Search Constraints

Number of results to display per page
Results for:

Search Results

  • Courseware 
    Computational Personal Genomics: Making Sense of Complete Genomes

    Computational Personal Genomics: Making Sense of Complete Genomes

    With the growing availability and lowering costs of genotyping and personal genome sequencing, the focus has shifted from the ability to obtain the sequence to the ability to make sense of the resulting information. This course is aimed at exploring the computational challenges associated with interpreting how sequence differences between individuals lead to phenotypic differences in gene expression, disease predisposition, or response to treatment.

    Subjects:
    Computing, Data Science and Artificial Intelligence and Biology
    Keywords:
    Genomes Genomics
    Resource Type:
    Courseware
     
  • Courseware 
    Ancient Greek Philosophy and Mathematics

    Ancient Greek Philosophy and Mathematics

    This course explores the relationship between ancient Greek philosophy and mathematics. We investigate how ideas of definition, reason, argument and proof, rationality / irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry. The course examines how discovery of the incommensurability of magnitudes challenged the Greek presumption that the cosmos is fully understandable. Students explore the influence of mathematics on ancient Greek ethical theories. We read such authors as: Euclid, Plato, Aristotle, Nicomachus, Theon of Smyrna, Bacon, Descartes, Dedekind, and Newton.

    Subjects:
    Mathematics and Statistics and Philosophy
    Keywords:
    Mathematics -- Philosophy Philosophy Ancient
    Resource Type:
    Courseware
     
  • Courseware 
    Statistics for Applications

    Statistics for Applications

    This course offers an in-depth 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
     
  • Courseware 
    Mathematical Statistics

    Mathematical Statistics

    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 
    Differential Analysis II: Partial Differential Equations and Fourier Analysis

    Differential Analysis II: Partial Differential Equations and Fourier Analysis

    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 Calderon-Zygmund 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 non-linear 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 
    Advanced Complexity Theory

    Advanced Complexity Theory

    This graduate-level 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 polynomial-time hierarchy; Interactive proof systems; Relativization; Definitions of randomness; Pseudo-randomness and derandomizations;Interactive proof systems and probabilistically checkable proofs.

    Subjects:
    Mathematics and Statistics
    Keywords:
    Computational complexity
    Resource Type:
    Courseware
     
  • Courseware 
    Work

    Elliptic Curves

    This graduate-level 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 
    Number Theory II: Class Field Theory

    Number Theory II: Class Field Theory

    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 hands-on 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 Class field theory Algebraic number theory
    Resource Type:
    Courseware
     
  • Courseware 
    Work

    Number Theory I

    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:
    Algebraic number theory Number theory
    Resource Type:
    Courseware
     
  • e-journal 
    OMICS International (Mathematics)

    OMICS International (Mathematics)

    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:
    e-journal