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Courseware
Like other scientists, medical researchers and clinicians must be capable of presenting their work to an audience of professional peers. Unlike many scientists, however, physicians must routinely translate their sophisticated knowledge into lay terms for their own patients and for the education of the public at large. A surprising number of physicians write for less utilitarian reasons as well, choosing the narrative essay as a means of exploring the non-technical issues that emerge in their clinical practice. Over the course of the semester, we will explore the full range of writings by physicians and other health practitioners.
- Subjects:
- English Language
- Keywords:
- Medical writing
- Resource Type:
- Courseware
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Courseware
This is a graduate-level 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
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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 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
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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 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
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Courseware
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
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Courseware
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
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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
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Courseware
Parasites require a hospitable organism to reproduce and spread and have evolved multiple strategies to subvert their hosts. Parasites scavenge nutrients directly from host cells, evade the host immune system and even modify host behavior to increase their transmission. This course will explore the strategies used by a ubiquitous and harmful class of parasites to hijack the biology of their host cells. We will discuss pathogens such as Plasmodium and Toxoplasma, responsible for some of the deadliest and most pervasive infectious diseases on the planet. By exploring how these pathogens invade a host cell and replicate while evading the immune system, students will gain a broad understanding of basic cell biology, biochemistry and immunology, as well as learn techniques commonly used in cell biology. Students will be challenged to think creatively and flexibly to understand, critique, interpret, and design scientific experiments in the field of host-pathogen interactions.
- Subjects:
- Biology
- Keywords:
- Pathogenic microorganisms Parasites
- Resource Type:
- Courseware
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Courseware
This first course in the physics curriculum introduces classical mechanics. Historically, a set of core concepts—space, time, mass, force, momentum, torque, and angular momentum—were introduced in classical mechanics in order to solve the most famous physics problem, the motion of the planets. The principles of mechanics successfully described many other phenomena encountered in the world. Conservation laws involving energy, momentum and angular momentum provided a second parallel approach to solving many of the same problems. In this course, we will investigate both approaches: Force and conservation laws. Our goal is to develop a conceptual understanding of the core concepts, a familiarity with the experimental verification of our theoretical laws, and an ability to apply the theoretical framework to describe and predict the motions of bodies.
- Subjects:
- Physics
- Keywords:
- Kinematics Torque Mass (Physics) Angular momentum Force energy Motion Mechanics
- Resource Type:
- Courseware
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Courseware
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