Full Code of ossu/math for AI

Repository: ossu/math
Branch: master
Commit: 37f7487bf0be
Files: 10
Total size: 32.7 KB

Directory structure:
gitextract_dztvh7ns/

├── .github/
│   ├── ISSUE_TEMPLATE/
│   │   └── request-for-comment-template.md
│   └── workflows/
│       └── delete-empty-issues.yml
├── CNAME
├── CONTRIBUTING.md
├── CURRICULAR_GUIDELINES.md
├── FAQ.md
├── HELP.md
├── LICENSE
├── README.md
└── documents/
    └── release.md

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FILE CONTENTS
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FILE: .github/ISSUE_TEMPLATE/request-for-comment-template.md
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---
name: Request for Comment Template
about: Template for creating an RFC to modify the curriculum
title: 'RFC: '
labels: ''
assignees: ''

---

**Problem:**
Give a 1 sentence description of a problem with the current OSSU Curriculum. Successful critiques of the curriculum will point out ways that OSSU is failing to uphold [our curricular guidelines](https://github.com/ossu/math/blob/master/CURRICULAR_GUIDELINES.md). Examples are:

* OSSU lists course X as required when the course's topics are elective in our curricular guidelines.
* OSSU does not having a course to cover required topic X from our curricular guidelines.
* OSSU lists courses X, Y and Z that cover the same topics when fewer courses could suffice.
* OSSU recommends course X to teach a topic, but there exists a higher quality course that covers the same material.

**Duration:**
This should most often be 1 month from the date of posting.

**Background:**
Give an in depth description of the problem. Describe a solution to the problem. Describe the advantages and disadvantages of this solution. This section should be a few paragraphs.

**Proposal:**
Give a bullet point list of changes that are being proposed. These can link to a Pull Request.

**Alternatives:**
Give a bullet point list of alternative ways to address the problem.


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FILE: .github/workflows/delete-empty-issues.yml
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name: Delete empty issues
on:
  issues:
    types:
      - opened
jobs:
  label_issues:
    runs-on: ubuntu-latest
    permissions:
      issues: write

    if: github.event.issue.body == '' || contains(github.event.issue.body, 'Give a 1 sentence description of a problem with the current OSSU Curriculum. Successful critiques of the curriculum will point out ways that OSSU is failing to uphold')
    steps:
      - name: Create comment
        uses: actions-cool/issues-helper@v3
        with:
          actions: 'create-comment'
          token: ${{ secrets.GITHUB_TOKEN }}
          issue-number: ${{ github.event.issue.number }}
          body: |
            Hello @${{ github.event.issue.user.login }}.
            It looks like you've opened an empty issue or one without a unique problem description.
            Please understand that this is a popular project, useful to many learners, and empty issues distract maintainers that are trying to help others.
            If you would like practice with issues, you can follow github documentation to create your own repo:
            https://docs.github.com/en/repositories/creating-and-managing-repositories/creating-a-new-repository
            And then in that repo practice creating and editing issues:
            https://docs.github.com/en/issues/tracking-your-work-with-issues/configuring-issues/quickstart

            We look forward to your future contributions to OSSU, when you are contributing to improve computer science education for learners all over the world!
      - name: Close issue
        uses: actions-cool/issues-helper@v3
        with:
          actions: 'close-issue'
          token: ${{ secrets.GITHUB_TOKEN }}
          issue-number: ${{ github.event.issue.number }}


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FILE: CNAME
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math.ossu.dev

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FILE: CONTRIBUTING.md
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# Changing the curriculum
OSSU thrives because of the changes made by our many contributors. Read on for details on how to help every student that follows you.
## Non-substantive changes
If you have non-substantive updates to make to the curriculum, such as a course's URL having been moved, spelling/syntax errors, etc., please send a [pull request](https://www.freecodecamp.org/news/how-to-make-your-first-pull-request-on-github-3/) to fix any mistakes that you have found.
## Substantive changes
If you have specific and substantive criticisms of the curriculum, i.e. problems related to the progression/content of courses it would be appropriate to [open an issue](https://help.github.com/articles/creating-an-issue/). While it is acceptable to point out problems, all successful changes naturally require a plan for fixing the problem.
OSSU’s curricular guidelines are [here](CURRICULAR_GUIDELINES.md). Successful critiques of the curriculum will point out ways that OSSU is failing to uphold these guidelines. Examples are:

