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The Agile Mathematician Chen Jingrun Jun 10, 2009
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I am not familiar with his work, but I found the story of Chen Jingrun (19331996) fascinating. He graduated from Xiamen University in 1953 and became a researcher at the Chinese Academy of Sciences. His work led to progress in analytic Chen_Jingrun
number theory. His Chinese home page is at
the Chinese Institute of Mathematics. A short biography "A great mathematician Chen Jingrun" is on http://city.chinaassistor.com/. His 1966 paper was on ""On the representation of a large even integer as the sum of a prime and the product of at most two primes". The cultural revolution put a halt to research, so Chen's 1966 Theorem was
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not made public until 1973. His work continues to be relevant to recent research in number
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theory. Mathematician Jason Dyer reports on "Carnival of Mathematics #43" in the blog
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"The Number Warrior". He explains why 47 is a Chen prime and 43 isn't. He also introduces Roth’s theorem, linking to a paper "Restriction theory of the Selberg sieve, with applications" by Ben Green and Terence Tao, which is available as a free PDF file or
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PostScript file from arXiv.org. There is a telling anecdote about Chen Jingrun at "Extraordinary Chinese Sayings, 1840-1999 - Part 1", from the book Extraordinary Sayings (非常道) by Yu Shicun (余世存). During the Cultural Revolution, the people criticizing Chen Jingrun (陈景润) said: "Let the Goldbach conjecture go to hell! What is so big deal about
1+2? Isn't 1+2 equal to 3? You eat the food grown by peasants, you live in a house built by workers, you are protected by the People's Liberation Army and your wages are paid by the nation so that you can study 1+2. What is this? This is fake science!" So Chen jumped on the table, went through the open window and leapt downwards. But when he jumped out of the third-floor window, he was nicked by an awning and therefore only suffered some scratches on his leg when he landed on the ground. A rebel leader looked at Chen and said: "It is no wonder that you are a famous mathematician. You even know how to
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select the angle when you jump out of the window!" Post a comment
Tags: math, mathematics, china, theory, prime, maths, number, conjecture …
Century Old Topology Problem Solved in 2006 Jun 8, 2009
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In case you missed the solution of the century old Poincaré conjecture in 2006, I'll repost a link
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to the New York Times article "Elusive Proof,
borne
Elusive Prover: A New Mathematical Mystery".
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The story of the brilliant Russian mathematician Grigory Perelman (photograph) who identified the solution in 2003 is as mysterious as Poincaré's problem. Wikipedia describes the
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"Solution of the Poincaré conjecture", for non-
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mathematician, explaining the problem with
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doughnuts, balls, a cigar and even mozzarella
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cheese that is stretched to represent Ricci flow, the method of solution. For further reading, there is a repository of original material here ARC
"Notes and commentary on Perelman's Ricci flow papers".
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Tags: mathematics, geometry, topology
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A New Game to Help Children Learn Mathematics Jun 6, 2009
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I reviewed the prototype of a web based graphical game that aims to help children learn mathematics. It was developed by Mr Veljko Sekelj, a freelance Internet consultant (LinkedIn profile). He invited me, via the "Math, Math Education, Math Culture" discussion group on Prototype_Mathematics_Game
LinkedIn.com, to try out the game and I was
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quite impressed. At first I couldn't understand its intuitive interface, because I am an adult accustomed to pull down menus and tabbed panes. The game aims to help children associate fractions with percentages. A cartoon Santa Clause introduces a snow scene with a group of identical parcels that contain either a fraction or a percentage. It is operated using the mouse, and the goal is to pair up matches, for example 1/3 and 33%, which pop out of the boxes. There are no instructions, but the game would be quite intuitive to children, though perhaps not to less inquisitive adults. It needs to be made more international, with alternative themes, as the snow scene The Trouble With
would not be familiar to children in the tropics. Use of red or green colouring to indicate Physics: T... by Lee Smolin
wrong and right selections might be a problem for someone who is colour blind. I was delighted to get all the correct answers, but I was greeted by a cartoon character in tears New Europe
of distress, with a sign telling me in German that I was “Zu Langsam!” orby“Too Slow!”. Michael Palin The game is at the prototype stage, so I hope that the feedback is made more constructive. The game is online at http://www.lernmathe.com/, where you may try it Blogging out for yourself or by Jill Walker Rettberg
Live
with your children. The author would be glad to hear your feedback. He is also seeking funding for developing the game. His development project "Innovating the way how children learn math" and "Contact Me" link, is at Kickstarter.com. Kickstarter.com is a new way for people in the USA to seek funding for ideas and endeavours. Read the Kickstarter FAQ to find out more about how it works. Post a comment
Tags: math, mathematics, flash, software, education, maths
Let Creativity Flourish at Work and University May 21, 2009
