Networks maths notes

This collection of Nuffield Maths resources explores Decision maths. The demand is roughly equivalent to that in GCE A level. They include slide shows to introduce the topics, student sheets and teacher notes, as well as other relevant resources. The teachers' notes start with a short overview of the activity, who and what it is designed for, and lists the necessary resources. The student sheets have background information where needed, and tasks for the students to work and reflect on.

Extensions and solutions are included in the teachers' notes. Then students to find an Eulerian trail for a network with four odd nodes. It involves students setting up their own network as the basis for a sightseeing tour. A cable TV problem introduces the topic and the rules for the two algorithms.

The students are then set a second problem involving a theme park. The tasks are based on decorating and furnishing a bedroom, and take students through the process of constructing an activity network and calculating the minimum completion time for the project.

The resources include slide shows to introduce the topics, student sheets and teacher notes, as well as other relevant resources.

A cable TV company wants to lay cables to connect the towns, laying the cable along the roads shown on a map of the Isle of Wight. They want to connect all of these towns to Networks Quality Assured.

Refurbishing a room Quality Assured.

networks maths notes

Sightseeing Tour Quality Assured. Cable TV Quality Assured. Subject s Mathematics Tags n.

networks maths notes

Nuffield Foundation. Add to favorites list. Email Twitter Facebook. Get in touch. Call us at: Email us.A little mouse called Delia lives in a hole in the bottom of a tree How many days will it be before Delia has to take the same route again? Investigate the number of paths you can take from one vertex to another in these 3D shapes.

Network Structure

Is it possible to take an odd number and an even number of paths to the same vertex? You can trace over all of the diagonals of a pentagon without lifting your pencil and without going over any more than once. Can the same thing be done with a hexagon or with a heptagon? Create your own networks. Can you draw one that is impossible to complete without lifting your pencil? Main menu Search.

Hide Menu. Redblue Investigate the number of paths you can take from one vertex to another in these 3D shapes. Diagonal Trace You can trace over all of the diagonals of a pentagon without lifting your pencil and without going over any more than once. Networks and Nodes.

Network Mathematics

Without taking your pencil off the paper or going over a line or passing through one of the points twice, can you follow each of the networks? If you are able to do this, mark your pathway and direction using arrows. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

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networks maths notes

University of Cambridge. All rights reserved.Rail Networks are quite familiar to most of us. Recently Passy visited Sydney in Australia, and found the rail network system to be far superior to that of Melbourne. This means that to get to many places we have to go into the City and then back out again. It also means that all trains have to go into the city loop and then back out again. Networks and Social Networking. The following video is an excellent introduction to Networks, including an overview of Social Networks.

Mathematical Components of a Network. Note that we have coloured in the Regions; however network diagrams are not usually coloured in like this. Note that Edges can be straight lines or curves. If the equation does not work out equal on both sides for a Network, then one of our counts of the Vertices, Edges, or Regions must be incorrect, and we need to go back and check through our work.

Answers to Examples. Tree Diagram Network. A tree diagram is a special type of open network. This Network has only one Region, but many Vertices and Edges. Each vertex connects to one or more other Vertices, making the Network branch out into more and more paths that can be taken from the original starting point.

Tree Diagrams are useful for organising tasks, and classifying situations into groupings. They are also used for breaking down complex items into sub-groups of simpler items.

Colouring in Networks. The rule for colouring in such diagrams is that two adjoining Regions next to each other must not be shaded in the same colour.

Not every region has to be a different colour, but we need to make sure we separate regions using colours, and do not have two regions next to each other as the exact same colour.

This first example is incorrect, because the two middle states have been coloured in the same red colour. This makes it appear as though they are one region instead of two separate regions.

The next example shown below is correct, where all regions can be seen as being separate from each other. It does not matter that we have used the colour pink for two separate regions, because they do not touch each other on the map. If we were asked to colour the map in using the least number of colours possible, then the following would be one of several possible correct solutions that use only four colours.

A flow must satisfy the restriction that the amount of flow into a node or Vertex equals the amount of flow out of it, except when it is a source, which has more outgoing flow, or a sink, which has more incoming flow. A flow network can be used to model traffic in a road system, fluids in pipes, currents in an electrical circuit, or anything similar in which something travels through a network of nodes.