* OSSU lists a course as required when the course topics are elective in the curricular guide.
* OSSU does not having a course to cover required topics from the curricular guide.
* OSSU lists multiple courses that cover the same topics when fewer courses could suffice.
* OSSU recommends a course to teach a topic, but there exists a higher quality course that covers the same material.
## Other ways to contribute
### Responding to Issues
Issues require more than just users to suggest them. Issues require active community members to read and respond to proposals. Even adding simple [emoji reactions](https://github.blog/2016-03-10-add-reactions-to-pull-requests-issues-and-comments/) can help the community.
### Engaging with other students
Learning is enhanced by engaged peers. You can be that peer for someone new to OSSU. When you see a new person posting in Gitter, ask them a question about themselves. When you see a cohort starting at _almost_ the right time, join in. Doing so will make OSSU a stronger program for everyone, including you.
# Personal Customization
If you want to customize the curriculum for yourself, you are encouraged to [fork this project](https://help.github.com/articles/fork-a-repo/)!


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FILE: CURRICULAR_GUIDELINES.md
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# Curricular Guidelines

[Committee on the Undergraduate Program in Mathematics Curriculum Guide](https://maa.org/resource/cupm-guide/)

The 2015 CUPM Curriculum Guide is prepared by the MAA’s Committee on the Undergraduate Program in Mathematics with the support of the Mathematical Association of America, the National Science Foundation DUE-1228636, the Educational Advancement Foundation, and the professional advice of more than 250 mathematicians and scientists in the community. The guide is written to help departments design and maintain robust math major programs.

## Organization publishing:

### Mathematical Association of America

_"The Mathematical Association of America is the world’s largest community of mathematicians, students, and enthusiasts. We further the understanding of our world through mathematics because mathematics drives society and shapes our lives. The mission of the MAA is to advance the understanding of mathematics and its impact on our world. Our members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; STEM professionals, and many others in academia, government, business, and industry. We welcome all who are interested in the mathematical sciences."_

## Curriculum Goals

The 2015 CUPM Curriculum Guide states:

> A successful [mathematics] major offers a program of courses to gradually and intentionally lead students from basic to advanced levels of critical and analytical thinking, while encouraging creativity and excitement about mathematics.

These cognitive and content goals are presented in the CUPM for the purpose of guiding curriculum design. OSSU has adopted these goals for the Mathematics curriculum:

### Cognitive Goals

1. Students should develop effective thinking and communication skills.

2. Students should learn to link applications and theory.

3. Students should learn to use technological tools.

4. Students should develop mathematical independence and experience
open-ended inquiry.

### Content Goals

1. Mathematical sciences major programs should include concepts and methods from calculus and linear algebra. 

2. Students majoring in the mathematical sciences should learn to read, understand, analyze, and produce proofs at increasing depth as they progress through a major.

3. Mathematical sciences major programs should include concepts and methods from data analysis, computing, and mathematical modeling.

4. Mathematical sciences major programs should present key ideas and concepts from a variety of perspectives to demonstrate the breadth of mathematics. 

5. Students majoring in the mathematical sciences should experience mathematics from the perspective of another discipline. 

6. Mathematical sciences major programs should present key ideas from
complementary points of view: continuous and discrete; algebraic and geometric; deterministic and stochastic; exact and approximate.

7. Mathematical sciences major programs should require the study of at least
one mathematical area in depth, with a sequence of upper-level courses.

8. Students majoring in the mathematical sciences should work, independently or in a small group, on a substantial mathematical project that involves techniques and concepts beyond the typical content of a single course.

9. Mathematical sciences major programs should offer their students an orientation to careers in mathematics.



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FILE: FAQ.md
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# Frequently Asked Questions

This page answers some questions that we frequently receive about the curriculum.
If you have questions that aren't answered here, try asking through one of our [community channels](README.md#community).
If it seems important enough or we get asked that question a lot, we will probably add it here.

Alternatively, you could [contribute](#CONTRIBUTING.md) an answer yourself.

