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A00Foundations & calculus
Prealgebra and Quantitative Foundations
Integers, fractions, decimals, percentages, ratios, measurement, and basic equations.
About this course
Learning outcome
Work reliably with numerical representations and distinguish arithmetic mistakes from conceptual ones.
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A10Foundations & calculus
Elementary Algebra
Linear equations and inequalities, graphs, systems, exponents, polynomials, factoring, rational expressions, and radicals.
About this course
Learning outcome
Translate quantitative relationships into algebra and explain each solution step.
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A20Foundations & calculus
Intermediate Algebra
Functions, quadratic and rational models, radicals, complex numbers, exponentials, logarithms, conics, and sequences.
About this course
Learning outcome
Enter precalculus with reliable symbolic fluency and a clear understanding of functions.
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A30Foundations & calculus
Precalculus and Trigonometry
Function transformations, polynomial and rational models, exponentials, logarithms, trigonometry, analytic geometry, systems, and introductory limits.
About this course
Learning outcome
Model with elementary functions and identify any algebra that needs reinforcement before calculus.
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B10Discrete mathematics & logic
Proof, Logic, and Discrete Structures
Propositional and predicate logic, sets, functions, relations, proof techniques, graphs, counting, and sequences.
About this course
Learning outcome
Read, construct, and critique elementary proofs before studying advanced theory.
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B20Foundations & calculus
Differential Calculus
Limits, continuity, derivatives, approximation, optimization, and mathematical modeling.
About this course
Learning outcome
Use derivatives computationally and conceptually, stating the hypotheses behind each argument.
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B30Foundations & calculus
Integral Calculus
Integration, the fundamental theorem, applications, sequences, series, and introductory differential equations.
About this course
Learning outcome
Choose and justify integration and series methods, connecting accumulation with local rates.
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B40Algebra
Linear Algebra
Linear systems, vector spaces, linear maps, matrices, determinants, eigenvalues, and applications.
About this course
Learning outcome
Connect computation, structure, and proof in finite-dimensional mathematics.
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B50Foundations & calculus
Multivariable Calculus
Multivariable geometry, partial derivatives, multiple integrals, constrained optimization, and coordinate systems.
About this course
Learning outcome
Analyze scalar functions of several variables and relate local linearization to geometry.
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B60Foundations & calculus
Vector Calculus
Vector fields, line and surface integrals, and the theorems of Green, Stokes, and divergence.
About this course
Learning outcome
Explain the integral theorems connecting local differential structure with global quantities.
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B70Foundations & calculus
Ordinary Differential Equations and Dynamical Systems
First-order and higher-order equations, systems, transforms, series, phase planes, and introductory Fourier methods.
About this course
Learning outcome
Formulate, analyze, approximate, and communicate solutions of standard differential-equation models.
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B80Computing & optimization
Mathematical Computing and Reproducible Experiments
Python, SageMath, symbolic and numerical computation, visualization, testing, literate notebooks, and reproducibility.
About this course
Learning outcome
Implement mathematical experiments while distinguishing computation, evidence, and proof.
B90Probability & statistics
Calculus-Based Probability
Discrete and continuous probability, conditioning, random variables, expectation, limits, simulation, and Markov chains.
About this course
Learning outcome
Construct probabilistic models and connect analytical results with simulation.
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B95Probability & statistics
Applied Statistics and Data Analysis
Data collection, summaries, inference, regression, and the interpretation of uncertainty.
About this course
Learning outcome
Analyze data reproducibly and communicate conclusions with their assumptions and limitations.
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C10Analysis
Real Analysis I
Real numbers, sequences, limits, continuity, differentiation, and integration with rigorous proofs.
About this course
Learning outcome
Move from calculus techniques to precise definitions and mathematical arguments.
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C20Analysis
Real Analysis II
Multivariable analysis, metric spaces, function sequences, and deeper convergence and integration results.
About this course
Learning outcome
Use analytical structure and carefully check the hypotheses of advanced results.
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C30Algebra
Abstract Algebra I
Groups, subgroups, homomorphisms, quotient structures, group actions, and examples.
About this course
Learning outcome
Reason structurally about algebraic objects using definitions and proofs.
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C40Algebra
Abstract Algebra II
Rings, ideals, fields, polynomial algebra, field extensions, and Galois theory.
About this course
Learning outcome
Analyze algebraic extensions and connect ring and field structure with solvability.
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C50Analysis
Complex Analysis
Holomorphic functions, complex integration, series, singularities, residues, and conformal ideas.
About this course
Learning outcome
Use the interaction of complex differentiability, geometry, and integration.
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C60Discrete mathematics & logic
Number Theory and Cryptology
Divisibility, congruences, primes, arithmetic functions, and cryptological applications.
