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  • 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 
    Mechanics of Material Systems: An Energy Approach

    Mechanics of Material Systems: An Energy Approach

    This course provides an introduction to continuum mechanics and material modelling of engineering materials based on first energy principles: deformation and strain; momentum balance, stress and stress states; elasticity and elasticity bounds; plasticity and yield design. The overarching theme is a unified mechanistic language using thermodynamics, which allows understanding, modelling and design of a large range of engineering materials.

    Subjects:
    Physics
    Keywords:
    Continuum mechanics Solid state physics Mechanics
    Resource Type:
    Courseware
     
  • Courseware 
    Molecular, Cellular, and Tissue Biomechanics

    Molecular, Cellular, and Tissue Biomechanics

    This course develops and applies scaling laws and the methods of continuum and statistical mechanics to biomechanical phenomena over a range of length scales, from molecular to cellular to tissue or organ level.

    Subjects:
    Biomedical Engineering and Biology
    Keywords:
    Biomedical engineering Biomechanics
    Resource Type:
    Courseware
     
  • Courseware 
    Neurotechnology in Action

    Neurotechnology in Action

    This course explores cutting-edge neurotechnology that is essential for advances in all aspects of neuroscience, including improvements in existing methods as well as the development, testing and discussion of completely new paradigms. Readings and in-class sessions cover the fields of electrophysiology, light microscopy, cellular engineering, optogenetics, electron microscopy, MRI / fMRI, and MEG / EEG.

    Subjects:
    Biomedical Engineering and Biology
    Keywords:
    Neurotechnology (Bioengineering)
    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
     
  • 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 
    Optics

    Optics

    This course provides an introduction to optical science with elementary engineering applications. Topics covered in geometrical optics include: ray-tracing, aberrations, lens design, apertures and stops, radiometry and photometry. Topics covered in wave optics include: basic electrodynamics, polarization, interference, wave-guiding, Fresnel and Fraunhofer diffraction, image formation, resolution, space-bandwidth product. Analytical and numerical tools used in optical design are emphasized. Graduate students are required to complete assignments with stronger analytical content, and an advanced design project.

    Subjects:
    Physics
    Keywords:
    Optics Geometrical optics
    Resource Type:
    Courseware
     
  • Courseware 
    Organic Chemistry I

    Organic Chemistry I

    This subject deals primarily with the basic principles to understand the structure and reactivity of organic molecules. Emphasis is on substitution and elimination reactions and chemistry of the carbonyl group. The course also provides an introduction to the chemistry of aromatic compounds.

    Subjects:
    Chemistry
    Keywords:
    Carbonyl compounds Molecular structure Chemistry Organic Aromatic compounds
    Resource Type:
    Courseware
     
  • Courseware 
    Peptides as Biological Signaling Molecules and Novel Drugs

    Peptides as Biological Signaling Molecules and Novel Drugs

    How do we sense hunger? How do we sense pain? What causes growth in our bodies? How are we protected from pathogens? The answer to many of these questions involves small polymers of amino acids known as peptides. Peptides are broadly used as signal molecules for intercellular communication in prokaryotes, plants, fungi, and animals. Peptide signals in animals include vast numbers of peptide hormones, growth factors and neuropeptides. In this course, we will learn about molecular bases of peptide signaling. In addition, peptides potentially can be used as potent broad-spectrum antibiotics and hence might define novel therapeutic agents.

    Subjects:
    Biology
    Keywords:
    Peptides
    Resource Type:
    Courseware
     
  • Courseware 
    Physics III: Vibrations and Waves

    Physics III: Vibrations and Waves

    Vibrations and waves are everywhere. If you take any system and disturb it from a stable equilibrium, the resultant motion will be waves and vibrations. Think of a guitar string—pluck the string, and it vibrates. The sound waves generated make their way to our ears, and we hear the string’s sound. Our eyes see what’s happening because they receive the electromagnetic waves of the light reflected from the guitar string, so that we can recognize the beautiful sinusoidal waves on the string.

    Subjects:
    Physics
    Keywords:
    Waves Vibration
    Resource Type:
    Courseware