python
College Algebra with Python Certification from freeCodeCamp is the only listed mathematics course with a free, verifiable certificate, issued at a public URL on freecodecamp.org. It is a one-semester college algebra course taught through Google Colaboratory notebooks: ratios and proportions, solving for x, functions and graphing, systems of equations, quadratics, polynomials, exponents and logarithms, simple and compound interest. freeCodeCamp now files it under archived coursework, so the content is no longer updated but remains available.
Paid certificate on a free audit track
Harvard's edX courses can be audited free while a run is active; the verified certificate costs $149 for Data Analysis: Basic Probability and Statistics and $209 for Calculus Applied!. MITx Online gives free audit access to all materials; the certificate track adds graded work and costs $100 for Calculus 1A: Differentiation and $300 for Probability - The Science of Uncertainty and Data. Cornell's A Hands-on Introduction to Engineering Simulations on edX follows the same pattern.
Learn math online free: where to start by level
The listed courses run from school algebra to graduate optimisation. Pick by the last topic you were comfortable with.
Algebra first
Algebra 1 on Khan Academy covers equations and inequalities, linear equations and their graphs, systems, functions, sequences, exponents and radicals, exponential growth and quadratics, with practice, quizzes and a unit test in every unit; the page points anyone who feels unready to a separate preparatory Get ready for Algebra 1 sequence. College Algebra with Python covers the same ground for adults who also want to learn some Python.
Calculus
Calculus 1 on Khan Academy runs from limits and continuity through derivatives, their applications, integrals and basic differential equations, self-paced with no stated duration. MIT offers it in two forms. Single Variable Calculus is the OpenCourseWare Scholar edition for independent study, with lecture and recitation videos, problem sets and solved exams. Calculus 1A: Differentiation and Calculus 1B: Integration are the MITx versions, instructor-paced at fourteen weeks and fifteen weeks respectively, with 8 to 10 hours a week expected for 1A. Harvard's Calculus Applied! is explicitly a supplement for people who already know derivatives, integrals and differential equations, not a course for learning calculus from scratch.
Linear algebra, discrete mathematics and beyond
Linear Algebra is Gilbert Strang's course in Scholar format, from elimination and the four fundamental subspaces to eigenvalues and the singular value decomposition; his Matrix Methods in Data Analysis, Signal Processing, and Machine Learning builds on it.
Mathematics for Computer Science covers proofs, induction, number theory, graph theory, counting and discrete probability, and names single variable calculus as its only prerequisite. Princeton's Analysis of Algorithms and Analytic Combinatorics are free in full on Coursera with no certificate, by Princeton policy. Stanford Engineering Everywhere publishes Introduction to Linear Dynamical Systems, The Fourier Transform and its Applications and Convex Optimization I and II.
Free statistics course online: probability and statistics options
For a first pass, Khan Academy's Statistics and probability goes from displaying data through probability and sampling distributions to confidence intervals, significance tests and regression inference. Harvard's Data Analysis: Basic Probability and Statistics builds probability up from counting over seven weeks at 3 to 5 hours a week and is pitched as a refresher before a college statistics course; Introduction to Probability is rated intermediate at 5 to 10 hours a week.
Harvard also teaches statistics through R in Data Science: Probability, Data Science: Linear Regression and Statistics and R. At the mathematical end, MIT's Statistics for Applications on OpenCourseWare covers maximum likelihood, hypothesis testing, regression, Bayesian statistics and principal component analysis with no grading, while Fundamentals of Statistics is the graded MITx counterpart, seventeen weeks at 10 to 14 hours a week, with a $300 certificate that can count toward the MicroMasters in Statistics and Data Science.
Free online math courses for adults returning to study
Khan Academy tracks every skill from Not started to Mastered, so you can skip what you already know. The OpenCourseWare Scholar courses were assembled for learners working without a classroom. The MITx and Harvard courses run on a schedule, and audit access on edX ends when the run does, so start them only when the weekly effort fits.
MIT mathematics: OpenCourseWare or MITx
OpenCourseWare publishes the recorded lectures, notes, problem sets and exams of campus courses under a Creative Commons licence, with no account, no deadlines and never a certificate. MITx Online runs graded versions of some of the same courses with a free audit track and a paid certificate. Single Variable Calculus pairs with the Calculus 1A and 1B modules, and Statistics for Applications with Fundamentals of Statistics. The MIT provider page and Does MIT OpenCourseWare give certificates? explain the policy in full.
Applied courses listed under mathematics
Some listed courses are physics, engineering or economics taught mathematically: MIT's Classical Mechanics, Oxford's Quantum Mechanics lecture series, Stanford's Introduction to Robotics, Cornell's engineering simulations course with Ansys, and Yale's Game Theory, which assumes introductory microeconomics and one-variable calculus. Courses that build on this mathematics sit on the free online data science courses and free online computer science courses hubs.