Applying to the Graduate School
- Please refer to the Korea University Graduate School website for more details on the application timeline and related announcements.
KOREA UNIVERSITY Graduate School
Go to Graduate School
- You may also access the same information at the official website of the Department of Mathematics: Graduate School → Graduate School Admissions.
|Algebra||Fundamental Notions on GroupsㆍRingsㆍFields, and Vector Spaces, Structures of Rings, Theories of Commutative Rings. Noetherian Rings and Modules, Lie’s Theorems, Primary Decomposition, Localization Tensor Product, Local Rings, Completeness, Group Representation Theory, Theory of Invariant Polynomials.||
|Analysis||Real Number Field, Lebesgue Measure, Lebesgue Measurable Functions , Lebesgue Integration, Differentiation and Integration, Spaces of Integrable Functions, Complex Measures, Lebesgue Integration as a Set Function, Radon-Nikodym’s Theorem, Daniell Integration, Measurers and Topologies The relation between the Probability and the Real Analysis, Fundamental Notions on Probability, Law of Large Numbers, The Conditional Expectation, Theory on Martingales, Ergodic Theorem, Elementary Properties of Analytic Functions, Harmonic Functions, Boundary Behaviors, Maximum Principles, Approximation by Rational Functions, Conformal Mapping, Analytic Continuation, Zeros of Holomorphic Functions. Stochastic Differential Equations, Stochastic Partial Differential Equations , Elliptic and Parabolic Partial Differential Equations.||
Yang, Chan Woo
Choe, Boo Rim
|Topology||Homotopies, Fundamental Groups, Van Kampen’s Theorem, Covering Spaces, Group Actions, Simplician and Singular Homologies, Mayer-Vietoris Sequences, Cohomology Groups, Poincare Duality Theorem, CW-Complexes||
|Geometry||Theories on Curves, Theories on Surfaces , Shape Operator, Geometries on Surfaces, Riemannian Geometry, Riemannian Metrics, Levi-Civita Connections, Curvatures and Jacobian Vector Fields, The Second Variation Theorem, Comparison Theorem, Minimal Geodesics, Homogeneous Spaces, Morse’s Theorem and Closed Geodesics, Sphere Theorem, Finiteness Theorems.||
|Applied Mathematics||Generalized Functions, Theories on Distributions, Green’s Functions and Boundary Value Problems, Fourier Transform, Euler’s Method, Milne’s Method, Hilbert Spaces, Operator Theory, Integral Equations, Runge-Kutta’s Method, Shooting method, Ideal Fluids, Newtonian Fluids||
Commencing with the first semester of 2015, all students serving as TAs receive a TA scholarship.
Mandatory courses for graduate school admission
Basic concept of analysis, linear algebra and algebra