LearningSpace

This unit looks at visualisation as it relates to mathematics, focusing upon how it can be used to improve learning. It will also identify ways in which to make more use of visualisation within the classroom.

This unit is concerned with two main topics. In Section 1, you will learn about another kind of graphical display, the boxplot. A boxplot is a fairly simple graphic, which displays certain summary statistics of a set of data. Boxplots are ...

This unit is concerned with two main topics. In Section 1, you will learn about another kind of graphical display, the boxplot. A boxplot is a fairly simple graphic, which displays certain summary statistics of a set of data. Boxplots are particularly useful for assessing quickly the location, dispersion, and symmetry or skewness of a set of data, and for making comparisons of these features in two or more data sets. Boxplots can also be useful for drawing attention to possible outliers in a data set. The other topic, which is covered in Sections 2 and 3, is that of dealing with data presented in tabular form. You are, no doubt, familiar with such tables: they are common in the media and in reports and other documents. Yet it is not always straightforward to see at first glance just what information a table of data is providing, and it often helps to carry out certain calculations and/or to draw appropriate graphs to make this clearer. In this unit, some other kinds of data tables and some different approaches are covered.

This unit looks at complex numbers. You will learn how they are defined, examine their geometric representation and then move on to looking at the methods for finding the nth roots of complex numbers and the solutions to simple polynominal equations.

This unit is aimed at teachers who wish to review how they go about the practice of teaching maths, those who are considering becoming maths teachers, or those who are studying maths courses and would like to understand more about the teaching ...

This unit is aimed at teachers who wish to review how they go about the practice of teaching maths, those who are considering becoming maths teachers, or those who are studying maths courses and would like to understand more about the teaching process.

This unit focuses on your initial encounters with research. It invites you to think about how perceptions of mathematics have influenced you in your prior learning, your teaching and the attitudes of learners.

In this unit you will see first how to convert vectors from geometric form, in terms of a magnitude and direction, to component form, and then how conversion in the opposite sense is accomplished. The ability to convert between these ...

In this unit you will see first how to convert vectors from geometric form, in terms of a magnitude and direction, to component form, and then how conversion in the opposite sense is accomplished. The ability to convert between these different forms of a vector is useful in certain problems involving displacement and velocity, as shown in Section 2, in which you will also work with bearings.

This unit introduces the topic of differential equations. The subject is developed without assuming that you have come across it before, but it is taken for granted that you have a basic grounding in calculus. In particular, you will need to have ...

This unit introduces the topic of differential equations. The subject is developed without assuming that you have come across it before, but it is taken for granted that you have a basic grounding in calculus. In particular, you will need to have a good grasp of the basic rules for differentiation and integration.

This unit shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and ...

This unit shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and basic familiarity with partial differential equations.

This unit extends the ideas introduced in the unit on first-order differential equations to a particular type of second-order differential equations which has a variety of applications. The unit assumes that you have previously had a basic ...

This unit extends the ideas introduced in the unit on first-order differential equations to a particular type of second-order differential equations which has a variety of applications. The unit assumes that you have previously had a basic grounding in calculus, know something about first-order differential equations and some familiarity with complex numbers.

This unit introduces the topic of vectors. The subject is developed without assuming you have come across it before, but the unit assumes that you have previously had a basic grounding in algebra and trigonometry, and how to use Cartesian ...

This unit introduces the topic of vectors. The subject is developed without assuming you have come across it before, but the unit assumes that you have previously had a basic grounding in algebra and trigonometry, and how to use Cartesian coordinates for specifying a point in a plane.

This unit lays the foundation of the subject of mechanics. Mechanics is concerned with how and why objects stay put, and how and why they move. In particular, this unit - Modelling Static Problems - considers why objects stay put. And it assumes ...

This unit lays the foundation of the subject of mechanics. Mechanics is concerned with how and why objects stay put, and how and why they move. In particular, this unit - Modelling Static Problems - considers why objects stay put. And it assumes that you have a good working knowledge of vectors.

