Mathematics Degrees

...and Galton-Watsom tree. The course requires basic knowledge in probability theory and linear algebra including conditional expectation and matrix...

...foundations for statistical methods that are useful in many applications. The goal is to understand the role of mathematics in the research and development... Learn about: GCSE Mathematics...

...1945 and deals with order statistics and ranks, allowing very general distributions. For multidimensional nonparametric statistics, an early approach...

...concentrating on specific statistical techniques used in science and industry. Topics include: Hypothesis testing and estimation, confidence intervals... Learn about: Confidence Training...

...Machine Learning refers to the automated identification of patterns in data. As such it has been a fertile ground for new statistical and algorithmic developments... Learn about: GCSE Mathematics...

...foundations for statistical methods that are useful in many applications. The goal is to understand the role of mathematics in the research and development... Learn about: GCSE Mathematics...

...rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory. Students...

...Students should plan to study this chapter on their own. Artin, M. Algebra (2nd Edition). Addison Wesley, 2010. ISBN: 9780132413770. This undergraduate...

...confidence intervals, and hypothesis testing. It introduces large sample theory, asymptotic efficiency of estimates, exponential families, and sequential analysis... Learn about: Confidence Training...

...including ideals and unique factorization in polynomial and Euclidean rings; field theory, including properties and applications of finite fields... Learn about: GCSE Mathematics...

...are based on the textbook below: Koblitz, Neal. Introduction to Elliptic Curves and Modular Forms. 2nd ed. New York: Springer-Verlag, 1993.... Learn about: GCSE Mathematics...

...and are provided with instruction and practice in written and oral communication. Some experience with proofs required. Linear Algebra... Learn about: Oral Communication, Communication Training...

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

...and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces. The prerequisites... Learn about: GCSE Mathematics...

...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...

...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...