Open Online Courses in Mathematics

What is Mathematics?

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.

What Can Online Courses in Mathematics Actually Teach Me?

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 consists of. While there is no accrediting body specific to mathematics in the United States, some applied mathematics online courses may be accredited by the Accreditation Board for Engineering and Technology (ABET).

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?

There is a lot to choose from when it comes to online mathematics courses, so before deciding you should consider the quality of the institution offering the course, the level of the instructor, and whether a program is offered by a regionally accredited college or university. You should only choose programs from accredited institutions and the professor should hold a Ph.D. in mathematics or a similar degree. In addition, if you want to receive high school or transfer credit upon completion, make sure the course you choose is accredited by an institution such as ABET.

Free Online Courses in Mathematics From Around the Web

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 (41)

Linear Partial Differential EquationsMassachusetts Institute of Technology

Open Courseware

Differential Equations, Applied Mathematics, Wave Equations
Taught by: Dr. Matthew Hancock

Fourier Analysis - Theory and ApplicationsMassachusetts Institute of Technology

Open Courseware

Probability, Fourier series, Fourier Integrals
Taught by: Prof. Richard Melrose

Geometry and Quantum Field TheoryMassachusetts Institute of Technology

Open Courseware

Quantum Field Theory, Geometry, Functional Integrals
Taught by: Prof. Pavel Etingof

Combinatorial OptimizationMassachusetts Institute of Technology

Open Courseware

Combinatorial Optimization, Linear Programming
Taught by: Prof. Santosh Vempala

Introduction to Numerical MethodsMassachusetts Institute of Technology

Open Courseware

Numerical Linear Algebra, Numerical Methods, Differential Equations
Taught by: Dr. Plamen Koev

Measure and IntegrationMassachusetts Institute of Technology

Open Courseware

Fourier Transform, Integration
Taught by: Prof. Jeff Viaclovsky

Topics in Several Complex VariablesMassachusetts Institute of Technology

Open Courseware

Harmonic Theory, Decomposition Theorem
Taught by: Prof. Victor Guillemin

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
Taught by: Professor Robert C. Vaughan

Complex Numbers and Ordinary Differential EquationsUniversity of Oxford

Open Courseware

Differentials, Complex Numbers

Nonlinear Dynamics and ChaosUniversity of Oxford

Open Courseware

Nonlinear Dynamics, Modeling, Forecasting
Taught by: Patrick McSharry

Geometry University of Oxford

Open Courseware

Algebraic Curves, Differentiable Manifolds, Geometry
Taught by: Nigel Hitchin

StatisticsUniversity of Oxford

Open Courseware

Statistics, Probability, Simulation
Taught by: Gesine Reinert

Analysis of Boolean FunctionsNew South Wales

Open Courseware

Boolean Functions, Linearity, Fourier Expansion
Taught by: Ryan O'Donnell

Polynomials of Random VariablesUniversity of California, Berkeley

Open Courseware

Polynomials, Random Variables, Probability, Statistics
Taught by: Elchanan Mossel

Analytic Number TheoryMassachusetts Institute of Technology

Open Courseware

Number Theory, Functions
Taught by: Prof. Kiran Kedlaya

Topics in Geometry: Dirac GeometryMassachusetts Institute of Technology

Open Courseware

Geometry, Symmetry
Taught by: Prof. Marco Gualtieri

Random Walks and DiffusionMassachusetts Institute of Technology

Open Courseware

Random Walks, Diffusion
Taught by: Prof. Martin Bazant

Single Variable CalculusMassachusetts Institute of Technology

Open Courseware

Calculus, Differentiation, Functions
Taught by: Prof. Jason Starr

Geometry of ManifoldsMassachusetts Institute of Technology

Open Courseware

Geometry, Manifolds
Taught by: Prof. Denis Auroux

Calculus of Several VariablesMassachusetts Institute of Technology

Open Courseware

Multivariable Calculus
Taught by: Prof. James McKernan

Introduction to Probability and StatisticsMassachusetts Institute of Technology

Open Courseware

Probability, Statistics
Taught by: Prof. Dmitry Panchenko

Honors Differential EquationsMassachusetts Institute of Technology

Open Courseware

Differential Equations, Existence Theorems
Taught by: Dr. Vera Mikyoung Hur

Single Variable CalculusMassachusetts Institute of Technology

Open Courseware

Calculus, Math, Mathematics
Taught by: Prof. David Jerison

Course Description:

This calculus course covers differentiation and integration of functions of one variable, and concludes with a brief discussion of infinite series. Calculus is fundamental to many scientific disciplines including physics, engineering, and economics.

Problem Solving SeminarMassachusetts Institute of Technology

Open Courseware

Math, Mathematics, Problem Solving, Techniques
Taught by: Prof. Hartley Rogers, Prof. Kiran Kedlaya, Prof. Richard Stanley

Course Description:

This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

Mathematics for Computer ScienceMassachusetts Institute of Technology

Open Courseware

Discrete Math, Mathematics, Computer Science
Taught by: Prof. Ronitt Rubinfeld, Prof. Albert R. Meyer

Course Description:

"This is an introductory course in Discrete Mathematics oriented toward Computer Science and Engineering. The course divides roughly into thirds: 1. Fundamental Concepts of Mathematics: Definitions, Proofs, Sets, Functions, Relations 2. Discrete Structures: Modular Arithmetic, Graphs, State Machines, Counting 3. Discrete Probability Theory A version of this course from a previous term was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5512 (Mathematics for Computer Science)."

Probabilistic Systems Analysis and Applied ProbabilityMassachusetts Institute of Technology

Open Courseware

Math, Mathematics, Probability, Statistics
Taught by: Prof. Munther Dahleh

Course Description:

This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.

Multivariable CalculusMassachusetts Institute of Technology

Open Courseware

Calculus, Math, Mathematics
Taught by: Prof. David Jerison, Prof. Arthur Mattuck

Course Description:

This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include Vectors and Matrices, Partial Derivatives, Double and Triple Integrals, and Vector Calculus in 2 and 3-space.

Elements of Calculus IUniversity of Notre Dame

Open Courseware

Calculus, Math, Mathematics
Taught by: Professor Alex Himonas, Ph.D.

Course Description:

This course is for students in arts and letters, architecture, or business. It studies basic calculus as part of a liberal education. It emphasizes conceptual learning and stresses the connections between mathematics and modern society. Topics include functions, limits, derivatives, and an introduction to integral, with interesting real-life applications throughout. Students are familiarized with the many different interpretations of the derivative as a rate of change, and the integral as a total rate of change. This enables them to learn and practice modeling in a variety of situations from economics the social and the life sciences.

Calculus II for BusinessUniversity of Notre Dame

Open Courseware

Calculus, Math, Mathematics, Business, Models
Taught by: Professor Alex Himonas, Ph.D.

Course Description:

In this course you will learn how to use calculus to understand and model real life situations such as those in business, environmental changes, population growth to name a few. As expected, real life situations are in general very complicated and are difficult to model but with the mathematics in this course we can understand some of the more basic models.

The Art of CountingMassachusetts Institute of Technology

Open Courseware

Math, Mathematics, Quantitative
Taught by: Prof. Richard Stanley

Course Description:

The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2n-1. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment.

Differential EquationsMassachusetts Institute of Technology

Video

Differential Equations, Engineering
Taught by: Prof. Haynes Miller, Prof. Arthur Mattuck

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

Video

Functions, Trigonometry, Exponentials, Theorems
Taught by: Adrian Banner

Search for RandomnessInstitute for Advanced Study

Video

Pseudorandomness, Cryptography, Numerical Simulation
Taught by: Jean Bourgain

The Practice of MathematicsInstitute for Advanced Study

Video

Algebra, Geometry
Taught by: Robert P. Langlands

Automorphic FormsInstitute for Advanced Study

Video

Theorems, Analytic Number Theory, Arithmetic, Geometry