## Contents

- [How can I review the math prerequisites?](#how-can-i-review-the-math-prerequisites)
- [In what order should I take the courses?](#in-what-order-should-i-take-the-courses)
- [Does every resource in the main curriculum have to be free?](#does-every-resource-in-the-main-curriculum-have-to-be-free)
- [Are Coursera courses free to access?](#are-coursera-courses-free-to-access)
- [Is it necessary to purchase the Verified Upgrade for edX courses?](#is-it-necessary-to-purchase-the-verified-upgrade-for-edx-courses)
- [Why doesn't the curriculum cover/ignore topic X?](#why-doesnt-the-curriculum-coverignore-topic-x)
- [Why is the curriculum missing some pre-requisites?](#why-is-the-curriculum-missing-some-pre-requisites)

## Questions

### How can I review the math prerequisites?

See our [Pre-College Math](https://ossu.dev/precollege-math) curriculum for a list of resources to use for reviewing the math prerequisites.

### In what order should I take the courses?

You have a few different options:
- You can progress linearly from top to bottom of the page.
- You can progress linearly through each individual section, but studying different sections in parallel.
- You can design your own custom progression using the pre-requisites to guide you.

We have designed the curriculum to work for any of the above three styles.

### Does every resource in the main curriculum have to be free?

Yes, that is a core goal of OSSU.

At the same time, we recognize that education is a resource that requires payment to instructors to make it sustainable in the long term.
Therefore, we respect the business model of websites like edX, which make their materials free but with some paid add-ons, like official certificates or extra interaction with course instructors.

So we only require that the *learning materials* of a resource be free to access, not that every possible add-on be free.
It would be ideal if graded assignments were always free. In the event that free assessments are not available OSSU looks for alternate assessments to pair with a course.

### Are Coursera courses free to access?

Some courses that require payment to access probably do exist on Coursera, but we don't put those on our curriculum.
All Coursera courses that we put on the curriculum must, at minimum, be **free to audit**.
For some courses, all course features are available for free;
for others (especially those that are part of a specialization), you may only be able to access the lecture videos.
(If you find the policies have changed for any courses on our curriculum, please tell us!)

Unfortunately, for some courses, Coursera's interface is [very aggressive](https://darkpatterns.org/) about convincing you that you have to pay.

You may see something like this on the course page:

<img src="http://i.imgur.com/MxOcYZv.png" alt="Free Trial" style="width: 400px;"/>

When attempting to enroll in such a course:
- Click the blue "Enroll" or "Enroll Now" button.
- A pop-up will appear.
- **Do not click** "Start Free Trial", unless you do want to pay.
- Find the text that says "Audit this course" at the bottom.
- Click **Audit**.

![Audit this course](https://user-images.githubusercontent.com/3349406/27321369-95ca12e6-55cc-11e7-9b5c-f8fedd8fd643.png)

### Is it necessary to purchase the Verified Upgrade for edX courses?

If you just want to watch the videos, it is never necessary for any edX course on our curriculum. Note that a number of edX courses only allow students to audit a course for the estimated number of weeks it takes to complete. Students should not begin a course until they are prepared to focus and complete the course.

### Why doesn't the curriculum cover/ignore topic X?

You can read more about our curricular guidelines and the qualifications of the guidelines' authors [here](CURRICULAR_GUIDELINES.md). If you find a topic that is required by our guidelines and is not included in the curriculum, we should make a change! Read more about [contributing to a change](CONTRIBUTING.md).

### Why is the curriculum missing some pre-requisites?

The curriculum assumes two things:
- You are reasonably fluent in English.
- You have gotten through a standard high school curriculum that included physics and pre-calculus.

Without these assumptions, the curriculum would be out of control with trying to fill in your knowledge gaps.
For those who want to study math pre-requisites, read more [here](#how-can-i-review-the-math-prerequisites)

Of course, if you find that the curriculum is missing a pre-requisite for a course that isn't part of a normal high school curriculum, please let us know!