This unit lays the foundation of Newtonian mechanics and in particular the procedure for solving dynamics problems. The preresquisite skills needed for this unit are the ability to solve first and second-order differential equations, a knowledge ...

This unit lays the foundation of Newtonian mechanics and in particular the procedure for solving dynamics problems. The preresquisite skills needed for this unit are the ability to solve first and second-order differential equations, a knowledge of vectors, and an understanding of the concept of a force

This unit shows how various situations can be modelled by a system of linear differential equations. The prerequisite requirements to gain full advantage from this unit are a basic understanding of differential equations, a familiarity with the ...

This unit shows how various situations can be modelled by a system of linear differential equations. The prerequisite requirements to gain full advantage from this unit are a basic understanding of differential equations, a familiarity with the properties of matrices and determinants and some understanding of eigenvalues and eigenvectors.

This unit is intended to further develop your understanding of Newtonian mechanics in relation to oscillating systems. In addition to a basic grounding in solving systems of differential equations, this unit assumes that you have some ...

This unit is intended to further develop your understanding of Newtonian mechanics in relation to oscillating systems. In addition to a basic grounding in solving systems of differential equations, this unit assumes that you have some understanding of eigenvalues and eigenvectors.

This unit is concerned with the technique of expressing a periodic function as a sum of terms, where each term is a constant, a sine function or a cosine function. There is a strong analogy with the technique of expressing a (non-periodic) ...

This unit is concerned with the technique of expressing a periodic function as a sum of terms, where each term is a constant, a sine function or a cosine function. There is a strong analogy with the technique of expressing a (non-periodic) function as a Taylor series, which is a sum of terms that are powers of the independent variable(s); in both cases, working with just the first few terms generally gives a useful approximation. This unit assumes the following background knowledge: the definition of the period; forced oscillations and resonance; integration by parts.

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 ...

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.

Graphs are a common way of presenting information. However, like any other type of representation, graphs rely on shared understandings of symbols and styles to convey meaning. Also, graphs are normally drawn specifically with the intention of ...

Graphs are a common way of presenting information. However, like any other type of representation, graphs rely on shared understandings of symbols and styles to convey meaning. Also, graphs are normally drawn specifically with the intention of presenting information in a particularly favourable or unfavourable light, to convince you of an argument or to influence your decisions.

Sometimes the best way to understand a set of data is to sketch a simple graph. This exercise can reveal hidden trends and meanings not clear from just looking at the numbers. In this unit you will review the various approaches to sketching ...

Sometimes the best way to understand a set of data is to sketch a simple graph. This exercise can reveal hidden trends and meanings not clear from just looking at the numbers. In this unit you will review the various approaches to sketching graphs and learn some more advanced techniques.

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.

This unit is designed to help those working with children between the ages of 3 and 8. You will be encouraged to explore your knowledge, feelings and attitudes in language, mathematics and science in order to understand the place that these ...

This unit is designed to help those working with children between the ages of 3 and 8. You will be encouraged to explore your knowledge, feelings and attitudes in language, mathematics and science in order to understand the place that these subjects have in the life of both individuals and society as a whole.

Are you about to undertake a PhD in science, technology or mathematics? If so, this unit will help you to examine your work processes. You will consider and develop the nature of postgraduate work and look at the planning of work needed at ...

Are you about to undertake a PhD in science, technology or mathematics? If so, this unit will help you to examine your work processes. You will consider and develop the nature of postgraduate work and look at the planning of work needed at doctoral level.

Numerical and mathematical skills are used to describe and tackle a wide range of problems. These key skills are about understanding when particular techniques should be used, how to carry them out accurately and which techniques should be ...

Numerical and mathematical skills are used to describe and tackle a wide range of problems. These key skills are about understanding when particular techniques should be used, how to carry them out accurately and which techniques should be applied in particular situations. Developing your numerical, graphical and algebraic skills means being able to plan how you are going to use your skills over a period of time, monitoring your progress and then reviewing your approach. In developing and assessing this key skill, you will learn to use and adapt your skills confidently and effectively in different situations and contexts. This unit is designed to be studied for 1 hour per week over 50 weeks.

