ossu/math

Contents

• Summary
• Community
• Code of conduct
• Curriculum
• 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 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)

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
• 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.
• 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
  • Introduction to Mathematical Thinking
  • Calculus
  • Introduction to Differential Equations
  • Discrete Mathematics
  • Linear Algebra
  • Probability & Statistics
  • Introduction to Analysis
  • Introduction to Abstract Algebra
• Advanced Topics
  • Differential Equations
  • Mathematical Logic
  • Geometry and Topology
  • Probability and Statistics
  • Mathematical Analysis
  • 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

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

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

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

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

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

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

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

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

Geometry and Topology

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

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

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