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

Algebra

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.

Acknowledgements

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.

Symmetry

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.

Maths everywhere

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

Prices

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

Developing Childrenâ€™s Skills in Mathematical Explanation

This is an article, written in 2001, which explores the extent to which it may be possible to teach, explicitly, the skills of explanation to primary pupils. It considers the impact of direct teaching on the pupilsâ€™ written mathematical work.

Mathematical language

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.

Acknowledgements

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.

1.4.2: Price indices

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.

Next steps

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.

8 An unsolved problem!

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.

7 Inequalities

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.

6.2 Inverse proportion

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.

5.1 Number tricks

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.