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  • 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 Algebraic number theory Class field 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:
    Number theory Algebraic number theory
    Resource Type:
    Courseware
     
  • Image 
    Open-i®

    Open-i®

    Open Access Biomedical Image Search Engine

    Keywords:
    Diagnostic imaging Medical photography Digital images
    Resource Type:
    Image
     
  • Image 
    Public Health Image Library (PHIL)

    Public Health Image Library (PHIL)

    Created by a Working Group at the Centers for Disease Control and Prevention (CDC), the PHIL offers an organized, universal electronic gateway to CDC's pictures. Public health professionals, the media, laboratory scientists, educators, students, and the worldwide public can use this material for reference, teaching, presentation, and public health messages. Most images are for free use.

    Keywords:
    Digital images Public health Medical photography
    Resource Type:
    Image
     
  • Image 
    MedPix®

    MedPix®

    A free open-access online database of medical images, teaching cases, and clinical topics, integrating images and textual metadata including over 12,000 patient case scenarios, 9,000 topics, and nearly 59,000 images.

    Keywords:
    Digital images Medical photography
    Resource Type:
    Image
     
  • e-journal 
    OMICS International (Bioinformatics & Systems Biology)

    OMICS International (Bioinformatics & Systems Biology)

    OMICS International is an interactive open access journal for the communication of all scientific and medical research.

    Subjects:
    Biology
    Keywords:
    Bioinformatics Systems biology
    Resource Type:
    e-journal
     
  • e-journal 
    OMICS International (Plant Sciences)

    OMICS International (Plant Sciences)

    OMICS International is an interactive open access journal for the communication of all scientific and medical research.

    Subjects:
    Food Science and Biology
    Keywords:
    Botany Food industry trade Nutrition Natural products
    Resource Type:
    e-journal
     
  • e-journal 
    OMICS International (Neuroscience & Psychology)

    OMICS International (Neuroscience & Psychology)

    OMICS International is an interactive open access journal for the communication of all scientific and medical research.

    Keywords:
    Psychiatry Brain -- Diseases Neurology
    Resource Type:
    e-journal