All classes under Core Mathematics are required, unless stated otherwise.
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 | 10 weeks | 4 hours/week | none |
| LaTeX | 1 week | 30 minutes/week | none |
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 | 13 weeks | 6-10 hours/week | high school math |
| Calculus 1B: Integration | 13 weeks | 5-10 hours/week | Calculus 1A |
| Calculus 1C: Coordinate Systems & Infinite Series | 6 weeks | 5-10 hours/week | Calculus 1B |
| Multivariable Calculus | 12 weeks | 6 hours/week | Calculus 1C |
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 | 14 weeks | 12 hours/week | Calculus 1C |
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 |
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.
| 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