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Courseware
This is a graduatelevel introduction to mathematics of information theory. We will cover both classical and modern topics, including information entropy, lossless data compression, binary hypothesis testing, channel coding, and lossy data compression.
 Subjects:
 Computing and Mathematics and Statistics
 Keywords:
 Information theory Information theory in mathematics
 Resource Type:
 Courseware

ebook
Covers over 5,000 reports published by the National Academies Press for the National Academy of Sciences, National Academy of Engineering, Institute of Medicine and National Research Council in the US.
 Subjects:
 Physics, Chemistry, and Mathematics and Statistics
 Keywords:
 Physics Mathematics Chemistry
 Resource Type:
 ebook

ejournal
OMICS International is an interactive open access journal for the communication of all scientific and medical research.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Statistics Mathematics
 Resource Type:
 ejournal

Courseware
This is the first semester of a one year graduate course in number theory covering standard topics in algebraic and analytic number theory. At various points in the course, we will make reference to material from other branches of mathematics, including topology, complex analysis, representation theory, and algebraic geometry.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Number theory Algebraic number theory
 Resource Type:
 Courseware

Courseware
This course is the continuation of 18.785 Number Theory I. It begins with an analysis of the quadratic case of Class Field Theory via Hilbert symbols, in order to give a more handson introduction to the ideas of Class Field Theory. More advanced topics in number theory are discussed in this course, such as Galois cohomology, proofs of class field theory, modular forms and automorphic forms, Galois representations, and quadratic forms.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Galois cohomology Algebraic number theory Class field theory
 Resource Type:
 Courseware

Courseware
This graduatelevel course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Curves Elliptic
 Resource Type:
 Courseware

Courseware
This graduatelevel course focuses on current research topics in computational complexity theory. Topics include: Nondeterministic, alternating, probabilistic, and parallel computation models; Boolean circuits; Complexity classes and complete sets; The polynomialtime hierarchy; Interactive proof systems; Relativization; Definitions of randomness; Pseudorandomness and derandomizations;Interactive proof systems and probabilistically checkable proofs.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Computational complexity
 Resource Type:
 Courseware

Courseware
In this course, we study elliptic Partial Differential Equations (PDEs) with variable coefficients building up to the minimal surface equation. Then we study Fourier and harmonic analysis, emphasizing applications of Fourier analysis. We will see some applications in combinatorics / number theory, like the Gauss circle problem, but mostly focus on applications in PDE, like the CalderonZygmund inequality for the Laplacian, and the Strichartz inequality for the Schrodinger equation. In the last part of the course, we study solutions to the linear and the nonlinear Schrodinger equation. All through the course, we work on the craft of proving estimates.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Fourier analysis Differential equations Partial
 Resource Type:
 Courseware

Courseware
This course provides students with decision theory, estimation, confidence intervals, and hypothesis testing. It introduces large sample theory, asymptotic efficiency of estimates, exponential families, and sequential analysis.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematical statistics
 Resource Type:
 Courseware

Courseware
This course offers an indepth the theoretical foundations for statistical methods that are useful in many applications. The goal is to understand the role of mathematics in the research and development of efficient statistical methods.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematical statistics
 Resource Type:
 Courseware