Mathematics
Learn calculus, proofs, algebra, analysis, and applied mathematics.
Curriculum outline
Year 1 · Calculus and proof
Single-variable calculus, linear algebra, logic, and introductory proofs.
Year 2 · Mathematical methods
Multivariable calculus, differential equations, discrete mathematics, and probability.
Year 3 · Analysis and algebra
Real analysis, abstract algebra, and a choice of complex analysis or numerical methods.
Year 4 · Advanced study and exposition
Choose a focus such as pure mathematics, applied mathematics, or probability. Write and present a proof or modeling project.
Curriculum reference · MIT
This roadmap is designed for university-level self-study.
Year 1 study guide and free resources
Read the assigned topics, work through examples, then solve problems from memory. At the end of each term, use a source problem set or a project to check what you can do independently.
Year 1 · Fall
- Calculus I
Review functions and graphs, then study limits and differentiation.
MIT OCW · Single Variable Calculus - Introduction to Proofs
Practice writing quantified statements, counterexamples and direct proofs.
MIT OCW · Mathematics for Computer Science
Year 1 · Winter
- Calculus II
Continue with integration techniques, sequences and series.
MIT OCW · Single Variable Calculus - Linear Algebra
Move from elimination to linear maps and eigenvalues. Check solutions by substitution.
MIT OCW · Linear Algebra
Introduction to Proofs · Direct proof and counterexamples
Introduction to Proofs · Mathematical induction
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