Networks and Traffic Flow. In the following video, Dr. Chris Bishop explains an interesting paradox that shows how the removal of very fast roads, like removing a tunnel through the middle of a citycan actually reduce average journey times. Additional Information. There is a great introduction to Network Mathematics written by Bruce Hoppe at the following web page:. The following article discusses some of the modern research and developments associated with Networks.Enter your mobile number or email address below and we'll send you a link to download the free Kindle App.

Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required. To get the free app, enter your mobile phone number. Would you like to tell us about a lower price? This book introduces the reader to the basic math used for neural network calculation. This book assumes the reader has only knowledge of college algebra and computer programming. This book begins by showing how to calculate output of a neural network and moves on to more advanced training methods such as backpropagation, resilient propagation and Levenberg Marquardt optimization.

The mathematics needed by these techniques is also introduced. Mathematical topics covered by this book include first, second, Hessian matrices, gradient descent and partial derivatives.

All mathematical notation introduced is explained. Neural networks covered include the feedforward neural network and the self organizing map.

This book provides an ideal supplement to our other neural books. This book is ideal for the reader, without a formal mathematical background, that seeks a more mathematical description of neural networks. Read more Read less. Kindle Cloud Reader Read instantly in your browser.

Customers who bought this item also bought. Page 1 of 1 Start over Page 1 of 1. The Math of Neural Networks. Michael Taylor. Make Your Own Neural Network.

Networks and Nodes

Tariq Rashid. Jeff Heaton. Dan Morris. Customer reviews. How does Amazon calculate star ratings?

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The model takes into account factors including the age of a rating, whether the ratings are from verified purchasers, and factors that establish reviewer trustworthiness. Top Reviews Most recent Top Reviews. There was a problem filtering reviews right now. Please try again later. Verified Purchase. Its freshman calculus and applied math rolled together in a developing brew.

This introduction is gentle and it will all make sense if you buy another few books on the subject. However, this is not a one stop shop for neural network design. The book is more a basic presentation of various mathematical tools that can be applied to neural networks. The book requires the reader to have familiarity with basic calculus and derivatives. Otherwise it's a walk in the park. After all, you are going to have to stretch a bit to benefit from this knowledge, so the effort is worth it.

The title does say that this is an introduction, so don't be too disappointed that everything isn't laid out for you. There is no effort to categorize the functions introduced or to produce an overall design process of selection appropriate for a particular task. That information comes from further study in this area.Co-authorship network map of physicians publishing on hepatitis C.

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This course will highlight common principles that permeate the functioning of networks and how the same issues related to robustness, fragility and interlinkages arise in several different types of networks. It will both introduce conceptual tools from dynamical systems, random graph models, optimization and game theory, and cover a wide variety of applications. Archived versions:. Mardavij Roozbehani, and Evan Sadler. Spring For more information about using these materials and the Creative Commons license, see our Terms of Use.

Course Home Syllabus Calendar Readings.There are seven units in this book and we have to work hard to make easy and suitable solutions for students and teachers so that it helps them learn things quickly and easily. Please click on the desired unit to view the solution of any particular exercise Of 2nd Year Math Notes. The understudies of F. Arithmetic is a vital subject for transitional f. The understudies of f.

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Related Articles. Posted on July 6, Author Rizwan Ali. Pingback: Chapter 1 Functions and Limits Exercise 1. Pingback: Exercise 1. Pingback: Exercise 2.

Leave a Reply Cancel reply Your email address will not be published. View Online. Download PDF.There are seven units in this book and we have to work hard to make easy and suitable solutions for students and teachers so that it helps them learn things quickly and easily.

Please click on the desired unit to view the solution of any particular exercise Of 2nd Year Math Notes. The understudies of F. Arithmetic is a vital subject for transitional f. The understudies of f.

Besides, it has fourteen parts and circuitous seventy-three activities. We have dealt with the arrangement notes for works out. We have attempted our best to decrease the blunder actualities while altering and setting up these simple notes for you in the event that you discover any harm interface, benevolently illuminate us by remarking underneath the notes.

If you want to remove this from Solutionemarks. Life is a great […]. This essay has great importance in all classes and this morning walk essay is in simple words which are easy to remember and get good marks in your classes. Download Essay. Before you join the education WhatsApp group you should realize the group rules. Your email address will not be published. Notify me of follow-up comments by email. Notify me of new posts by email. Skip to content. Related Articles. Posted on July 6, Author Rizwan Ali.

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