{"id":13458343,"url":"https://github.com/ossu/math","last_synced_at":"2026-01-28T23:33:05.980Z","repository":{"id":37633723,"uuid":"294762339","full_name":"ossu/math","owner":"ossu","description":"🧮  Path to a free self-taught education in Mathematics!","archived":false,"fork":false,"pushed_at":"2025-06-27T05:52:08.000Z","size":64,"stargazers_count":7956,"open_issues_count":13,"forks_count":740,"subscribers_count":110,"default_branch":"master","last_synced_at":"2025-10-05T02:03:51.597Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":null,"language":null,"has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/ossu.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":"CONTRIBUTING.md","funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null}},"created_at":"2020-09-11T17:28:20.000Z","updated_at":"2025-10-04T15:55:30.000Z","dependencies_parsed_at":"2023-02-09T20:45:27.339Z","dependency_job_id":"59582f81-6eb3-446a-afc5-7f825e61d986","html_url":"https://github.com/ossu/math","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/ossu/math","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ossu%2Fmath","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ossu%2Fmath/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ossu%2Fmath/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ossu%2Fmath/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/ossu","download_url":"https://codeload.github.com/ossu/math/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ossu%2Fmath/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":28855154,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-01-28T22:56:21.783Z","status":"ssl_error","status_checked_at":"2026-01-28T22:56:00.861Z","response_time":57,"last_error":"SSL_connect returned=1 errno=0 peeraddr=140.82.121.6:443 state=error: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":[],"created_at":"2024-07-31T09:00:51.181Z","updated_at":"2026-01-28T23:33:05.974Z","avatar_url":"https://github.com/ossu.png","language":null,"funding_links":[],"categories":["Acknowledgement","Others","Cheat Sheets\u003ca name=other_cheat_sheets\u003e\u003c/a\u003e","计算机编程_数据结构与算法"],"sub_categories":["Selected Posts and Essays\u003ca name=community_blogs_selected_posts_and_essays\u003e\u003c/a\u003e","资源传输下载"],"readme":"\u003cdiv align=\"center\"\u003e\n\u003cimg src=\"http://i.imgur.com/kYYCXtC.png\" alt=\"Open Source Society logo\"/\u003e\n\n\u003ch3\u003eOpen Source Society University\u003c/h3\u003e\n\u003cp\u003e\n  :abacus: Path to a free self-taught education in Math!\n\u003c/p\u003e\n\u003cp\u003e\n  \u003ca href=\"https://github.com/open-source-society/math\"\u003e\n    \u003cimg alt=\"Open Source Society University - Math\" src=\"https://img.shields.io/badge/OSSU-math-blue.svg\"\u003e\n  \u003c/a\u003e\n\u003c/p\u003e\n\u003c/div\u003e\n\n# Contents\n\n- [Summary](#summary)\n- [Community](#community)\n- [Code of conduct](#code-of-conduct)\n- [Curriculum](#curriculum)\n- [License](#license)\n\n# Summary\n\nThe OSSU curriculum is a **complete education in mathematics** using online materials.\nIt's for those who want a proper grounding in concepts fundamental to all math disciplines,\nand for those who have the discipline, will, and good habits to obtain this education largely on their own,\nbut with support from a worldwide community of fellow learners.\n\nIt is designed according to the degree requirements of undergraduate math majors, minus general education (non-math) requirements,\nas it is assumed most of the people following this curriculum are already educated outside the field of math.\nThe courses themselves are among the very best in the world, often coming from Harvard, MIT, Stanford, etc.,\nbut specifically chosen to meet the following criteria.\n\n**Courses must**:\n- Match our [curricular guidelines](CURRICULAR_GUIDELINES.md) the 2015 CUPM Guide.\n- Be open for enrollment\n- Run regularly (ideally in self-paced format, otherwise running multiple times per year)\n- Be of high quality in teaching materials and pedagogical practice\n\nWhen no course meets the above criteria, the coursework is supplemented with a book.