18.091 Mathematical Exposition (MIT)
This course provides techniques of effective presentation of mathematical material. Each section of this course is associated with a regular mathematics subject, and uses the material of that subject as a basis for written and oral presentations. The section presented here is on chaotic dynamical systems.
14.12 Economic Applications of Game Theory (MIT)
Game Theory is a misnomer for Multiperson Decision Theory, the analysis of situations in which payoffs to agents depend on the behavior of other agents. It involves the analysis of conflict, cooperation, and (tacit) communication. Game theory has applications in several fields, such as economics, politics, law, biology, and computer science. In this course, I will introduce the basic tools of game theoretic analysis. In the process, I will outline some of the many applications of game theory, pr
9.29J Introduction to Computational Neuroscience (MIT)
This course gives a mathematical introduction to neural coding and dynamics. Topics include convolution, correlation, linear systems, game theory, signal detection theory, probability theory, information theory, and reinforcement learning. Applications to neural coding, focusing on the visual system are covered, as well as Hodgkin-Huxley and other related models of neural excitability, stochastic models of ion channels, cable theory, and models of synaptic transmission. Visit the Seung Lab Web s
10.34 Numerical Methods Applied to Chemical Engineering (MIT)
This course focuses on the use of modern computational and mathematical techniques in chemical engineering. Starting from a discussion of linear systems as the basic computational unit in scientific computing, methods for solving sets of nonlinear algebraic equations, ordinary differential equations, and differential-algebraic (DAE) systems are presented. Probability theory and its use in physical modeling is covered, as is the statistical analysis of data and parameter estimation. The finite di
20.420J Biomolecular Kinetics and Cellular Dynamics (BE.420J) (MIT)
This subject deals primarily with kinetic and equilibrium mathematical models of biomolecular interactions, as well as the application of these quantitative analyses to biological problems across a wide range of levels of organization, from individual molecular interactions to populations of cells.
10.442 Biochemical Engineering (MIT)
This course focuses on the interaction of chemical engineering, biochemistry, and microbiology. Mathematical representations of microbial systems are featured among lecture topics. Kinetics of growth, death, and metabolism are also covered. Continuous fermentation, agitation, mass transfer, and scale-up in fermentation systems, and enzyme technology round out the subject material.
18.086 Mathematical Methods for Engineers II (MIT)
This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization.
3.016 Mathematics for Materials Scientists and Engineers (MIT)
This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigen
Mini project : ROM based sine wave generator : document transcript
This is Mini Project documentation introducing a ROM-Based Sine Wave Generator. It is part of the 2009/10 BEng in Digital Systems and Computer Engineering (course number 2ELE0065) from the University of Hertfordshire. All the mini projects are designed as level two modules of the undergraduate programmes. It includes an introduction, project briefs for days 1 and 2 and a preparation session. This project requires the establishment of a communication protocol between two 68000-based microco
3.91 Mechanical Behavior of Plastics (MIT)
This course is aimed at presenting the concepts underlying the response of polymeric materials to applied loads. These will include both the molecular mechanisms involved and the mathematical description of the relevant continuum mechanics. It is dominantly an "engineering" subject, but with an atomistic flavor. It covers the influence of processing and structure on mechanical properties of synthetic and natural polymers: Hookean and entropic elastic deformation, linear viscoelasticity, composit
18.369 Mathematical Methods in Nanophotonics (MIT)
Find out what solid-state physics has brought to Electromagnetism in the last 20 years. This course surveys the physics and mathematics of nanophotonics—electromagnetic waves in media structured on the scale of the wavelength. Topics include computational methods combined with high-level algebraic techniques borrowed from solid-state quantum mechanics: linear algebra and eigensystems, group theory, Bloch's theorem and conservation laws, perturbation methods, and coupled-mode theories, to u
21L.017 The Art of the Probable: Literature and Probability (MIT)
"The Art of the Probable" addresses the history of scientific ideas, in particular the emergence and development of mathematical probability. But it is neither meant to be a history of the exact sciences per se nor an annex to, say, the Course 6 curriculum in probability and statistics. Rather, our objective is to focus on the formal, thematic, and rhetorical features that imaginative literature shares with texts in the history of probability. These shared issues include (but are not limited to)
18.085 Computational Science and Engineering I (MIT)
This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications. Note: This course was previously called "Mathematical Methods for Engineers I."
12.086 Modeling Environmental Complexity (MIT)
This course provides an introduction to the study of environmental phenomena that exhibit both organized structure and wide variability—i.e., complexity. Through focused study of a variety of physical, biological, and chemical problems in conjunction with theoretical models, we learn a series of lessons with wide applicability to understanding the structure and organization of the natural world. Students will also learn how to construct minimal mathematical, physical, and computational mod
18.312 Algebraic Combinatorics (MIT)
This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected.
18.311 Principles of Applied Mathematics (MIT)
This course is about mathematical analysis of continuum models of various natural phenomena. Such models are generally described by partial differential equations (PDE) and for this reason much of the course is devoted to the analysis of PDE. Examples of applications come from physics, chemistry, biology, complex systems: traffic flows, shock waves, hydraulic jumps, bio-fluid flows, chemical reactions, diffusion, heat transfer, population dynamics, and pattern formation.
18.034 Honors Differential Equations (MIT)
This course covers the same material as Differential Equations (18.03) with more emphasis on theory. In addition, it treats mathematical aspects of ordinary differential equations such as existence theorems.
2.1 Two examples
This unit introduces ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the first in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘foreground level’ of voice leading. As you work through this unit, you will become familiar with five complete movements of Mozart’s piano
Virtual Maths - Shapes, Space and Measure, Theodolite Survey simulation
Simulation of using a thodolite to calculate the height of a building.
Hendrik Lenstra, University of Leiden: "Escher and the Droste Effect" - April 3, 2007
In 1956 the Dutch graphic artist M. C. Escher made an unusual lithograph with the title "Print Gallery." It shows a young man viewing a print in an exhibition gallery. Among the buidlings depicted on the print, he sees paradoxically the very same gallery that he is standing in. A lot is known about the way in which Escher made his lithograph. It is not nearly as well known that it contains a hidden "Droste effect," or infinite repetition; but this is brought to light by a mathematical analysis o