This site is a free resource for math review material from algebra to differential equations. It provides more than 2,500 pages of short and easy-to-understand explanations for subjects including algebra, trigonometry, calculus, differential equations, complex variables, matrix algebra, and various mathematical tables. The materials on this site are designed for high school students, college students, and adult learners. Links to recommended books and other math education websites are also provi
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
When I started teaching this subject I found three kinds of texts. There were applications books that avoid proofs and cover the linear algebra only as needed for their applications. There were advanced books that assume that students can understand their elegant proofs and know how to answer the homework questions having seen only one or two examples. And, there were books that spend a good part of the semester multiplying matrices and computing determinants and then suddenly change level to wo
Focuses on modeling, quantification, and analysis of uncertainty by teaching random variables, simple random processes and their probability distributions, Markov processes, limit theorems, elements of statistical inference, and decision making under uncertainty. This course extends the discrete probability learned in the discrete math class. It focuses on actual applications, and places little emphasis on proofs. A problem set based on identifying tumors using MRI (Magnetic Resonance Imaging) i
Private Universe Project in Mathematics: Workshop 3. Inventing Notations
We learn how to foster and appreciate students notations for their richness and creativity. We also look at some of the possibilities that early work in creating notation systems might open up for students as they move on toward algebra.,15 min. Pizzas in the Classroom In Englewood, New Jersey, Blanche Young, who attended the summer workshop, tries out one of the problems with her fourth-grade students. Later, she meets with Arthur Powell to discuss the lesson. 5 min. New Brunswick, New Jersey
Private Universe Project in Mathematics: Workshop 1. Following Children's Ideas in Mathematics
An unprecedented long-term study conducted by researchers at Rutgers University followed the development of mathematical thinking in a randomly selected group of students for 12 yearsfrom first grade through high schoolwith surprising results. In an overview of the study, we look at some of the conditions that made the students math achievement possible.,10 min Building Towers Five-High The Kenilworth students in the fourth grade are seen working on the Towers problem (How many different
Introduction to Economic Analysis
This book presents standard intermediate microeconomics material and some material that, in the authors' view, ought to be standard but is not. Introductory economics material is integrated. Standard mathematical tools, including calculus, are used throughout. The book easily serves as an intermediate microeconomics text, and can be used for a relatively sophisticated undergraduate who has not taken a basic university course in economics. Podcast also available
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
Impact of Computer Aided Learning on Children with Specific Learning Disabilities
The Technology Initiatives Division of Azim Premji Foundation has launched programmes for use of computers in rural schooling. One such programme is Computer Aided Leaning (CAL) that envisages deployment of computers as a media to impact learning competencies and to create an attractive environment in the schools. The state government provides the computers in schools and the Foundation has developed required software content designed to aid classroom learning process in specific areas such as m
InterMath is a professional development effort designed to support teachers in becoming better mathematics educators. It focuses on building teachers' mathematical content knowledge through mathematical investigations that are supported by technology. InterMath includes a workshop component and materials to support instructors. For each of the following problems, consider how you would pose the same problem to your students. Would the wording need to change? Would you need to include more pictur
Fourier: Making Waves
Learn how to make waves of all different shapes by adding up sines or cosines. Make waves in space and time and measure their wavelengths and periods. See how changing the amplitudes of different harmonics changes the waves. Compare different mathematical expressions for your waves.
Active galaxies provide a prime example of high energy processes operating in the Universe. This unit gives an overview of active galaxies, including the supermassive black holes that power the engines at their centres, and the emission processes by which we detect and study them. It also gives practice in mathematical techniques for analysing data and theoretical models.
Quantum field theory
This is a module framework. It can be viewed online or downloaded as a zip file. Last taught in Spring Semester 2006 A compilation of fourteen lectures in PDF format on the subject of quantum field theory. This module is suitable for 3rd or 4th year undergraduate and postgraduate level learners. Suitable for year 3/4 undergraduate and postgraduate study. Dr Kirill Krasnov, School of Mathematical Sciences Dr Kirill Krasnov is a Lecturer at the University of Nottingham. After studying physic
How and why we do mathematical proofs
This is a module framework. It can be viewed online or downloaded as a zip file. As taught in Autumn Semester 2009/10 The aim of this short unit is to motivate students to understand why we might want to do proofs (why proofs are important and how they can help us) and to help students with some of the relatively routine aspects of doing proofs. In particular, the student will learn the following: * proofs can help you to really see why a result is true; * problems that are easy to state
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 tables and groups through exercises, audio and video.
This unit explores reasons for studying mathematics, practical applications of mathematical ideas and aims to help you to recognise mathematics when you come across it. It introduces the you to the graphics calculator, and takes you through a series of exercises from the Calculator Book, Tapping into Mathematics With the TI-83 Graphics Calculator. The unit ends by asking you to reflect on the process of studying mathematics. In order to complete this unit you will need to have obtained a Texas I
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 by comparing its predictions against data from the lakes before finally reflecting on the techniques used. This unit assumes you have studied Modelling pollution in the Great Lakes (MSXR209_1), Analysing skid marks (MSXR209_2), Developing model
This unit looks at a wide variety of ways of comparing prices and the construction of a price index. You will also look at the Retail Price Index (RPI) and the Consumer Price Index (CPI), indices used by the UK Government to calculate the percentage by which prices in general have risen over any given period. You wil also look at the important statistical and mathematical ideas that contribute to the construction of a price index.
Starting with maths: Patterns and formulas
Patterns occur everywhere in art, nature, science and especially mathematics. Being able to recognise, describe and use these patterns is an important skill that helps you to tackle a wide variety of different problems. This unit explores some of these patterns ranging from ancient number patterns to the latest mathematical research.
Analysing skid marks
This unit is the second in the MSXR209 series of five units on mathematical modelling. In this unit you are asked to relate the stages of the mathematical modelling process to a previously formulated mathematical model. This example, that of skid mark produced by vehicle tyres, is typical of accounts of modelling that you may see in books, or produced in the workplace. The aim of this unit is to help you to draw out and to clarify mathematical modelling ideas by considering the example. It assum