\n\n**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.\n\n**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.\n\nDecide how much or how little to spend based on your own time and budget;\njust remember that you can't purchase success!\n\n**Process**. Students can work through the curriculum alone or in groups, in order or out of order.\n- For simplicity, we recommend working through courses in order from top to bottom, as they have already been sorted by their prerequisites.\n- 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.\n- 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).\n\n**Content policy**. If you plan on showing off some of your coursework publicly, you must share only files that you are allowed to.\n*Respect the code of conduct that you sign in the beginning of each course!*\n\n**[How to contribute](CONTRIBUTING.md)**\n\n**[Getting help](HELP.md)** (Details about our FAQ and chatroom)\n\n# Community\n\n- 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](https://discord.gg/5pUhfpX)\n- You can also interact through [GitHub issues](https://github.com/ossu/math/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](CONTRIBUTING.md).\n- Add **Open Source Society University** to your [Linkedin](https://www.linkedin.com/school/11272443/) profile!\n\n# Code of conduct\n[OSSU's code of conduct](https://github.com/ossu/code-of-conduct).\n\n# Curriculum\n\nThe curriculum is separated into two parts:\n\n- [Core Mathematics](#core-mathematics)\n  - [Introduction to Mathematical Thinking](#introduction-to-mathematical-thinking)\n  - [Calculus](#calculus)\n  - [Introduction to Differential Equations](#introduction-to-differential-equations)\n  - [Discrete Mathematics](#discrete-mathematics)\n  - [Linear Algebra](#linear-algebra)\n  - [Probability \u0026 Statistics](#probability--statistics)\n  - [Introduction to Analysis](#introduction-to-analysis)\n  - [Introduction to Abstract Algebra](#introduction-to-abstract-algebra)\n- [Advanced Topics](#advanced-topics)\n  - [Differential Equations](#differential-equations)\n  - [Mathematical Logic](#mathematical-logic)\n  - [Geometry and Topology](#geometry-and-topology)\n  - [Probability and Statistics](#probability-and-statistics)\n  - [Mathematical Analysis](#mathematical-analysis)\n  - [Abstract Algebra](#abstract-algebra)\n  \n## Core Mathematics\n\nAll classes under Core Mathematics are **required**, unless stated otherwise.\n\n### Introduction to Mathematical Thinking\nMost 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. \n\n**Topics covered:**\n`Mathematical mindset`\n`Number Theory`\n\nCourses | Duration | Effort | Prerequisites\n:-- | :--: | :--: | :--:\n[Introduction to Mathematical Thinking](https://www.coursera.org/learn/mathematical-thinking) | 10 weeks | 4 hours/week | none\n[LaTeX](https://www.overleaf.com/learn/latex/Learn_LaTeX_in_30_minutes) | 1 week | 30 minutes/week | none\n\n### Calculus \nCalculus is the study of change (differential calculus) and accumulation of quantities (integral calculus). As the cornerstone of geometry and physics, it serves as the foundation for understanding many natural phenomena and plays an essential role in modern technology, scientific discovery, and many fields, including engineering, economics, and medicine.\n\n**Topics Covered:**\n`Derivatives`\n`Integrals`\n`Infinity`\n\nCourses | Duration | Effort | Prerequisites\n:-- | :--: | :--: | :--:\n[Calculus 1A: Differentiation](https://openlearninglibrary.mit.edu/courses/course-v1:MITx+18.01.1x+2T2019/about) | 13 weeks | 6-10 hours/week | [high school math](https://ossu.dev/precollege-math)\n[Calculus 1B: Integration](https://openlearninglibrary.mit.edu/courses/course-v1:MITx+18.01.2x+3T2019/about) | 13 weeks | 5-10 hours/week | Calculus 1A \n[Calculus 1C: Coordinate Systems \u0026 Infinite Series](https://openlearninglibrary.mit.edu/courses/course-v1:MITx+18.01.3x+1T2020/about) | 6 weeks | 5-10 hours/week | Calculus 1B\n[Multivariable Calculus](https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/) | 12 weeks | 6 hours/week | Calculus 1C \n\n### Introduction to Differential Equations\nDifferential 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. It provides us a mathematical language to describe physical, chemical, and biological systems and their evolution.