Online courses directory (19947)

This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.

This course is an introduction to arithmetic geometry, a subject that lies at the intersection of algebraic geometry and number theory. Its primary motivation is the study of classical Diophantine problems from the modern perspective of algebraic geometry.

In this subject, we consider two basic topics in cellular biophysics, posed here as questions:

1. Which molecules are transported across cellular membranes, and what are the mechanisms of transport? How do cells maintain their compositions, volume, and membrane potential?
2. How are potentials generated across the membranes of cells? What do these potentials do?

Although the questions posed are fundamentally biological questions, the methods for answering these questions are inherently multidisciplinary. As we will see throughout the course, the role of mathematical models is to express concepts precisely enough that precise conclusions can be drawn. In connection with all the topics covered, we will consider both theory and experiment. For the student, the educational value of examining the interplay between theory and experiment transcends the value of the specific knowledge gained in the subject matter.

This course is jointly offered through four departments, available to both undergraduates and graduates.

This course elaborates on the application of the principles of energy and mass flow to major human organ systems. It discusses mechanisms of regulation and homeostasis. It also discusses anatomical, physiological, and pathophysiological features of the cardiovascular, respiratory, and renal systems. There is emphasis on those systems, features, and devices that are most illuminated by the methods of physical sciences.

This course illustrates how knowledge and principles of biology, biochemistry, and engineering are integrated to create new products for societal benefit. It uses a case study format to examine recently developed products of pharmaceutical and biotechnology industries: how a product evolves from initial idea, through patents, testing, evaluation, production, and marketing. Emphasizes scientific and engineering principles; the responsibility scientists, engineers, and business executives have for the consequences of their technology; and instruction and practice in written and oral communication.

The topic focus of this class will vary from year to year. This version looks at inflammation underlying many diseases, specifically its role in cancer, diabetes, and cardiovascular disease.

This course addresses the scientific basis for the development of new drugs. The first half of the semester begins with an overview of the drug discovery process, followed by fundamental principles of pharmacokinetics, pharmacodynamics, metabolism, and the mechanisms by which drugs cause therapeutic and toxic responses. The second half of the semester applies those principles to case studies and literature discussions of current problems with specific drugs, drug classes, and therapeutic targets.

This seminar-format course provides an in-depth presentation and discussion of how engineering and biological approaches can be combined to solve problems in science and technology, emphasizing integration of biological information and methodologies with engineering analysis, synthesis, and design. Emphasis is placed on molecular mechanisms underlying cellular processes, including signal transduction, gene expression networks, and functional responses.

LEGO® robotics uses LEGO®s as a fun tool to explore robotics, mechanical systems, electronics, and programming. This seminar is primarily a lab experience which provides students with resources to design, build, and program functional robots constructed from LEGO®s and a few other parts such as motors and sensors.

This course is an introduction to Markov chains, random walks, martingales, and Galton-Watsom tree. The course requires basic knowledge in probability theory and linear algebra including conditional expectation and matrix.

This course covers empirical strategies for applied micro research questions. Our agenda includes regression and matching, instrumental variables, differences-in-differences, regression discontinuity designs, standard errors, and a module consisting of 8–9 lectures on the analysis of high-dimensional data sets a.k.a. "Big Data".

Mechanical forces play a decisive role during development of tissues and organs, during remodeling following injury as well as in normal function. A stress field influences cell function primarily through deformation of the extracellular matrix to which cells are attached. Deformed cells express different biosynthetic activity relative to undeformed cells. The unit cell process paradigm combined with topics in connective tissue mechanics form the basis for discussions of several topics from cell biology, physiology, and medicine.

This class analyzes complex biological processes from the molecular, cellular, extracellular, and organ levels of hierarchy. Emphasis is placed on the basic biochemical and biophysical principles that govern these processes. Examples of processes to be studied include chemotaxis, the fixation of nitrogen into organic biological molecules, growth factor and hormone mediated signaling cascades, and signaling cascades leading to cell death in response to DNA damage. In each case, the availability of a resource, or the presence of a stimulus, results in some biochemical pathways being turned on while others are turned off. The course examines the dynamic aspects of these processes and details how biochemical mechanistic themes impinge on molecular/cellular/tissue/organ-level functions. Chemical and quantitative views of the interplay of multiple pathways as biological networks are emphasized. Student work culminates in the preparation of a unique grant application in an area of biological networks.

This course, intended for both graduate and upper level undergraduate students, will focus on understanding of the basic molecular structural principles of biological materials. It will address the molecular structures of various materials of biological origin, such as several types of collagen, silk, spider silk, wool, hair, bones, shells, protein adhesives, GFP, and self-assembling peptides. It will also address molecular design of new biological materials applying the molecular structural principles. The long-term goal of this course is to teach molecular design of new biological materials for a broad range of applications. A brief history of biological materials and its future perspective as well as its impact to the society will also be discussed. Several experts will be invited to give guest lectures.

This course focuses on the fundamentals of tissue and organ response to injury from a molecular and cellular perspective. There is a special emphasis on disease states that bridge infection, inflammation, immunity, and cancer. The systems approach to pathophysiology includes lectures, critical evaluation of recent scientific papers, and student projects and presentations.

This term, we focus on hepatocellular carcinoma (HCC), chronic-active hepatitis, and hepatitis virus infections. In addition to lectures, students work in teams to critically evaluate and present primary scientific papers.

This design course targets the solution of clinical problems by use of implants and other medical devices. Topics include the systematic use of cell-matrix control volumes; the role of stress analysis in the design process; anatomic fit, shape and size of implants; selection of biomaterials; instrumentation for surgical implantation procedures; preclinical testing for safety and efficacy, including risk/benefit ratio assessment evaluation of clinical performance and design of clinical trials. Student project materials are drawn from orthopedic devices, soft tissue implants, artificial organs, and dental implants.

This course analyzes cooperative processes that shape the natural environment, now and in the geologic past. It emphasizes the development of theoretical models that relate the physical and biological worlds, the comparison of theory to observational data, and associated mathematical methods.

This course encourages creative thinking through hands-on experience via building, observing and manipulating micro-and nano-scale structures. Students learn about underlying science and engineering principles and possible applications.

This course teaches the design of contemporary information systems for biological and medical data. Examples are chosen from biology and medicine to illustrate complete life cycle information systems, beginning with data acquisition, following to data storage and finally to retrieval and analysis. Design of appropriate databases, client-server strategies, data interchange protocols, and computational modeling architectures. Students are expected to have some familiarity with scientific application software and a basic understanding of at least one contemporary programming language (e.g. C, C++, Java, Lisp, Perl, Python). A major term project is required of all students. This subject is open to motivated seniors having a strong interest in biomedical engineering and information system design with the ability to carry out a significant independent project.

This course was offered as part of the Singapore-MIT Alliance (SMA) program as course number SMA 5304.

This course covers the analysis and design at a molecular scale of materials used in contact with biological systems, including biotechnology and biomedical engineering. Topics include molecular interactions between bio- and synthetic molecules and surfaces; design, synthesis, and processing approaches for materials that control cell functions; and application of state-of-the-art materials science to problems in tissue engineering, drug delivery, vaccines, and cell-guiding surfaces.

22.56J aims to give graduate students and advanced undergraduates background in the theory and application of noninvasive imaging methods to biology and medicine, with emphasis on neuroimaging. The course focuses on the modalities most frequently used in scientific research (X-ray CT, PET/SPECT, MRI, and optical imaging), and includes discussion of molecular imaging approaches used in conjunction with these scanning methods. Lectures by the professor will be supplemented by in-class discussions of problems in research, and hands-on demonstrations of imaging systems.