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FILE: HELP.md
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# Getting help
## Check the FAQ!
Please check our [Frequently Asked Questions](FAQ.md) to see if your question has been addressed.
## Ask in the chat room
Join the OSSU [Discord server](https://discord.gg/5pUhfpX)! Discord is an online chat service, similar to Slack or IRC where you can chat with other students and get help.
### Specific problems
If you need help successfully completing the content of a course or are having general technical difficulties, first reach out to the resources provided by the course (e.g. the course forum on Coursera, edX, etc). If you need additional help after that, post in Discord. **In your post, mention what steps you have already taken to try and solve the problem**.
### General problems
If you have general problems with the program not specific to any course, such as preferring textbook-style learning over MOOCs, Discord is a good place to reach out to people who may have great suggestions. You might form a working group that makes the next improvement to OSSU Math! Read more about contributing [here](CONTRIBUTING.md).


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FILE: LICENSE
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MIT License

Copyright (c) 2020 Open Source Society University

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.


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FILE: README.md
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<div align="center">
<img src="http://i.imgur.com/kYYCXtC.png" alt="Open Source Society logo"/>

<h3>Open Source Society University</h3>
<p>
  :abacus: Path to a free self-taught education in Math!
</p>
<p>
  <a href="https://github.com/open-source-society/math">
    <img alt="Open Source Society University - Math" src="https://img.shields.io/badge/OSSU-math-blue.svg">
  </a>
</p>
</div>

# Contents

- [Summary](#summary)
- [Community](#community)
- [Code of conduct](#code-of-conduct)
- [Curriculum](#curriculum)
- [License](#license)

# 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](CURRICULAR_GUIDELINES.md) 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](CONTRIBUTING.md)**

**[Getting help](HELP.md)** (Details about our FAQ and chatroom)

# Community

- 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)
- 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).
- Add **Open Source Society University** to your [Linkedin](https://www.linkedin.com/school/11272443/) profile!

# Code of conduct
[OSSU's code of conduct](https://github.com/ossu/code-of-conduct).

# Curriculum

The curriculum is separated into two parts:

- [Core Mathematics](#core-mathematics)
  - [Introduction to Mathematical Thinking](#introduction-to-mathematical-thinking)
  - [Calculus](#calculus)
  - [Introduction to Differential Equations](#introduction-to-differential-equations)
  - [Discrete Mathematics](#discrete-mathematics)
  - [Linear Algebra](#linear-algebra)
  - [Probability & Statistics](#probability--statistics)
  - [Introduction to Analysis](#introduction-to-analysis)
  - [Introduction to Abstract Algebra](#introduction-to-abstract-algebra)
- [Advanced Topics](#advanced-topics)
  - [Differential Equations](#differential-equations)
  - [Mathematical Logic](#mathematical-logic)
  - [Geometry and Topology](#geometry-and-topology)
  - [Probability and Statistics](#probability-and-statistics)
  - [Mathematical Analysis](#mathematical-analysis)
  - [Abstract Algebra](#abstract-algebra)
  
## Core Mathematics

All classes under Core Mathematics are **required**, unless stated otherwise.

### 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](https://www.coursera.org/learn/mathematical-thinking) | 10 weeks | 4 hours/week | none
[LaTeX](https://www.overleaf.com/learn/latex/Learn_LaTeX_in_30_minutes) | 1 week | 30 minutes/week | none

### Calculus 
Calculus 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.

**Topics Covered:**
`Derivatives`
`Integrals`
`Infinity`

Courses | Duration | Effort | Prerequisites
:-- | :--: | :--: | :--:
[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)
[Calculus 1B: Integration](https://openlearninglibrary.mit.edu/courses/course-v1:MITx+18.01.2x+3T2019/about) | 13 weeks | 5-10 hours/week | Calculus 1A 
[Calculus 1C: Coordinate Systems & Infinite Series](https://openlearninglibrary.mit.edu/courses/course-v1:MITx+18.01.3x+1T2020/about) | 6 weeks | 5-10 hours/week | Calculus 1B
[Multivariable Calculus](https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/) | 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. It provides us a mathematical language to describe physical, chemical, and biological systems and their evolution.