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I recently responded to a survey by creativity trainer, Karen Sieczka, who blogs at GROWING GREAT IDEAS. She created the survey on creativity at work to collect research for an update to her book Growing Great Ideas: Unleashing Creativity at Work. The survey was useful to me, as it gave me a few minutes to think about creativity from the perspective of a university lecturer. I share my answers to the survey at The Hub. If you intend to do the Growing_Great_Ideas
survey, please complete it before reading my answers. The Hub for Productive Thinking is a
new social network, that I found on Ning.com, for exchange of ideas on productive thinking and other creativity models, tools and techniques. Post a comment
Tags: business, training, creativity, education, innovation
Thoughts About Creating A Mathematics Social Network May 14, 2009
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Are you thinking about creating a new social network for discussing mathematics? That would be a responsible undertaking, and you would need to have sufficient time and energy to make the commitment. If you are too busy, there are existing social networks for mathematics that you can join. I discuss some of the considerations below. BoundedArea
Websites like Vox.com and Ning.com enable you to create and manage your own social network. Ease of use is the advantage of Ning as a TechCrunch article describes. If you need more control and are willing to write HTML and do some programming, a more ambitious alternative would be to host your own website. Another approach would be to use a Content Management System (CMS) to provide the framework. Creating and maintaining a social network would be a significant project, so find some friends who share your research or teaching interests. Before you begin, make sure
that you understand each other's goals, motives and responsibilities. If the social network is just an academic experiment, then say so. Make this especially clear to any users who sign on. You will have to overhaul or disconnect your website at some time in the future. Plan for that in advance so that you don't upset your users when you turn off the lights. If you are creating the website for a business or organisation, there will be other considerations that are beyond the scope of this article. Creating a mathematics discussion group within an existing social network is a less demanding approach than starting a new social network. Choose what type of discussions you hope for:
Students looking for help with their homework
Teachers discussing science or mathematics education
Research news
People asking questions which interest them
I host the "Mirimatics" mathematics discussion group on Friendster.com. I chose not to make it a forum for solving mathematical problems. Rather, I write short posts about recent mathematics news, with links to articles that give further explanation or background. Unfortunately, it was not successful; nobody else contributed any articles or comments. You will need to figure out the secret of marketing your forum, so that you avoid the same fate. The most successful topics originate from questions initiated by members. I noticed this on my Sarawak Science group on Friendster. It is not necessary that you create a new social network for this type of discussion, as there are plenty of "ask a scientist" or Ask.com style websites. Sometimes a blog is the best platform for discussing mathematics topics. It is the personal character of the author that makes it interesting. A good example is the Redneck Math blog, which combines mathematical theory with storytelling. Interactive content is also important, for example a number guessing exercise on the Programaths website. The blog Teaching Math Creatively is a fine expression of mathematics teaching, which makes good use of photographs. Posting photographs of the classroom whiteboard is a good technique, as it's easier to solve problem on a whiteboard than on a word processor. An advantage of a blog is that anyone on the Internet can read it, whereas users must register in order to see articles on a social network. The Vox.com service as reviewed at cnet news provides an innovative blend of blogging and social networking features. This article, for example is on both my blog and in the Mathematics group at Vox.com. There are also good professional forums where you can discuss mathematics, such as "Math, Math Education, Math Culture" on LinkedIn.com and "Mathematics/Mathematik" on Xing.com. The online service Ning.com allows you to create and manage your own social network. A disadvantage of Ning is that the PHP source code is not available to the administrators, so they have limited control over their social network. On a self hosted site, the administrator has full control, and a choice of scripting languages. Python and Java are powerful languages for encoding interactive demos and simulations, but they might not be supported on all hosting services. Web surfers are expecting more multimedia content today, and that takes a lot of work to produce. Even a simple Powerpoint presentation requires a surprising amount of
creative effort. Sometimes you can burn the candle at both ends to meet a deadline, but that is not sustainable for maintaining an online forum. As a social network grows, the administrator will need to stay focused on managing the site, and encourage other volunteers generate the content. Due to limited time, I decided not to create a new social network, but to contribute articles to an existing social network, http://mathematics24x7.ning.com/. I created a blog there, where I can post topical articles that relate to the interests of the readers. Articles in Friendster groups are in plain text, which is not very attractive for online education. I enhanced one of my solutions from Friendster, by using a spreadsheet to draw a graph. I posted the article as “Using a Spreadsheet to Check a Calculus Problem” on mathematics24x7, and included a screenshot of the spreadsheet application. Online mathematical articles may be enhanced by using multimedia features, such as:
Attaching a screenshot or plot from a mathematics software package.
