18.369 Mathematical Methods in Nanophotonics (MIT)
Find out what solid-state physics has brought to Electromagnetism in the last 20 years. This course surveys the physics and mathematics of nanophotonics—electromagnetic waves in media structured on the scale of the wavelength. Topics include computational methods combined with high-level algebraic techniques borrowed from solid-state quantum mechanics: linear algebra and eigensystems, group theory, Bloch's theorem and conservation laws, perturbation methods, and coupled-mode theories, to u
Author(s): Johnson, Steven G.

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1.77 Water Quality Control (MIT)
The course material emphasizes mathematical models for predicting distribution and fate of effluents discharged into lakes, reservoirs, rivers, estuaries, and oceans. It also focuses on formulation and structure of models as well as analytical and simple numerical solution techniques. Also discussed are the role of element cycles, such as oxygen, nitrogen, and phosphorus, as water quality indicators; offshore outfalls and diffusion; salinity intrusion in estuaries; and thermal stratification, eu
Author(s): Adams, Eric

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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

2.4.1 Reductionism and ‘ownership’ of the body

Social scientists interested in changing relationships between workers and users of health care often draw attention to what is termed the loss of ownership or loss of governance of the body. These terms mean that a person's body is treated in some health situations as more important than the person themselves. It is almost as if they are purely a case, an example of a type of disease, or a set of symptoms. Traditionally, such criticisms were levelled against biomedical approach
Author(s): The Open University

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1.3 The very early Universe

Time: <10−36 s

Temperature: >1028 K

Energy: >3 × 1015 GeV (i.e. >3 × 1024 eV)

At the very earliest times in the history of the Universe, we can only presume that a superunification of the four interactions was in operation. Unfortunately, no reliable theory of superunification is yet available, so nothing can be said about the contents or behaviour of the Universe in its earliest moments. Indeed, it
Author(s): The Open University

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18.312 Algebraic Combinatorics (MIT)
This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected.
Author(s): Musiker, Gregg

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3 Subtraction rules – order matters

It’s important to remember that subtraction has different rules from addition.

For example, when you add up numbers, it doesn’t matter what order you add them up in. So 6 + 4 is exactly the same as 4 + 6. The result is 10 in both cases.

But in subtraction, order matters. So 6 – 4 is different from 4 – 6.

With the first, you start with 6, subtract 4, and are left with 2.

But with the second you start with 4 and if you subtract 6, which is a bigger number, you a
Author(s): The Open University

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Standing Stones
Description not set
Author(s): Mike Pennington

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Rights not set

From Seed to Flower
The growth and development of a plant is one of the most spectacular events in nature. Yet, because it happens so slowly, over the course of days or weeks, it is difficult to observe in real time. This video segment depicts plant growth in time-lapse format, allowing the viewer to observe in just a few seconds some of the most important life stages of a plant, from germination to the formation of a flower, and several phases in between. Footage from NOVA: "The Shape of Things." Set to music.  N
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Acknowledgements

The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.

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

The content acknowledged below is Proprietary and is used under
Author(s): The Open University

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How Changes in the Cost of Living are Measured
OpenStax College
By the end of this section, you will be able to: Use the Consumer Price Index (CPI) to calculate U.S. inflation rates Identify several ways the Bureau of […]

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3.3.1 Increasing by a percentage

Our everyday experience of percentages includes percentage increases (like VAT at %, or a service charge of 15%) and percentage decreases (such as a discount of 15%).

For example, £8 plus
Author(s): The Open University

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6 What you should present

This assessment course has two parts. Part A requires you to plan, monitor, evaluate and reflect upon your skills, and present evidence of that process. Part B requires you to select concise examples of your work that demonstrate what you have done to improve and apply your skills. Together the two parts form a portfolio of your achievements. You can use the guidance, Bookmarks and Skills Sheets included in the OpenLearn course U529_1 Key skills – making a difference to help
Author(s): The Open University

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Using a Function Machine to Create a Math Rule
The video appears dark because the instructor has a projector on in a darkened room. However, the information is demonstrated fairly well. The teacher shows how to use the function machine to find the unknown rule to a set of number pairs by investigating the pattern. (1:21)
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Lesson 04 - One Minute Romanian
In lesson 4 of One Minute Romanian you will learn how to say you don't understand something. Remember - even a few phrases of a language can help you make friends and enjoy travel more. Find out more about One Minute Romanian at our website - http://www.oneminutelanguages.com. One Minute Romanian is brought to you by the Radio Lingua Network and is ©Copyright 2008.Author(s): No creator set

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3.4.1 Try some yourself

1 A new train operator boasts ‘Train times reduced by 12%’. Decrease 90 minutes by 12%. Give your answer as minutes and seconds.

Answer

A 12% decrease would reduce
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Learning outcomes

After studying this course, you should be able to:

  • demonstrate knowledge about cuneiform and how it was used to represent numbers for mathematical problem solving and computation;

  • understand the relationship between a decimal place-value system and a sexagesimal one;

  • appreciate the advanced understanding of mathematics in Ancient Mesopotamia in relation to anyone in medieval Christian Europe 3000 years later.


Author(s): The Open University

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References

Cowie, F. and Bradney, A. (2000), English Legal System in Context, London, Butterworths, pp. 88–90.
‘Extending and developing your thinking skills’, Open University Student Toolkit 9.
Slapper, G. (2000) ‘Castles built on law’, New Law Journal, 23 June.
Slapper, G. and Kelly, D. (2003) The English Legal
Author(s): The Open University

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Alien Encounter
Mathematical Logical puzzle.
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18.305 Advanced Analytic Methods in Science and Engineering (MIT)
Advanced Analytic Methods in Science and Engineering is a comprehensive treatment of the advanced methods of applied mathematics. It was designed to strengthen the mathematical abilities of graduate students and train them to think on their own.
Author(s): Cheng, Hung

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