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 ...

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 Instruments TI-83 calculator and the book Tapping into Mathematics With the TI-83 Graphics Calculator (ISBN 0201175479).

This Unit will introduce you to a number of ways of representing data graphically and of summarising data numerically. You will learn the uses for pie charts, bar charts, histograms and scatterplots. You will also be introduced to various ways of ...

This Unit will introduce you to a number of ways of representing data graphically and of summarising data numerically. You will learn the uses for pie charts, bar charts, histograms and scatterplots. You will also be introduced to various ways of summarising data and methods for assessing location and dispersion.

This unit is intended to develop your understanding of Newtonian mechanics in relation to oscillating systems. In addition to a basic grounding in calculus, this unit assumes that you have some understanding of how to solve second-order linear ...

This unit is intended to develop your understanding of Newtonian mechanics in relation to oscillating systems. In addition to a basic grounding in calculus, this unit assumes that you have some understanding of how to solve second-order linear constant-coefficient differential equations; how to take the dot product of two vectors; of solving statics problems; and of applying Newton's second law to mechanical problems.

Many of us struggle to understand the fractions, formulas and calculations needed for everyday tasks. This unit provides an overview of Open University course Y162 Starting with maths, which is designed to help develop the skills needed for ...

Many of us struggle to understand the fractions, formulas and calculations needed for everyday tasks. This unit provides an overview of Open University course Y162 Starting with maths, which is designed to help develop the skills needed for higher level study while also developing knowledge and understanding about maths.

This unit is the first in the MSXR209 series of five units that introduce the idea of modelling with mathematics. This unit centres on a mathematical model of how pollution levels in the Great Lakes of North America vary over a period of time. It ...

This unit is the first in the MSXR209 series of five units that introduce the idea of modelling with mathematics. This unit centres on a mathematical model of how pollution levels in the Great Lakes of North America vary over a period of time. It demonstrates that, by keeping the model as simple as possible extremely complex systems can be understood and predicted.

This unit is the third in the MSXR209 series of five units on mathematical modellng. It provides an overview of the processes involved in developing models, starting by explaining how to specify the purpose of the model. It then moves on to look ...

This unit is the third in the MSXR209 series of five units on mathematical modellng. It provides an overview of the processes involved in developing models, starting by explaining how to specify the purpose of the model. It then moves on to look at aspects involved in creating models, such as simplifying problems, choosing variables and parameters, formulating relationships and finding solutions. You will also look at interpreting results and evaluating models. This unit assumes that you have previously studied Modelling pollution in the Great Lakes (MSXR209_1) and Analysing skid marks (MSXR209_2).

This unit is the fourth in the MSXR209 series of five units on mathematical modelling. In this unit you will be taken through the whole modelling process in detail, from creating a first simple model, through evaluating it, to the subsequent ...

This unit is the fourth in the MSXR209 series of five units on mathematical modelling. In this unit you will be taken through the whole modelling process in detail, from creating a first simple model, through evaluating it, to the subsequent revision of the model by changing one of the assumptions. The problem that will be examined is one based on heat transfer. This unit assumes you have studied Modelling pollution in the Great Lakes (MSXR209_1), Analysing skid marks (MSXR209_2) and Developing modelling skills (MSXR209_3).

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 ...

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 modelling skills (MSXR209_3) and Modelling heat transfer (MSXR209_4).

You're about to start a course in science and technology and you're wondering whether your level of maths is going to be enough to get you through. This unit will show you how to reflect on what you know, identify which skills you might need for ...

You're about to start a course in science and technology and you're wondering whether your level of maths is going to be enough to get you through. This unit will show you how to reflect on what you know, identify which skills you might need for your course, and help you to learn those skills using worked examples and activities.