Free Online Mathematics Courses

Mathematics is a branch of science that encompasses numbers, quantity, and space. Mathematics is divided into two categories: pure and applied mathematics. Pure mathematics, or theoretical mathematics, looks at numbers abstractly through the use of theorems and proofs that may not have any applications in the real world, but are carried out for the sake of knowledge itself. Applied mathematics, on the other hand, comprises calculations and equations done for other branches of science such as physics and engineering in order to solve specific problems.

Mathematics comprises many different branches, such as geometry (the study of points, lines, and shapes), algebra (the study of equations, using letters and other symbols to solve equations), and calculus (the study of functions and their derivatives and integrals). The most basic component of mathematics, however, is the manipulation of numbers through addition, subtraction, division, and multiplication.

Why Take Online Mathematics Courses?

Mathematics is used throughout most courses in the sciences, computer sciences, and engineering, and online mathematics courses can help you better understand branches of mathematics you will encounter such as geometry or calculus or teach you specific topics such as differential equations, algorithms, or non-linear geometry. Online mathematics courses are very beneficial for students of engineering, physics, chemistry, or other scientific or technical subjects that will require the extensive use of applied mathematics. However, you can also take an online mathematics class just to improve your logical and mathematical thinking, or to supplement college mathematics programs. Many online courses are taught by professional mathematicians working in academia, and can give you an idea of what a career in mathematics requires. .

You can take an online mathematics course in many different subjects, including college algebra, calculus, statistics, or trigonometry. Students of these online courses are taught to answer questions such as:

  • What are the applications of calculus in the real world?
  • How are differential equations constructed and solved?
  • What are some of the most important mathematical theorems throughout history?
  • How is the study of logic related to the study of mathematics?
  • What kinds of software and other tools do mathematicians use?

Free Online Mathematics Courses

Below you will find a list of online resources that will aid in your study of mathematics. These include videos, test materials, online textbooks, and lecture notes. These free courses will give you a solid introduction to several topics in mathematics and can help you review and better understand concepts you have already learned.

Subjects

Math (37)

Differential EquationsMassachusetts Institute of Technology

Video

Differential Equations, Engineering

The Calculus Lifesaver: All the Tools You Need to Excel at CalculusPrinceton University

Video

Functions, Trigonometry, Exponentials, Theorems

Search for RandomnessInstitute for Advanced Study

Video

Pseudorandomness, Cryptography, Numerical Simulation

The Practice of MathematicsInstitute for Advanced Study

Video

Algebra, Geometry

Automorphic FormsInstitute for Advanced Study

Video

Theorems, Analytic Number Theory, Arithmetic, Geometry

Linear Partial Differential EquationsMassachusetts Institute of Technology

Open Courseware

Differential Equations, Applied Mathematics, Wave Equations

Geometry and Quantum Field TheoryMassachusetts Institute of Technology

Open Courseware

Quantum Field Theory, Geometry, Functional Integrals

Combinatorial OptimizationMassachusetts Institute of Technology

Open Courseware

Combinatorial Optimization, Linear Programming

Introduction to Numerical MethodsMassachusetts Institute of Technology

Open Courseware

Numerical Linear Algebra, Numerical Methods, Differential Equations

Measure and IntegrationMassachusetts Institute of Technology

Open Courseware

Fourier Transform, Integration

Topics in Several Complex VariablesMassachusetts Institute of Technology

Open Courseware

Harmonic Theory, Decomposition Theorem

Discrete Mathematics for Computer Science University of California, Berkeley

Open Courseware

Modular Arithmetic, Polynomials, Probability, Statistics

Abstract AlgebraUniversity of Illinois at Urbana-Champaign

Open Courseware

Group Fundamentals, Algebraic Number Theory, Geometry

Algebraic Number TheoryUniversity of Illinois at Urbana-Champaign

Open Courseware

Prime Ideals, Discriminants, Number Theory

Commutative AlgebraUniversity of Illinois at Urbana-Champaign

Open Courseware

Algebra, Ring Theory, Dimension Theory

Complex VariablesUniversity of Illinois at Urbana-Champaign

Open Courseware

Elementary Theory, Complex Variables, Analytic Functions

StatisticsUniversity of Illinois at Urbana-Champaign

Open Courseware

Statistics, Probability

Analytic Number Theory IPenn State University

Open Courseware

Analytic Techniques, Number Theory

Complex Numbers and Ordinary Differential EquationsUniversity of Oxford

Open Courseware

Differentials, Complex Numbers

Geometry University of Oxford

Open Courseware

Algebraic Curves, Differentiable Manifolds, Geometry

StatisticsUniversity of Oxford

Open Courseware

Statistics, Probability, Simulation

Analysis of Boolean FunctionsNew South Wales

Open Courseware

Boolean Functions, Linearity, Fourier Expansion

Polynomials of Random VariablesUniversity of California, Berkeley

Open Courseware

Polynomials, Random Variables, Probability, Statistics

Topics in Geometry: Dirac GeometryMassachusetts Institute of Technology

Open Courseware

Geometry, Symmetry

Random Walks and DiffusionMassachusetts Institute of Technology

Open Courseware

Random Walks, Diffusion

Single Variable CalculusMassachusetts Institute of Technology

Open Courseware

Calculus, Differentiation, Functions

Geometry of ManifoldsMassachusetts Institute of Technology

Open Courseware

Geometry, Manifolds

Calculus of Several VariablesMassachusetts Institute of Technology

Open Courseware

Multivariable Calculus

Honors Differential EquationsMassachusetts Institute of Technology

Open Courseware

Differential Equations, Existence Theorems

Single Variable CalculusMassachusetts Institute of Technology

Open Courseware

Calculus, Math, Mathematics

Problem Solving SeminarMassachusetts Institute of Technology

Open Courseware

Math, Mathematics, Problem Solving, Techniques

Mathematics for Computer ScienceMassachusetts Institute of Technology

Open Courseware

Discrete Math, Mathematics, Computer Science

Probabilistic Systems Analysis and Applied ProbabilityMassachusetts Institute of Technology

Open Courseware

Math, Mathematics, Probability, Statistics

Multivariable CalculusMassachusetts Institute of Technology

Open Courseware

Calculus, Math, Mathematics

Elements of Calculus IUniversity of Notre Dame

Open Courseware

Calculus, Math, Mathematics

Calculus II for BusinessUniversity of Notre Dame

Open Courseware

Calculus, Math, Mathematics, Business, Models

The Art of CountingMassachusetts Institute of Technology

Open Courseware

Math, Mathematics, Quantitative