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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.
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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 || Prerequisites :-- | :--: Introduction to Mathematical Thinking | none
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 | 14 weeks | 6-8 hours/week | Calculus 1C |
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 | - | - | high school math |
Linear Algebra | 14 weeks | 12 hours/week | Essence of Linear Algebra |
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, Math for Computer Science, Linear Algebra |
Statistics for Applications | 14 weeks | 12-16 hours/week | Probability |
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 | 14 weeks | 8-10 hours/week | Multivariable Calculus |
Supplemental Lecture Videos | 16 weeks | 8-10 hours/week | Multivariable Calculus |
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 | 8 weeks | 8-10 hours/week | high school math |
Introduction to Rings and Fields | 8 weeks | 8-10 hours/week | Introduction to Abstract Group Theory |
Courses | Duration | Effort | Prerequisites |
---|---|---|---|
Introduction to Formal Logic | 15 weeks | 9 hours/week | - |
Courses | Duration | Effort | Prerequisites |
---|---|---|---|
Topology Without Tears | 15 weeks | 14 hours/week | high school math, Set Theory, Knowledge of axiomatic branch of mathematics such as Introduction to Abstract Algebra |
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 |
Combinatorics, probability, statistics, game theory, applied stats
Real analysis, numerical analysis, complex analysis, optimization theory
Abstract algebra, category theory, algebraic geometry and topology
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