20.181 Computation for Biological Engineers (MIT)
This course covers the analytical, graphical, and numerical methods supporting the analysis and design of integrated biological systems. Topics include modularity and abstraction in biological systems, mathematical encoding of detailed physical problems, numerical methods for solving the dynamics of continuous and discrete chemical systems, statistics and probability in dynamic systems, applied local and global optimization, simple feedback and control analysis, statistics and probability in pat
18.366 Random Walks and Diffusion (MIT)
This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.
Waterpower in Austria
Short film on alternativ energy production in Austria, by Lebensministerium Austria (duration 2 min.).
2.035 Special Topics in Mathematics with Applications: Linear Algebra and the Calculus of Variations
This course forms an introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory, optimization techniques, calculus of variations and linear algebra. The topics covered in any particular year depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in mechanical engineering. This year, the subject
NASA CONNECT Proportionality: Modeling the Future
In NASA CONNECT Proportionality: Modeling the Future, students learn why scaling and proportion are important in the design of small aircraft transportation systems. Mathematical patterns are described through practical applications such as the growth of transportation, the Golden Ratio, and the Fibonacci sequence. Grades 4-8.
These are my lecture notes for a course I teach on mathematical biology at the Hong Kong University of Science & Technology. My main emphasis is on mathematical modeling, with biology the sole application area.
Notes on OpenOffice Writer: large and complex documents
This book is about how to use OpenOffice Writer to create large and complex documents. It explains how Writer organises text into paragraphs and pages and shows how styles and formatting control the appearance of the document. It discusses how to create headings, tables, figures, frames and mathematical expression. It discusses how to handle citation and referencing in the three common styles, and shows how to create tables of contents and indices.
The Development and Use of Representations in Teaching and Learning about Problem Solving: Exploring
Tim Boerst has explored instructional approaches that foster the development of representational skill and routine use of multiple representations in problem solving. In particular he has used the 'Rule of 3' (a structure employed in calculus reform materials that highlights the use of numerical, algebraic, and/or graphic representations in mathematical learning) to see whether an emphasis on multiple representations would deepen mathematical learning opportunities for a wide variety of students
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
Environmental Decision Making
Using the Extend 'connect-the-components' visual programming, students can model and simulate ecosystems including social and economic forces as well as study parameter variations to develop an understanding of ecosystem function and productivity. By making 'what if...' changes in the model, the effects of various proposed decisions about the environment can then be shown. EDM includes three ecological systems: Ponds, Grasslands, and Logging. Students can predict results of changes in the mode
Essential Physics I
Essential Physics 1, is an intensive introduction to classical and special relativity, Newtonian dynamics and gravitation, Einsteinian dynamics and gravitation, and wave motion. Mathematical methods are discussed, as needed; they include: elements of differential geometry, linear operators and matrices, ordinary differential equations, calculus of variations, orthogonal functions and Fourier series, and non-linear equations for chaotic systems. The contents of this book can be taught in one seme
Introduction to Groups, Invariants and Particles
Introduction to Groups, Invariants & Particles is a book for Seniors and advanced Juniors who are majoring in the Physical Sciences or Mathematics. The book places the subject matter in its historical context with discussions of Galois groups, algebraic invariants, Lie groups and differential equations, presented at a level that is not the standard fare for students majoring in the Physical Sciences. A sound mathematical basis is thereby provided for the study of special unitary groups and their
Written with the advanced undergraduate or graduate student in mind, Electromagnetic Field Theory is a textbook on the theory of electrodynamics, at roughly the same level as the well-known textbooks by Jackson and Panofsky&Phillips. The book is written mainly from a classical field theoretical point of view, emphasising fundamental and subtle properties of the EM field and includes a comprehensive appendix on the mathematical methods used.
Mathematics Under the Microscope
This book inevitably asks the question "How does the mathematical brain work?" The author tries to reflect on the explosive development of mathematical cognition, an emerging branch of neurophysiology which purports to locate structures and processes in the human brain responsible for mathematical thinking. PDF file.
Basic Analysis: Introduction to Real Analysis
This free online textbook is a one semester course in basic analysis. These were my lecture notes for teaching Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in fall 2009. The course is a first course in mathematical analysis aimed at students who do not necessarily wish to continue a graduate study in mathematics. A Sample Darboux sums prerequisite for the course is a basic proof course. The course does not cover topics such as metric spaces, which a more advanced course woul
From Algorithms to Z-Scores: Probabilistic and Statistical Modeling in Computer Science
The materials here form a textbook for a course in mathematical probability and statistics for computer science students. Computer science examples are used throughout, in areas such as: computer networks; data and text mining; computer security; remote sensing; computer performance evaluation; software engineering; data management; etc.
SkyMath: Mathematics for a Blue Planet
SkyMath is a set of middle school mathematics modules incorporating weather data. The modules require teachers and students to acquire and use current environmental and real-time weather data in ways that embrace the dynamic and uncertain natures of these data, in order to promote the teaching and learning of significant mathematics, consistent with the standards set by the National Council of Teachers of Mathematics. The module includes 16 activities and can be incorporated as a replacement uni
Children Play - The Foundation for Mathematical Learning
Children acquire mathematical concepts from games such as rope, dice and cards. This book identifies the games as a foundation for mathematical learning in Grades 1 to 3.
Helping Your Child Learn Mathematics and Statistics
This site features dozens of fun activities parents can use to help children (K-5th grade) have fun learning geometry, algebra, measurement, statistics, probability and other important mathematical concepts. Activities relate math to everyday life and can be done at home, at the grocery store, or while traveling. It includes sections for parents on what math is like in schools today and a parents' booklist for helping children learn math.
Every month we will give you a math/statistics brain teaser that lets you test your knowledge with a fun problem.Many of the ideas in these Teasers come from thoughts formed by some of the great mathematical/statistical geniuses in history.