Mathematics Degrees

...helpful as we'll be doing plenty of those in class and homework. However, if you aren't used to mathematical proofs, don't despair! You will hopefully...

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

...problems from the modern perspective of algebraic geometry. Topics include: Each topic represents 1-2 weeks of lectures There is no required...

...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...

...at the level of Rudin's "Principles of Mathematical Analysis" (18.100B here at MIT.) This background is essential both for the knowledge of the subject... Learn about: GCSE Mathematics...

...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...

...Lectures will be delivered by the students, with two students speaking at each class. There are no exams. There will be some homework assignments and a final paper...

...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...

...centered on the notion of curvature. Analysis I (18.100) plus Linear Algebra (18.06 or 18.700) or Algebra I (18.701) Kuhnel, Wolfgang. Differential Geometry...

...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...

...and Michael Spivak's Calculus on Manifolds, Manfredo Do Carmo's Curves and Surfaces. Lars Ahlfors' Complex Analysis will also be referred to at various points... Learn about: GCSE Mathematics...

...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...