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:
- Match our curricular guidelines the 2015 CUPM Guide.
- Be open for enrollment
- Run regularly (ideally in self-paced format, otherwise running multiple times per year)
- Be of high quality in teaching materials and pedagogical practice
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.
- For simplicity, we recommend working through courses in order from top to bottom, as they have already been sorted by their prerequisites.
- Courses in Core Mathematics are the basic requirements for all OSSU Math students, and provide a foundation for deeper study. Take all of these courses.
- Courses in Advanced Topics are electives. Take one course in each topic area. Then choose one topic you want to become an expert in and take all the courses under that heading. You can also create your own custom subject (we recommend getting validation from the community on the subject you choose).
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)
- We have a Discord server! This should be your first stop to talk with other OSSU students. Why don’t you introduce yourself right now? Join the OSSU Discord
- You can also interact through GitHub issues. If there is a problem with a course, or a change needs to be made to the curriculum, this is the place to start the conversation. Read more here.
- Subscribe to our newsletter.
- Add Open Source Society University to your Linkedin profile!
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
- Single-Variable Calculus
- Multi-Variable Calculus
- Introduction to Differential Equations
- Discrete Math
- Linear Algebra
- Probability & Statistics
- Intro to Analysis
- Intro to Abstract Algebra
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
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
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
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
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
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
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
Advanced Topics
Once you’ve completed all courses in Core Mathematics, you are free to take elective courses in Advanced Topics, which include:
- Differential Equations
- Mathematical Logic
- Geometry
- Probability and Statistics
- Mathematical Analysis
- Abstract Algebra
To complete your study of Advanced Topics, complete both the Breadth requirement and the Depth requirement.
- Breadth Requirement: For each of the 6 Advanced Topics below, select one course to take as an elective.
- Depth Requirement: Select one Advanced Topic below and take 3 additional courses from that topic.
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:
- Look for a job. Mathematicians go into careers as statisticians, financial analysts, actuaries and more!
- Join a local math club (e.g. via meetup.com).
- Pay attention to emerging ideas in mathematics by subscribing to a math journal or joining a professional math organization.
How to show your progress
- Create an account in Trello.
- 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
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.