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Conclusion

I hope you now have a better idea of what it means to visualise a piece of mathematics.

Visualising is a critically important process when mathematicians and others actually do mathematics. Unfortunately, the process of visualising does not appear in publications, which all tend to be displayed very formally and are mostly restricted to the final results.

As teachers we need to ensure that we are very aware of all the processes of mathematics and so we must always attempt to know
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1 Structural devices: a static role

The superb manufacturing techniques of microelectronics enable designers of integrated circuits to exercise complete control over the electrical characteristics of each component, such as a transistor, by specifying the shapes and sizes of their active regions. Using photolithographic mask-drawing software on their workstations, they can copy and paste blocks of identical devices all over the chip, knowing that when the design is finally realised in silicon, this extreme uniformity wil
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Damien Sneed in Migration Rhapsody
See the full performance: https://www.youtube.com/watch?v=6e4cvzuHwjg In conjunction with the "One-Way Ticket" exhibition, Terrance McKnight, a host on New York City classical music station WQXR, curates an evening of music and performance with artists including Jim Davis, Kevin Maynor, Karen Chilton, Bill T. Jones, Alicia Hall Moran, Jason Moran, Damien Sneed, Bill Sims Jr., Ricky Gordon, Bob Stewart, and others.
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An optimization method of the facility location by genetic algorithm
In planning of community-facilities, it is important to decide the facility location to provide the effective service for residents. The behavior of residents using the facility and the evaluation methods of the location have been studied. But, finding the optimum location is very hard in actual planning because the volume of calculation depends on the number of feasible locating points of facilities. To conquer the difficulty of searching the optimum location, we propose an optimization method
Author(s): Aoke, Yoshitsugu and Muraoka, Naoto

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21L.703 Studies in Drama: Stoppard and Churchill (MIT)
What is the interplay between an event and its "frames"? What is special and distinctive about stage events? How and why do contemporary dramatists turn back in time for their settings, models, and materials? How do they play with this material to create performance pieces of importance and delight for modern audiences? How do they create distinct, fresh perspectives using the stage in an era of mass and multi-media? What is the implied audience for these plays, and how does that clash or coinci
Author(s): Henderson, Diana

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Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative C

6.1 Introduction

As a student, you're likely to engage in a variety of writing tasks. You'll almost certainly handle significant amounts of text and, depending on your course, perhaps also numbers or diagrams.

This section looks at the different way that you write using a computer, and also provides some referencing advice.


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3 Group axioms

Section 3 is an audio section. We begin by defining the terms group, Abelian group and order of a group. We then demonstrate how to check the group axioms, and we extend the examples of groups that we use to include groups of numbers – the modular arithmetics, the integers and the real numbers.

Click the link below to open Section 3 (11 pages, 703KB).

Author(s): The Open University

1.2.3 Mechanical methods of contraception

While hormone-containing pills represent a very sophisticated kind of contraceptive, mechanical contraceptives are a straightforward idea: they act by preventing sperm and egg from meeting. Mechanical contraceptives in their simplest form have been around since before Roman times; some are shown in Figure 4. The earliest ‘penis protectors’ were allegedly used less for contraception than as protection against disease, and as a badge of rank.

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18.3 Characteristics of consumers and the market

As well as the characteristics of an innovation affecting the extent of its take-up, the nature of the market and the purchasing behaviour of consumers can influence success. Some people will always try to be among the first to buy a new product – Rogers (2003) calls people in this group innovators (Author(s): The Open University

Keep on learning

Study another free course

There are more than 800 courses on OpenLearn for you to c
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7.1 Introduction

This section continues with the theme of networked devices by looking at a system of electronic tagging known as Radio Frequency Identity (RFID). In this system, an electronic tag is attached to an object (for example, the pin described in the The Road Ahead extract in the previous section) and an RFID reader is used to interrogate the tag wirelessly and receive information stored on it. We are using the word 'interrogate' here because the reader sends out a signal and the tag responds
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2 The future of wind energy

A great advantage of using wind energy is that, unlike power generation from combustion of fossil fuels, it produces no gas emissions. Even a small 750 kW wind turbine operating with wind speeds just above that of turbine cut-off would reduce annual emissions to the atmosphere by 1200 t of carbon dioxide, 6.9 t of sulphur dioxide and 4.3 t of nitrogen dioxide, compared with the equivalent power output from coal-fired generators. Nevertheless, wind turbines and their infrastructures are substa
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Acknowledgements

Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

Grateful acknowledgement is made to the following sources for permission to reproduce material in this unit:


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Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

4.3 Stationary states and barrier penetration

The example of tunnelling we have just been examining can be regarded as a special case of scattering; it just happens to have E0 < V0. As long as we keep this energy range in mind, we can apply the same stationary-state methods to the study of tunnelling that we used earlier when studying scattering.

As before, we shall start by considering the finite square step, whose potential energy function was defined in Equations
Author(s): The Open University

7.1 What is a business model?

The aim of this section is to look at some of the business models which have been used to drive internet applications. A business model is a high-level description of an application type which contains all the common features which can be found in specific examples of the model. For example, one of the most popular business models is the e-shop which describes a website that sells products. The model is general in that it does not describe the item that is sold or the mechanisms that a
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3.2.1 Try some yourself

1 Convert each of the following to percentages. Round off the percentages to whole numbers.

  • (a)

    • (i) 0.8

    • (ii) 0.21

    • (iii) 0.70<
      Author(s): The Open University

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The week ahead: The Trump test

One year after President Trump was elected, we quiz our correspondents' knowledge about his time in office. What is the connection between Larry Flynt and Mr. Trump? And what was behind that pained expression in Sean Spicer's eyes? We answer all those pressing questions and more


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4.6 Global coal reserves and their life expectancy

In 2003, global proven coal reserves were estimated at 984.5 × 109 t, of which slightly over half (52.7%) was anthracite and bituminous coal and the rest (47.3%) was sub-bituminous coal and lignite.

Figure 37 shows the breakdown of global reserves by continental regions. North America has 26% of total g
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Learning in the first professional job: the first year of full time employment after college for acc
This paper reports findings from the first phase of a four-year research project funded by the UK Economic and Social Research Council as part of its Teaching and Learning Research Programme. The major component of this project is a longitudinal study of trainee accountants, graduate trainee engineers, and newly qualified nurses in England. This critical period of introduction to professional work has not been previously studied by a longitudinal series of observations and interviews, though a n
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4.2.4 CCD light sensor

The CCD light sensor is a transducer that converts light to an electrical signal. CCD stands for 'charge coupled device', and physically a CCD light sensor is an integrated circuit with a transparent cover. A photograph of one is shown in Figure 6. Under the cover is a rectangular array of light-sensitive electronic components cal
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