Mathematics Postgraduate Degrees

...Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs, filtrations...

...Lectures: 2 sessions / week, 1.5 hours / session There are no prerequisite courses, but 18.705 Commutative Algebra must be taken concurrently...

...This semester, 18.727 will be a graduate course on algebraic surfaces. The main aims will be to go over the classification of surfaces...

...some flavor of TeX (e.g., LaTeX). It is strongly recommended that all figures be drawn with some graphics package (such as xfig) that can be incorporated into LaTeX...

...graded ring, etc. Lectures: 2 sessions / week, 1.5 hours / session An important feature of category theory is that it allows one to imitate...

...Lectures: 2 sessions / week, 1.5 hours / session Double affine Hecke algebras, also called Cherednik algebras, were introduced by Cherednik in 1993... Learn about: GCSE Physics, Mathematical Physics...

...The exponential mapping for a Lie group emerges as a special case. The relationship between Lie subgroups and Lie subalgebras via the exponential mapping...

...including an overview of the proof of Fermat's Last Theorem. Each of the topics listed below corresponds to roughly one week of lectures (a total of three hours)...

...2 sessions / week, 1.5 hours / session 18.785 Number Theory I This course is the continuation of 18.785 Number Theory I. It begins with an analysis...

...18.705 Commutative Algebra Historically, number theory has often been separated into algebraic and analytic tracks, but we will not make such a sharp distinction... Learn about: GCSE Mathematics...

...18.781) is strongly recommended. This course is an introduction to algebraic number theory. We will follow Samuel's book Algebraic Theory of Numbers to start...

...This is a course on the singular homology of topological spaces. Topics include: Singular homology, CW complexes, Homological algebra, Cohomology... Learn about: GCSE Mathematics...

...Hatcher. Algebraic Topology. Cambridge, New York, NY: Cambridge University Press, 2002. ISBN: 052179160X. (Available online.) May. A Concise Course in Algebraic Topology...

...in symplectic geometry, representation theory, and combinatorics. Lectures: 3 sessions / week, 1 hour / session 18.906 Algebraic Topology II The Kan seminar—named... Learn about: Professor Training...

...(the theory of unstable modules over the Steenrod algebra) which enter into the proof of Sullivan's conjecture. Algebraic Topology II, (18...

...Analysis II (18.101) and Algebraic Topology (18.905) 100% of the grading is based on the assignments. Bott, Raoul, R. Bott, and Loring W...

...It is aimed at students who already have some basic knowledge in symplectic and complex geometry (18.966, or equivalent). The geometric concepts needed...

...for students who are ready to work on challenging research problems. Each lecture will discuss: Lectures: 1 session / week, 3 hours / session Tom Leighton... Learn about: Communication Training...

...For this reason, the latter is intimately related to the ideas of mirror symmetry. Lectures: 2 sessions / week, 1.5 hours / session This will be an introductory...

...1.5 hours / session This is an advanced topics course in model theory whose main theme is simple theories. We treat simple theories in the framework of compact abstract theories...