Use LaTeX markup or MathML fonts to display mathematical formulae correctly.
Interactive graphics that permits the viewer to adjust parameters with the mouse, and view the changes in the geometry.
A video or slide show demonstrating the steps of using a spreadsheet.
Audio narrative which is present in the class room but is usually absent on the web.
Those enhancements would involve a lot of production work: in programming, graphic design and commentary. Conversely, students who want help with their homework seek quick and terse solutions, on mathematics discussion groups, as found on Orkut.com and Friendster.com. In conclusion, if you want to discuss mathematics online, I suggest that you start a blog, or create a discussion group on an existing social network. If you are motivated and have enough free time, go ahead and start a new social network, but ask some friends to help you, and agree on your goals before you go online. This article sprang from discussions that I had with some online contacts on Facebook. I thank Christian (website) and Monica (blog) for participating in that discussion. 1 comment Tags: mathematics, science, social networking, social-networking, education, socialnetworking, friendster, ning …
Openness and Social Networking May 6, 2009
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I have just given a presentation about social networking at UNIMAS and thank the staff there for a warm reception. I explored openness in social networking, business communications and cloud computing. The Powerpoint presentation OpennessFrontSlide
OpennessAndSocialNetworking.ppt is on Slideshare.net for anyone who is interested. A PDF version of the slide show is on Scribd.com.
For a more detailed discussion, I refer you to UseCloudGetClue.pdf on Scribd.com, as I noted in my September 2008 post on Vox.com. Through my presentation and discussion paper, I have appealed for more openness and try to justify my arguments by exploration
of a variety of online services, and by drawing attention of the adverse consequences of a lack of openness. I quote United Nations' Article 19, and summarise the unjust treatment of bloggers, journalists, activists and others in countries that do not respect it.
Post a comment Tags: web20, technology, social networking, social-networking, open source, socialnetworking, computing, freedom …
Software Development: The Six Ls Apr 11, 2009
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The essence of journalism was expressed succinctly by Rudyard Kipling's Five Ws and one H. Can we reduce the profession of programming computers to such a simple formula? Here is my attempt at the Six Ls of Software Development:
Software_Development
Legitimate? Does the proposed software meet the legitimate needs of the
users, or would it remove any liberties that we have? An early answer to this question will help prevent the project being abandoned later.
Life Cycle? Is the project life cycle being managed in a methodical way? A Waterfall or Agile method can be adapted to the needs of your development team.
Length of Time? How long will the project take to develop? Fred Brookes' 1975 book: "The Mythical Man-Month" is essential reading on this point.
Layers? A layered architecture will help you to design software that will be flexible, secure and cost effective over decades of use and reuse.
Language? Choose a programming language according to the need for portability, or efficiency, or ease of development.
Licence? Your choice of an Open Source or Closed Source software licence will involve more passion and consequence than I can describe in this short space.
