Ordered subject guides linking qualifying-exam problems by subject. The wiki covers the same subjects as notes filed by topic.
- Algebra
Algebra: finite groups, commutative rings, modules, field extensions, and linear algebra.
- Applied Algebra
The qualifying exam syllabus in applied algebra: spectral theory and factorizations of matrices, representations and characters of finite groups, symmetric functions and the representation theory of the symmetric groups, Gröbner bases and polynomial systems, and invariant theory of finite groups.
- Complex Analysis
The qualifying exam syllabus in complex analysis: complex arithmetic and the elementary functions, power series, holomorphy and the Cauchy–Riemann equations, harmonic functions, Cauchy’s theorem and integral formula, zeros and isolated singularities, the argument principle, residues and contour integration, conformal maps of the disc, normal families and the Riemann mapping theorem, and infinite products and special functions. The last section groups qualifying-exam problems by type.
- Prelim
Preliminary-exam problems in calculus, linear algebra, and abstract algebra: logic and proof, limits and continuity, integration, sequences and series, multivariable calculus, linear algebra, groups, rings and modules, fields and Galois theory, complex numbers, and counterexamples.
- Real Analysis
Real analysis: metric spaces, differentiation, integration, measure theory, functional analysis, and Fourier analysis.
- Topology
General and algebraic topology: topological spaces, homotopy, covering spaces, cell complexes, and homology.
Across the subjects
Guides that order problems from several subjects. Their problems also appear in the subject guides, and the wiki files each of their pages under its subject.
- Workshops
Problems from the qualifying-exam workshops in algebra, real analysis, complex analysis, and topology, listed in the order of the workshop sessions.