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Mathematics Resources

Open Source Society University (OSSU)

Open Source Society University

Path to a free self-taught education in Math!

Contents

Summary

The OSSU curriculum is a complete education in mathematics using online materials. It’s for those who want a proper grounding in concepts fundamental to all math disciplines, and for those who have the discipline, will, and good habits to obtain this education largely on their own, but with support from a worldwide community of fellow learners.

It is designed according to the degree requirements of undergraduate math majors, minus general education (non-math) requirements, as it is assumed most of the people following this curriculum are already educated outside the field of math. The courses themselves are among the very best in the world, often coming from Harvard, MIT, Stanford, etc., but specifically chosen to meet the following criteria.

Courses must:

When no course meets the above criteria, the coursework is supplemented with a book.

Duration. It is possible to finish the curriculum within about 2 years if you plan carefully and devote roughly 18-22 hours/week to your studies.

Cost. OSSU strives to identify free resources to reach your learning goal. However, some courses may charge money for assignments/tests/projects to be graded.

Decide how much or how little to spend based on your own time and budget; just remember that you can’t purchase success!

Process. Students can work through the curriculum alone or in groups, in order or out of order.

Content policy. If you plan on showing off some of your coursework publicly, you must share only files that you are allowed to. Respect the code of conduct that you sign in the beginning of each course!

How to contribute

Getting help (Details about our FAQ and chatroom)

Community

Code of conduct

OSSU’s code of conduct.

Curriculum

The curriculum is separated into two parts:

Core Mathematics

All OSSU Math students need to take all of these courses. Subjects include:

Introduction to Mathematical Thinking

Most people’s views of mathematics are destroyed in school by focusing on memorization and regurgitation. But mathematicians see math as an elegant way to explain the world around us. This class covers how to think like a mathematician and solve problems.

Topics covered: Mathematical mindset Number Theory

Courses Duration Effort Prerequisites
Introduction to Mathematical Thinking 10 weeks 4 hours/week none

Calculus

Calculus is the study of infinity. As the cornerstone of geometry and physics, it serves as the foundation of our world, explaining the phenomena that underly our technology, our planets, and our hearts.

Topics Covered: Derivatives Integrals Infinity

Courses Duration Effort Prerequisites
Calculus 1A: Differentiation alt 13 weeks 6-10 hours/week high school math
Calculus 1B: Integration alt 13 weeks 5-10 hours/week Calculus 1A
Calculus 1C: Coordinate Systems & Infinite Series alt 6 weeks 5-10 hours/week Calculus 1B
Multivariable Calculus 12 weeks 6 hours/week Calculus 1C

Introduction to Differential Equations

Differential equations describe the science of change: the route by which natural and man-made systems move from one state to another. Epidemics, population growth, and weather patterns are all modeled using differential equations.

Topics covered: First-order ODEs Second-order ODEs Higher-order ODEs Laplace Transforms

Courses Duration Effort Prerequisites
Introduction to Differential Equations 14 weeks 3-6 hours/week Calculus 1C

Discrete Mathematics

Discrete mathematics is the mathematics of objects and ideas. The topics discussed here also form the basis of the field of computer science. For mathematics majors, a discrete math course is usually also a first introduction to formal proofs.

Topics covered: Counting Grouping Classifying Logic and Reasoning

Courses Duration Effort Prerequisites
Mathematics for Computer Science 14 weeks 6-8 hours/week Calculus 1C

Linear Algebra

Linear algebra is the mathematics of spatial relationships. It provides an elegant way to consider many simultaneous equations, to visualize arbitrarily-many dimensions, and to explain complex phenomena in simple terms.

Topics covered: Vector and matrix calculations Linear transformations Vector spaces Eigenvalues and Eigenvectors

Courses Duration Effort Prerequisites
Essence of Linear Algebra - - high school math
Linear Algebra 14 weeks 12 hours/week Essence of Linear Algebra

Probability & Statistics

Probability is the mathematics of uncertainty. Statistics is the mathematical framework for quantifying uncertainty in real-world data. These two related but distinct fields of study help us describe variation and uncertainty in the world around us. These courses make heavy use of discrete mathematics, linear algebra, and calculus, and serve as a first opportunity to apply what you’ve learned in the other core courses.