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

Courses | Duration | Effort | Prerequisites
:-- | :--: | :--: | :--:
[Differential Equations](https://ocw.mit.edu/courses/18-03sc-differential-equations-fall-2011/) | 14 weeks | 12 hours/week | Calculus 1C

### Discrete Mathematics
Discrete 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. 

**Topics covered:**
`Counting`
`Grouping`
`Classifying`
`Logic and Reasoning`

Courses | Duration | Effort | Prerequisites
:-- | :--: | :--: | :--:
[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

### Linear Algebra
Linear 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.

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

Courses | Duration | Effort | Prerequisites
:-- | :--: | :--: | :--:
[Essence of Linear Algebra](https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab) | - | - | [high school math](https://ossu.dev/precollege-math)
[Linear Algebra](https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/) | 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](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
[Statistics for Applications](https://ocw.mit.edu/courses/mathematics/18-650-statistics-for-applications-fall-2016/) | 14 weeks | 12-16 hours/week | Probability

### Introduction to Analysis
Analysis 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.

**Topics covered:**
`Proofs`
`Real analysis`

Courses | Duration | Effort | Prerequisites
:-- | :--: | :--: | :--:
[Introduction to Analysis](https://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/) | 14 weeks | 8-10 hours/week | Multivariable Calculus
[Supplemental Lecture Videos](https://www.youtube.com/watch?v=EaKLXK4hFFQ&list=PLmU0FIlJY-MngWPhBDUPelVV3GhDw_mJu&index=1) | 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. 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.

**Topics covered:**
`Group Theory`
`Rings and fields`

Courses | Duration | Effort | Prerequisites
:-- | :--: | :--: | :--:
[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) 
[Introduction to Rings and Fields](https://nptel.ac.in/courses/111106131) | 8 weeks | 8-10 hours/week | Introduction to Abstract Group Theory


## Advanced Topics

Upon 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.

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

- **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.

### Mathematical Logic

Courses | Duration | Effort | Prerequisites
:-- | :--: | :--: | :--:
[Introduction to Formal Logic](https://forallx.openlogicproject.org/) | 15 weeks | 9 hours/week | -

### Geometry and Topology

Courses | Duration | Effort | Prerequisites
:-- | :--: | :--: | :--:
[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) 
[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
[Geometry with an Introduction to Cosmic Topology](https://mphitchman.com) | 14 weeks | 14 hours/week | Multivariable Calculus
[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

### 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](https://www.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

1. Create an account in [Trello](https://trello.com/).
1. Copy [this board](https://trello.com/b/zIlcyFSH/ossu-math) to your personal account.
See how to copy a board [here](https://help.trello.com/article/802-copying-cards-lists-or-boards).

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
<a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png" /></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.


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# OSSU Releases Free Undergraduate Math Curriculum
Open Source Society University (OSSU) has released [an undergraduate math curriculum for self study](https://math.ossu.dev). Contributors are encouraged to improve the recommendations in this alpha release.

“Young people across the globe want to learn,” OSSU President Waciuma Wanjohi says. “Guiding them to high quality, low cost educational resources unlocks a world of possibilities. We’ve had a steady stream of learners asking us for guidance in learning college level math. We’re happy to provide answers to those questions.”

The OSSU curriculum is an education in mathematics using freely available online materials. It is designed according to the degree requirements of undergraduate math majors, minus general education (non-math) requirements. OSSU benchmarks its curriculum against the 2015 Mathematics Curriculum Guide, prepared by the Mathematical Association of America’s Committee on the Undergraduate Program in Mathematics.

Resources in the guide range from MOOCs on popular education platforms, to open courseware released directly from universities, to Creative Commons licensed textbooks written by open educational resource collectives.

Mathematics is the fourth curriculum developed by OSSU, following Computer Science, Data Science and Bioinformatics. Previous contributors to OSSU led the way in creating the math curriculum.

“As a student, I found the OSSU CS curriculum to be an invaluable supplement to my education,” states OSSU contributor Hassam Uddin. “There is an abundance of free and open-source materials that can supplement or even replace a formal math education. It's just a matter of organizing and creating a community, which OSSU has done.”

"OSSU provides amazing opportunities for students who prefer an alternative to the traditional college experience. The only requirement is a willingness to learn. I'm excited for the opportunity to make education more accessible" continued OSSU contributor Bradley Grant.

Since 2015 OSSU has developed guides for learners to master undergraduate curricula. OSSU additionally supports students with discussion forums, where hundreds of students message one another each day. OSSU alumni have gone on to graduate school as well as into full time software engineering. Curricula are open for users to contribute, as well as to copy and modify for individual use.

[math.ossu.dev](https://math.ossu.dev)