I omit "Lines of Code" as a concern in the 21st Century, as that measurement had more value when programs were stored on punched-cards. There is nothing magical about the letter L, or about the number of bullet points, so I do not claim that my list captures the essence of professional computer programming. Your comments are welcome. Post a comment engineering …
Tags: development, technology, programming, software, project, system,
Science and Sci-Fi Social Networks on Ning
Apr 7, 2009
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Looking for an alternative science forum to match your interests? Here is one online community, that I discovered today, about astronomy and space exploration: "PlanetSpace" on Ning.com. If you are interested in Science Fiction rather than science fact, then check out "Space Age Magazine" on Ning. Ning is an online service that you can use to easily create your own social network. You could build a community there to discuss any DiscussionGroup
topic of your choice. An article "Ning In Full" at TechCrunch.com gives a good overview of the
service. Another review "Ning's Infinite Ambition" at FastCompany.com describes how you can use viral marketing to increase interest in your ideas or business. The domain Ning.com provides an umbrella for many small social networks. When you sign up, it is easy to explore and join other user-created forums. Ning was co-founded by Marc Andreessen, who also co-founded Netscape. I thank a contributor (Deborah) of the Distance Learning and Distance Education group on Xing.com (that's Xing, not Ning) for alerting me to the relevance of Ning as a platform for science discussions. Post a comment
Tags: scifi, science, space, social networking, education, forum, planet, ning …
Discussions about Insects on a Friendster Science Group Mar 8, 2009
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I photographed this dragonfly today; a delicate looking animal, but deadly to its prey. I invite you to participate in INSECT WEEK on the Sarawak Science group at Friendster.com. What news have you heard about insects and their role in the environment? Have you seen any unusual insects or bugs recently? A DragonflyInSarawak
Zoologist posted the informative topic "Why insect?"; thank you Phormia. Discussions include: The Common Blue Damselfly, Why
insect?, The Devastating Effects of Pesticides on Marine Life, New Insect Order Mantophasmatodea Discovered, and A Facebook Cause for Western Honey Bees. I am not a biologist, but simply refer to insecteresting discoveries that I noticed on science related web sites. 1 comment
Tags: insect, biology, ecology, environment, entomology, pesticide, sarawak, zoology …
How (Not) To Advise on a Homework Question Feb 23, 2009
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If you respond to a homework question on a
forum, provide a hint, but do not tell the answer. People learn by doing, not by being told the solution. As a Physicist, needing to sharpen my maths skills, I attempted to advise on the following question on the Friendster.com group "ELITE MATH CIRCLE": STUDENTS QUESTION: monkey business... (integral Calculus) A 5-lbs monkey is attached to the end of a 30-ft Crab Eating Macaque
hanging chain that weighs 0.2 lb/ft. It climbs the chain to the top. How much work does it do?
MY FIRST REPLY: Drawing a diagram of the before and after situations would help you with this one. Can you imagine how to convert it into a simpler problem, involving a 30ft rod that is hinged at the centre point? On your diagrams, mark the centre point (7.5ft) of both 15ft sections. (This is just a hint which should help you solve the problem yourself). Everyone makes mistakes, so it is helpful to take a break and review your answer later. Or, have someone else review it; that is what online forums are good for. On review, I noticed that I needed to correct my first answer, as follows: MY SECOND REPLY: On reflection, I believe that I have given you the wrong solution. I answered as a Physicist, trained to identify the simplest model before solving the problem. From your title (integral Calculus), it is clear that your teacher requires you to use the process of integration in solving this problem. Choose a variable for the monkey's position, relative to the starting point. Since this is a 1-dimensional problem, you can use 'x', even though the monkey is moving vertically. What is the formula for the mass of the portion of chain that the monkey is carrying, as a function of x? What is the formula for the position of the centre-of-gravity of that mass of chain as a function of x? Next, express the equation which needs to be integrated. Then do the integration according to the rule that you have been taught. Education can be fun, and both tutors and students can learn from the exercise. From this exercise, I learned: That it is important to read the question, as I overlooked the important word 'integral' in the title. I also learned that Physicists should avoid online mathematics forums, and leave them to the Mathematicians. Post a comment elearning, tuition …
Tags: teaching, mathematics, integration, physics, education, distance education,
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