9 Summary
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.
Author(s): The Open University

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8.4 Line spectra: line flux and equivalent width
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.
Author(s): The Open University

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Appendix
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.
Author(s): The Open University

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5 Little Christmas Trees (Song)
This video is great for children to learn how to count and subtract with objects.  This is a teacher-made video.  Adult voice is singing in the background while 5 Christmas trees are displayed on a felt board.  Run time 02:49.
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Looking at Learning ... Again, Part 2: Workshop 2. Mathematics: A Community Focus
With Dr. Marta Civil. As teachers, we often make assumptions about the knowledge children are exposed to at home. Sometimes it seems that we focus on only reading and writing,Dr. Civil contends that we need to look more carefully at the mathematical potential of the home and that it is essential that schools learn to be more flexible and knowledgeable about students’ home environments. See and hear from Dr. Civil, the teachers she works with, and a long-standing parent mathematics group, and fo
Author(s): Harvard-Smithsonian Center for Astrophysics

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Smithsonian Institution Astrophysical Observatory "All Rights Reserved"

Acknowledgements
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
Author(s): The Open University

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3.2 QSO spectra
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.
Author(s): The Open University

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In Pursuit of the Salesman: Mathematics at the Limit of Computation - December 16, 2009
Lunch 'n Learn presentation: The traveling salesman problem, or TSP for short, is easy to state: given a number of cities along with the cost of travel between each pair of them, find the cheapest way to visit them all and return to your starting point. Easy to state, but difficult to solve! Despite decades of research by top applied mathematicians around the world, in general it is not known how to significantly improve upon simple brute-force checking. It is a real possibility that there may n
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18.100A Analysis I (MIT)
Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications whe
Author(s): Mattuck, Arthur

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Traffic Paradoxes and Route Guidance: Effective Ways of Reducing Congestion Effects?
It is well know that we cannot engineer our way out of traffic congestion by building new roads. In fact, expanding the road network may paradoxically attract new traffic, and increase gridlock. Andreas Schulz provides a mathematical explanation for this conundrum. Using Nash equilibria and related game-theoretic concepts he
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6.251J Introduction to Mathematical Programming (MIT)
This course offers an introduction to optimization problems, algorithms, and their complexity, emphasizing basic methodologies and the underlying mathematical structures. The main topics covered include: Theory and algorithms for linear programming Network flow problems and algorithms Introduction to integer programming and combinatorial problems
Author(s): John Tsitsiklis

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References
The Egyptians are known for being ahead of their time in comparison to some civilisations that came after them. This unit looks at how the Egyptians solved mathematical problems in everyday life and the technology they used. An understanding of this area has only been possible following the translation of the Rosetta Stone.
Author(s): The Open University

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Learning outcomes
The Egyptians are known for being ahead of their time in comparison to some civilisations that came after them. This unit looks at how the Egyptians solved mathematical problems in everyday life and the technology they used. An understanding of this area has only been possible following the translation of the Rosetta Stone.
Author(s): The Open University

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Guide to Homeschooling - How to Homeschool
Are you looking for a guide to homeschooling? Inside this video you'll discover how to get started homeschooling.

Topics Covered Include:
Homeschool Methods & Homeschool Styles
Homeschool State Laws
Homeschoolers Guide, Guide to Homeschooling
How to Homeschool
Choosing a Homeschool Curriculum
Homeschooling Guide, Homeschool Manual
Homeschooling Questions
Homeschooling Help
Home Schooling Book
Help with Home Schooling

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References

Bills, C. (2002) ‘Mental mathematics’ in Haggarty, L. (ed.), Aspects of Teaching Secondary Mathematics: Perspectives on Practice, London, Routledge.
Mason, J. (1988) ‘Imagery, imagination and mathematics classrooms’ in Pimm, D. (ed.), Mathematics, Teachers and Children, Sevenoaks, Hodder and Stoughton.
The Open University (1988) ME234 Using
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Licensed under a Creative Commons Attribution - NonCommercial-ShareAlike 2.0 Licence - see http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ - Original copyright The Open University

Acknowledgements
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 pr
Author(s): The Open University

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Acknowledgements
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
Author(s): The Open University

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Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2

Learning outcomes
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
Author(s): The Open University

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Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2

Acknowledgements
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
Author(s): The Open University

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Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2

Learning outcomes
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
Author(s): The Open University

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Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2