About this course
Learning outcome
Prove arithmetic results and explain the mathematical assumptions of cryptographic constructions.
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C70Discrete mathematics & logic
Applied Combinatorics
Counting, graphs, generating functions, recurrence relations, and combinatorial structures.
About this course
Learning outcome
Model discrete problems and justify combinatorial algorithms and arguments.
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C80Discrete mathematics & logic
Mathematical Logic, Set Theory, and Computability
Formal logic, model and proof concepts, sets, computability, and metamathematical limits.
About this course
Learning outcome
Distinguish syntax, semantics, and computation in rigorous mathematical reasoning.
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C90Geometry & topology
Point-Set Topology
Topological spaces, continuity, bases, compactness, connectedness, and separation.
About this course
Learning outcome
Construct examples and proofs using intrinsic topological definitions.
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C100Geometry & topology
Euclidean and Non-Euclidean Geometry
Euclidean, affine, projective, and non-Euclidean perspectives with proof and problem solving.
About this course
Learning outcome
Compare geometric axioms and connect constructions with deductive arguments.
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C110Computing & optimization
Numerical Analysis
Approximation, linear systems, interpolation, numerical calculus, and differential equations.
About this course
Learning outcome
Choose numerical methods and analyze their error, stability, and convergence.
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C120Computing & optimization
Mathematical Modeling and Nonlinear Dynamics
Model formulation, scaling, discrete and continuous dynamics, computation, and interpretation.
About this course
Learning outcome
Develop, analyze, test, and critique mathematical models.
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C130Computing & optimization
Linear and Integer Optimization
Linear and integer programming, modeling, algorithms, duality, and computational examples.
About this course
Learning outcome
Formulate optimization problems and interpret solutions and certificates.
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C140Probability & statistics
Mathematical Statistics
Estimation, sufficiency, completeness, hypothesis tests, and statistical decision principles.
About this course
Learning outcome
Derive statistical procedures and justify their assumptions and properties.
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D10Analysis
Measure and Integration
Measures, measurable functions, integration, convergence, and product constructions.
About this course
Learning outcome
Use measure-theoretic definitions and theorems with careful control of hypotheses.
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D20Analysis
Functional Analysis
Normed and Hilbert spaces, operators, functional-analytic methods, and operator algebras.
About this course
Learning outcome
Connect infinite-dimensional structure with analytical and spectral arguments.
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D30Probability & statistics
Measure-Theoretic Probability and Stochastic Processes
Advanced probability, conditional expectation, Markov processes, and continuous-time models.
About this course
Learning outcome
Analyze stochastic models using measure-theoretic tools and explicit assumptions.
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D40Analysis
Partial Differential Equations
First- and second-order equations, classical methods, boundary problems, and numerical laboratories.
About this course
Learning outcome
Connect differential equations, boundary data, analytical methods, and computation.
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D50Geometry & topology
Smooth Manifolds and Differential Geometry
Smooth manifolds, tangent constructions, differential geometry, and bridging material.
About this course
Learning outcome
Reason geometrically with local coordinates and coordinate-independent structures.
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D60Geometry & topology
Algebraic Topology
Homotopy, fundamental groups, covering spaces, homology, and algebraic invariants.
About this course
Learning outcome
Use algebraic constructions to study topological spaces and maps.
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D70Algebra
Graduate Algebra
Advanced algebraic structures, representation theory, and commutative algebra.
About this course
Learning outcome
Work with structural algebraic methods and connect multiple algebraic perspectives.
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D80Algebra
Category Theory and Homological Methods
Categories, functors, natural transformations, and homological constructions.
About this course
Learning outcome
Organize mathematical structures and arguments with categorical and homological tools.
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D90Computing & optimization
Advanced Optimization and Convex Analysis
Convexity, duality, optimality conditions, and advanced optimization methods.
About this course
Learning outcome
Prove and apply optimization results while tracking their assumptions.
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D100Geometry & topology
Algebraic Geometry Bridge
Algebraic curves, bundles, sheaves, cohomology, and an introductory scheme-theoretic bridge.
About this course
Learning outcome
Connect algebraic and geometric viewpoints in preparation for further study.
D110Research practice
Formalized Mathematics in Lean
Interactive theorem proving, mathematical libraries, tactics, and checked mathematical development.
About this course
Learning outcome
Build and explain machine-checked mathematical proofs.
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D120Research practice
Research Reading and Reproducible Mathematical Work
Research reading, mathematical exposition, evidence, reproducibility, and traceable workflows.
About this course
Learning outcome
Produce clear mathematical work with inspectable reasoning and reproducible supporting artifacts.