Stability and Complexity in Model Banking Systems
The recent banking crises have made it clear that increasingly complex strategies for managing risk in individual banks and investment funds (pension funds, etc) has not been matched by corresponding attention to overall systemic risks. Simple mathematical caricatures of 'banking ecosystems', which capture some of the essential dynamics and which have some parallels (along with significant differences) with earlier work on stability and complexity in ecological food webs, have interesting implic
Langford's Cubes Answer
Mathematical patterns with building blocks.
The biology of the 21st Century
Professor Denis Noble, who was a pioneer in the field of systems biology building the first working mathematical model of the heart and has been given an honorary degree at Warwick, talks about how the future study of biology will change in the 21st Century.
Learning to Think Mathematically
Concerned that most students leave college thinking of mathematics as a fixed body of knowledge to be memorized, Cooperstein designed a new course to help students learn to think mathematically for themselves. This website serves as a course portfolio that documents the new class, Introduction to Mathematical Problem Solving. The principal activity in the class involved students working on and discussing novel problems which required them to formulate experiments, work out cases, look for patter
DNA Microarrays: Background, Interactive Databases, and Hands-on Data Analysis
DNA microarrays are influencing many areas of biology. DNA microarrays allow investigators to measure simultaneously the activity of every gene in a genome. This paper provides the reader with background information, a set of interactive questions, and most importantly, free software (MAGIC Tool) for use in the undergraduate curriculum. MAGIC Tool (www.bio.davidson.edu/MAGIC) resources allow the user to understand how DNA microarray data are analyzed by providing raw data, instructions, mathemat
18.755 Introduction to Lie Groups (MIT)
This course is devoted to the theory of Lie Groups with emphasis on its connections with Differential Geometry. The text for this class is Differential Geometry, Lie Groups and Symmetric Spaces by Sigurdur Helgason (American Mathematical Society, 2001).
Much of the course material is based on Chapter I (first half) and Chapter II of the text. The text however develops basic Riemannian Geometry, Complex Manifolds, as well as a detailed theory of Semisimple Lie Groups and Symmetric
Classroom Innovations through Lesson Study
Classroom Innovations through Lesson Study is an APEC EDNET Project that aims to improve the quality of education in the area of Mathematics. This project is sponsored by APEC Members Japan and Thailand. The APEC-Tsukuba International Conference III was broadcast live from Tokyo, December 9-10, 2007. The project has produced useful papers describing mathematical thinking, lesson videos of classroom instruction.
This project focuses on Lesson Study with the goal of improving the quality of educat
Introduction to Nanoscale Science: Surface Area to Volume Ratio Module
Many intriguing phenomena observed in the "nanoworld" can be attributed to the increase in the surface to volume ratio ( SVR ) at the nanoscale. Understanding the surface area effects to volume changes is thus crucial to the understanding of nanoscale phenomena and nanotechnology applications. As an introduction to the nanoworld, the major goals of this module are to (1) give students a feel for just how small the nanoscale is, (2) give students practice in mathematically communicating nanoscale
MAS.450 Holographic Imaging (MIT)
MAS.450 is a laboratory course about holography and holographic imaging.
This course teaches holography from a scientific and analytical point of view, moving from interference and diffraction to imaging of single points to the display of three-dimensional images. Using a "hands-on" approach, students explore the underlying physical phenomena that make holograms work, as well as designing laboratory setups to make their own images. The course also teaches mathematical techniques that allow the b
Private Universe Project in Mathematics: Workshop 2. Are You Convinced?
Proof making is one of the key ideas in mathematics. Looking at teachers and students grappling with the same probability problem, we see how two kinds of proofproof by cases and proof by inductionnaturally grow out of the need to justify and convince others.,Englewood, New JerseyTeachers Workshop Englewood, a town with unsatisfactory student test scores, is implementing a long-term project to improve math achievement. As part of a professional development workshop designed in part to give
The Great Magnet, the Earth
This site provides a non-mathematical introduction to the magnetism of the Earth, the Sun, the planets and their environments, following a historical thread. In 1600, four hundred years ago William Gilbert, later physician to Queen Elizabeth I of England, published his great study of magnetism, "De Magnete"--"On the Magnet". It gave the first rational explanation to the mysterious ability of the compass needle to point north-south: the Earth itself was magnetic. "De Magnete" opened the era of mo
How to use Microsoft Excel in the Classroom
I am finding my students are increasingly using spreadsheets to solve mathematical problems in class and represent their data and findings in meaningful ways. Th
18.238 Geometry and Quantum Field Theory (MIT)
Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and String Theory.
15.075 Applied Statistics (MIT)
This course is an introduction to applied statistics and data analysis. Topics include collecting and exploring data, basic inference, simple and multiple linear regression, analysis of variance, nonparametric methods, and statistical computing. It is not a course in mathematical statistics, but provides a balance between statistical theory and application. Prerequisites are calculus, probability, and linear algebra.
We would like to acknowledge the contributions that Prof. Roy Welsch (MIT), Pro
18.413 Error-Correcting Codes Laboratory (MIT)
This course introduces students to iterative decoding algorithms and the codes to which they are applied, including Turbo Codes, Low-Density Parity-Check Codes, and Serially-Concatenated Codes. The course will begin with an introduction to the fundamental problems of Coding Theory and their mathematical formulations. This will be followed by a study of Belief Propagation--the probabilistic heuristic which underlies iterative decoding algorithms. Belief Propagation will then be applied to the dec
18.305 Advanced Analytic Methods in Science and Engineering (MIT)
Advanced Analytic Methods in Science and Engineering is a comprehensive treatment of the advanced methods of applied mathematics. It was designed to strengthen the mathematical abilities of graduate students and train them to think on their own.
8.591J Systems Biology (MIT)
This course introduces the mathematical modeling techniques needed to address key questions in modern biology. An overview of modeling techniques in molecular biology and genetics, cell biology and developmental biology is covered. Key experiments that validate mathematical models are also discussed, as well as molecular, cellular, and developmental systems biology, bacterial chemotaxis, genetic oscillators, control theory and genetic networks, and gradient sensing systems. Additional specific t
6.881 Representation and Modeling for Image Analysis (MIT)
Most algorithms in computer vision and image analysis can be understood in terms of two important components: a representation and a modeling/estimation algorithm. The representation defines what information is important about the objects and is used to describe them. The modeling techniques extract the information from images to instantiate the representation for the particular objects present in the scene. In this seminar, we will discuss popular representations (such as contours, level sets,
6.435 System Identification (MIT)
This course is offered to graduates and includes topics such as mathematical models of systems from observations of their behavior; time series, state-space, and input-output models; model structures, parametrization, and identifiability; non-parametric methods; prediction error methods for parameter estimation, convergence, consistency, and asymptotic distribution; relations to maximum likelihood estimation; recursive estimation; relation to Kalman filters; structure determination; order estima
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.
