Choose who walks with you

Mathematics (PhD): 7 courses in the order to take them, starting with Measure Theory & Real Analysis. Every course has two AI teachers, a woman and a man, who work with you one-on-one by email.

Doctoral Degrees

Mathematics (PhD)

7 courses in order · 14 teachers

Agents in Training

Still learning · not yet available to request

Mathematics (PhD) · courses in order

Measure Theory & Real Analysis

A Measure Theory & Real Analysis Teacher takes you through doctoral-level real analysis — sigma-algebras and measures, Lebesgue measure, measurable functions and the Lebesgue integral, the convergence theorems, product measures, Radon-Nikodym, differentiation and Lp spaces — by checking which hypothesis does the work in every theorem. They check your proofs, build counterexamples with you and make practice and qualifying exam plans. AI teaching companions, not your instructor or school.

Graduate Complex Analysis

A Graduate Complex Analysis Teacher takes you through doctoral-level complex analysis — holomorphic functions and power series, conformal maps, Cauchy's theorem and integral formula, singularities and Laurent series, residues and the argument principle, harmonic functions, infinite products, normal families, the Riemann mapping theorem and analytic continuation — by asking what holomorphy forces. They check your proofs and contour integrals and build practice and qualifying exam plans. AI teaching companions, not your instructor or school.

Graduate Abstract Algebra

A Graduate Abstract Algebra Teacher takes you through first-year graduate algebra — group actions and Sylow theory, rings and ideals, PIDs and UFDs, modules and tensor products, canonical forms, field extensions and Galois theory — by asking what each map preserves and what it forces. They check your proofs, test ideas on small examples with you and make practice and qualifying exam plans. AI teaching companions, not your instructor or school.

Topology

A Topology Teacher takes you through graduate topology — topological spaces, product and quotient topologies, connectedness and compactness, separation axioms, the fundamental group, covering spaces, van Kampen and homology — by pairing every picture with a precise definition. They check your proofs and computations, help you read your textbook and make practice and qualifying exam plans. AI teaching companions, not your instructor or school.

Functional Analysis

A Functional Analysis Teacher takes you through graduate functional analysis — Banach and Hilbert spaces, bounded operators, Hahn-Banach, the Baire category theorems, duality and weak topologies, compact operators and spectral theory — by naming which norm, topology and completeness assumption each step uses. They check your proofs, build counterexamples with you and make practice and qualifying exam plans. AI teaching companions, not your instructor or school.

Partial Differential Equations

A Partial Differential Equations Teacher takes you through graduate PDE — the Laplace, heat, wave and transport equations, characteristics and conservation laws, Sobolev spaces, elliptic theory and evolution equations — by asking what each estimate controls and what each hypothesis buys. They check your proofs and estimates, help you read your textbook and make practice and qualifying exam plans. AI teaching companions, not your instructor or school.

Differential Geometry

A Differential Geometry Teacher takes you through graduate differential geometry — smooth manifolds, tangent bundles, submersions and embeddings, vector fields and Lie groups, differential forms and Stokes' theorem, de Rham cohomology, Riemannian metrics, geodesics and curvature — by computing in coordinates and then asking what is invariant. They check your proofs and computations and make practice and qualifying exam plans. AI teaching companions, not your instructor or school.