\n\n**Topics covered:**\n`First-order ODEs`\n`Second-order ODEs`\n`Higher-order ODEs`\n`Laplace Transforms`\n\nCourses | Duration | Effort | Prerequisites\n:-- | :--: | :--: | :--:\n[Differential Equations](https://ocw.mit.edu/courses/18-03sc-differential-equations-fall-2011/) | 14 weeks | 12 hours/week | Calculus 1C\n\n### Discrete Mathematics\nDiscrete mathematics is the mathematics of objects and ideas. It includes topics such as combinatorics, graph theory, and logic. 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. \n\n**Topics covered:**\n`Counting`\n`Grouping`\n`Classifying`\n`Logic and Reasoning`\n\nCourses | Duration | Effort | Prerequisites\n:-- | :--: | :--: | :--:\n[Mathematics for Computer Science](https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-fall-2010/) | 14 weeks | 6-8 hours/week | Calculus 1C\n\n### Linear Algebra\nLinear algebra is the mathematics of spatial relationships that deals with the manipulation of vectors and matrices. It provides an elegant way to consider many simultaneous equations, visualize arbitrarily-many dimensions, and explain complex phenomena in simple terms.\n\n**Topics covered:**\n`Vector and matrix calculations`\n`Linear transformations`\n`Vector spaces`\n`Eigenvalues and Eigenvectors`\n\nCourses | Duration | Effort | Prerequisites\n:-- | :--: | :--: | :--:\n[Essence of Linear Algebra](https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab) | - | - | [high school math](https://ossu.dev/precollege-math)\n[Linear Algebra](https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/) | 14 weeks | 12 hours/week | Essence of Linear Algebra\n\n### Probability \u0026 Statistics\nProbability 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.\n\n**Topics covered:**\n`Random variables`\n`Expectation and Variance`\n`Probability Distributions`\n\nCourses | Duration | Effort | Prerequisites\n:-- | :--: | :--: | :--:\n[Probability](https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/) | 14 weeks | 12-16 hours/week | Multivariable Calculus, Math for Computer Science, Linear Algebra\n[Statistics for Applications](https://ocw.mit.edu/courses/mathematics/18-650-statistics-for-applications-fall-2016/) | 14 weeks | 12-16 hours/week | Probability\n\n### Introduction to Analysis\nAnalysis is the mathematics of sequences and limits. Intro to Analysis is a course that builds on the concepts of Calculus and provides a rigorous and formalized study of the foundations of Calculus. This course will use formal proofs to establish mathematical results, starting by proving the existence of real numbers and building the foundation of single-variable Calculus from scratch.\n\n**Topics covered:**\n`Proofs`\n`Real analysis`\n\nCourses | Duration | Effort | Prerequisites\n:-- | :--: | :--: | :--:\n[Introduction to Analysis](https://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/) | 14 weeks | 8-10 hours/week | Multivariable Calculus\n[Supplemental Lecture Videos](https://www.youtube.com/watch?v=EaKLXK4hFFQ\u0026list=PLmU0FIlJY-MngWPhBDUPelVV3GhDw_mJu\u0026index=1) | 16 weeks | 8-10 hours/week | Multivariable Calculus\n\n### Introduction to Abstract Algebra\nAbstract algebra (occasionally called modern algebra) is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras. Abstract algebra was coined in the early 20th century to distinguish this area of study from older parts of algebra, more specifically from elementary algebra, using variables to represent numbers in computation and reasoning.