Topics covered: Random variables Expectation and Variance Probability Distributions

Courses Duration Effort Prerequisites
Probability 14 weeks 12-16 hours/week Multivariable Calculus, Linear Algebra, Math for Computer Science
Statistics for Applications 14 weeks 12-16 hours/week Probability

Introduction to Analysis

Analysis is the mathematics of mathematics itself. Analysis makes extensive use of the formal proof to build important mathematical concepts from the ground up. Starting by proving the existence of real numbers, this course will show you how to create single-variable calculus entirely from scratch.

Topics covered: Proofs Real analysis

Courses Duration Effort Prerequisites
Introduction to Analysis 14 weeks 8-10 hours/week Multivariable Calculus
Supplemental Lecture Videos 16 weeks 8-10 hours/week Multivariable Calculus

Introduction to Abstract Algebra

Abstract algebra (occasionally called modern algebra) is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras. The term abstract algebra was coined in the early 20th century to distinguish this area of study from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning.

Topics covered: Group Theory Rings and fields

Courses Duration Effort Prerequisites
Introduction to Abstract Group theory 8 weeks 8-10 hours/week High school mathematics
Introduction to Rings and Fields 8 weeks 8-10 hours/week Introduction to Abstract Group Theory

Advanced Topics

Once you’ve completed all courses in Core Mathematics, you are free to take elective courses in Advanced Topics, which include:

To complete your study of Advanced Topics, complete both the Breadth requirement and the Depth requirement.

Differential Equations

Courses | Duration | Effort | Prerequisites :– | :–: | :–: | :–: Differential Equations: 2x2 Systems | 8 weeks | 2-5 hours/week | Introduction to Differential Equations Differential Equations: Linear Algebra and NxN Systems of Differential Equations | 12 weeks | 5-8 hours/week | Differential Equations 2x2 Systems, Linear Algebra Differential Equations: Fourier Series and Partial Differential Equations | 11 weeks | 5-8 hours/week | Differential Equations: Linear Algebra and NxN Systems of Differential Equations Transfer Functions and the Laplace Transform | 10 weeks | 3-6 hours/week | Introduction to Differential Equations

Mathematical Logic

Courses | Duration | Effort | Prerequisites :– | :–: | :–: | :–: Introduction to Formal Logic | 15 weeks | 9 hours/week | -

Geometry and Topology

Courses | Duration | Effort | Prerequisites :– | :–: | :–: | :–: Topology Without Tears | 15 weeks | 14 hours/week | Set Theory, Mathematical Matturity in Algebra and Geometry Euclidean plane and its relatives | 14 weeks | 4-6 hours/week | Elementary Set Theory, Calculus 1c, Linear Algebra Geometry with an Introduction to Cosmic Topology | 14 weeks | 14 hours/week | Multivariable Calculus Differential Geometry (Supplementary Video Lectures) | 10 weeks | 6-8 hours/week | Multivariable Calculus, Introduction To Analysis and Linear Algebra

Probability and Statistics

Combinatorics, probability, statistics, game theory, applied stats

Mathematical Analysis

Real analysis, numerical analysis, complex analysis, optimization theory

Abstract Algebra

Abstract algebra, category theory, algebraic geometry and topology

Congratulations

After completing the requirements of the curriculum above, you will have completed the equivalent of a full bachelor’s degree in Mathematics. Congratulations!

What is next for you? The possibilities are boundless and overlapping:

How to show your progress

  1. Create an account in Trello.
  2. Copy this board to your personal account. See how to copy a board here.

Now that you have a copy of our official board, you just need to pass the cards to the Doing column or Done column as you progress in your study.

License

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.