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.
Policy Analysis of Multi-Actor Systems
This course is about solving complex problems. Our favorite problems are not just technically complex but also characterized by the presence of many different social actors that hold conflicting interests, objectives, and perceptions and act strategically to get the best out of a problem situation. This course offers guidance for policy analysts who want to assess if and how their analysis could be of help, based on the premise that problem formulation is the cornerstone in addressing complex pr
Introduction to Vectors and Tensors, Vol. 1, Linear and Multilinear Algebra
Introduction to Vectors and Tensors, Vol. 1, Linear and Multilinear Algebra is a typed revision that was originally published by Plenum Press in 1976 as Volume 1 in a series on Mathematical Concepts and Methods in Science and Engineering, edited by Angelo Miele. PDF File.
Introduction to Vectors and Tensors, Vol. 2, Vector and Tensor Analysis
Introduction to Vectors and Tensors, Vol. 2, Vector and Tensor Analysis is a typed revision of the book originally published by Plenum Press in 1976 as Volume 2 in their series on Mathematical Concepts and Methods in Science and Engineering, edited by Angelo Miele. PDF File.
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
We all encounter symmetry in our everyday lives, in both natural and man-made structures. The mathematical concepts surrounding symmetry can be a bit more difficult to grasp. This unit explains such concepts as direct and indirect symmetries, Cayley table
In our everyday lives we use we use language to develop ideas and to communicate them to other people. In this unit we examine ways in which language is adapted to express mathematical ideas.
Modelling pollution in the Great Lakes: a review
This is the fifth and final unit in the MSXR209 series on mathematical modelling. In this unit we revisit the model developed in the first unit of this series on pollution in the Great Lakes of North America. Here we evaluate and revise the original model
Living on the Grid - Playing and Deconstructing Logic Games
In this lesson, students play and deconstruct the mathematical and strategic principles of logic puzzles, including tic-tac-toe and sudoku, as well as new games like kakuro, masyu, and nurikabe. They then prepare strategies for a user's guide to one game.
Proving (a Theorem) and Disproving (a Theory). Applying the Pythagorean Theorem to Real Life
In this lesson, students share thoughts about careers and gender roles. They then work together to prepare a proof of the Pythagorean theorem and synthesize their learning by preparing a creative representation of Pythagoras' ideas.