\n\n**Topics covered:**\n`Group Theory`\n`Rings and fields`\n\nCourses | Duration | Effort | Prerequisites\n:-- | :--: | :--: | :--:\n[Introduction to Abstract Group theory](https://nptel.ac.in/courses/111106113) | 8 weeks | 8-10 hours/week | [high school math](https://ossu.dev/precollege-math) \n[Introduction to Rings and Fields](https://nptel.ac.in/courses/111106131) | 8 weeks | 8-10 hours/week | Introduction to Abstract Group Theory\n\n\n## Advanced Topics\n\nUpon finishing **all the core mathematics courses**, students can choose to take elective courses in advanced topics of their choice. It is not necessary to take *every* course within a subcategory, but it is recommended to take courses relevant to the intended field of study.\n\nTo complete your study of Advanced Topics, meet both the Breadth and Depth requirements.\n\n- **Breadth Requirement:** For each of the 6 Advanced Topics below, select one course to take as an elective.\n- **Depth Requirement:** Select one Advanced Topic below and take 3 additional courses from that topic.\n\n### Mathematical Logic\n\nCourses | Duration | Effort | Prerequisites\n:-- | :--: | :--: | :--:\n[Introduction to Formal Logic](https://forallx.openlogicproject.org/) | 15 weeks | 9 hours/week | -\n\n### Geometry and Topology\n\nCourses | Duration | Effort | Prerequisites\n:-- | :--: | :--: | :--:\n[Topology Without Tears](https://www.topologywithouttears.net) | 15 weeks | 14 hours/week | [high school math](https://ossu.dev/precollege-math), Set Theory, Knowledge of axiomatic branch of mathematics such as [Introduction to Abstract Algebra](#introduction-to-abstract-algebra) \n[Euclidean plane and its relatives](https://arxiv.org/pdf/1302.1630v19.pdf) | 14 weeks | 4-6 hours/week | Elementary Set Theory, Calculus 1C, Linear Algebra\n[Geometry with an Introduction to Cosmic Topology](https://mphitchman.com) | 14 weeks | 14 hours/week | Multivariable Calculus\n[Differential Geometry](https://ocw.mit.edu/courses/mathematics/18-950-differential-geometry-fall-2008/) [(Supplementary Video Lectures)](https://www.youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP)  | 10 weeks | 6-8 hours/week | Multivariable Calculus, Introduction To Analysis and Linear Algebra\n\n### Probability and Statistics\nCombinatorics, probability, statistics, game theory, applied stats\n\n### Mathematical Analysis\nReal analysis, numerical analysis, complex analysis, optimization theory\n\n### Abstract Algebra\nAbstract algebra, category theory, algebraic geometry and topology\n\n\n## Congratulations\n\nAfter completing the requirements of the curriculum above, you will have completed the equivalent of a full bachelor's degree in Mathematics. Congratulations!\n\nWhat is next for you? The possibilities are boundless and overlapping:\n\n- Look for a job. Mathematicians go into careers as statisticians, financial analysts, actuaries, and more!\n- Join a local math club (e.g. via [meetup.com](https://www.meetup.com/)).\n- Pay attention to emerging ideas in mathematics by subscribing to a math journal or joining a professional math organization.\n\n## How to show your progress\n\n1. Create an account in [Trello](https://trello.com/).\n1. Copy [this board](https://trello.com/b/zIlcyFSH/ossu-math) to your personal account.\nSee how to copy a board [here](https://help.trello.com/article/802-copying-cards-lists-or-boards).\n\nNow 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.\n\n# License\n\u003ca rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-sa/4.0/\"\u003e\u003cimg alt=\"Creative Commons License\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png\" /\u003e\u003c/a\u003e\u003cbr /\u003eThis work is licensed under a \u003ca rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-sa/4.0/\"\u003eCreative Commons Attribution-NonCommercial-ShareAlike 4.0 International License\u003c/a\u003e.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fossu%2Fmath","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fossu%2Fmath","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fossu%2Fmath/lists"}