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Math Accessibility Online - An Open Discussion 2 hours ago
5 comments
The open discussion document Math Accessibility Online (PDF file on Scribd.com) is about support for mathematics, and more specifically algebra and calculus, on Web 2.0 and social networking sites. If you wish to add your opinion to it or modify it, please email your request to me at: colin dot [email protected] (Substitute a period or dot for the "dot" word in my email address). Then, I will give you write access to the original on Google Docs. Alternatively, email your mathematical opinion to me, and I will paste it into the document along with your name. I have also added a public wiki, http://onlinemathematicsaccess.wikispaces.com/, where you may record your opinion about Math Accessibility Online. I wish to thank Maria Droujkova for organising the 22nd July online meeting at Mathfuture on this topic. I prepared this document and wiki, because I am unable to attend her online meeting. 5 comments
Tags: math, mathematics, science, education, collaboration, maths, algebra, calculus …
ABO
Colin Malay View m
Comm lecture in this opinio busine way.
Se
New Mathematics Problem Solving Group 4 days ago
Post a comment
You are welcome to join the new "Math Problem Solving" group at Mathematics24x7.ning.com. Rashmi Kathuria, creator of the Mathematics24x7 social
Links Bo
Id
M
Li
No
network, has kindly permitted me to add the discussion group. The social network has 145 members including maths teachers and maths enthusiasts. I'm sure that some of them will
MY G
be happy to join you in discussing and solving maths problems. Pose your maths problems there, or add comments that lead towards a solution or understanding. Embed equations in your text as images, if they improve the presentation of your discussion. Mathematics24x7 has diverse blog posts and topics about teaching mathematics at all stages. Although I am not a mathematician, I have added three problems to get the discussion started: Algebra and Graph Theory Combine Resistors to Achieve Minimum Current and save the planet! Based on Ohm's Law, Kirchhoff's Rules and 10% tolerance resistors. Geometry and Algebra of Irrational Numbers
NEIG
Largest Semicircle Inscribable in a Unit Square or Corn Circles 101. From the topic "maxima & minima" on a Mathematics forum on Orkut.com Algebra and Differential Calculus. Problem of Monkey Climbing a Chain Can you solve it faster than the monkey?
Explor family
From the Friendster group "ELITE MATH CIRCLE". The Combine Resistors problem is my own design. The other two problems are borrowed from maths groups on Friendster.com and Orkut.com, and have hyperlinks to those groups for reference.
TAG
borne
Problems may range from Kindergarten to Postgraduate level and may cover any subject
edu
involving mathematics. Discussions on Ning.com social networks support images
mat
embedded within the text, which is useful for algebra. You may render equations as
mat
images, using an on line equation editor, and upload them into your discussion.
mat nort
Post a comment education …
Tags: electronics, math, mathematics, science, geometry, teacher, physics,
geome
nw200
sara
seasi
Editing Equations on Web 2.0 Sites Jul 7, 2009
softwa
3 comments
Support for equation
ARC
editing is a weakness of all Web 2.0 sites that I have Quadratic_Solutions
encountered. Students and lecturers of science and
mathematics need to use equations and formulae to develop their work. The blackboard or whiteboard is convenient in the classroom, but academics also need to share their work
Jul
Jun
Ma
Ap
Ma
online. Social networks and Web 2.0 sites are the ideal forum for sharing, but they are not
200
geared for academic use. Programmers of FORTRAN, ALGOL and C already have a
200
solution; they have been expressing equations in plain text for half a century. It is common
SUB
to see x-squared written as x^2, and the square root of x as x^.5, (x to the power of one half), but many people would not be familiar with that shorthand. Some Web 2.0 sites
Su po
support HTML markup when editing posts and comments, and provide format controls like
Power
Bold and Italics on the toolbar. Academic discussions would be considerably improved if
Theme Gardn
Web 2.0 sites would add just three buttons: Superscript, Subscript and Greek letters to the editing toolbar. Some social networks, such as LinkedIn.com and Friendster.com do not
Us
support any HTML editing. The Hi5.com social network supports HTML in discussions, but you need to code it by hand, or with HTML editing software such as Kompozer, and paste it into the edit box. Most blogs let you attach an image to your post, so a solution is to use an online equation editor, as at CodeCogs or Thornahawk, to generate an image of your equation. For example, the expression "\frac{-b\pm{\sqrt[]{(b^2 - 4*a*c)}}}{2a}" renders the formula for solutions to the quadratic equation a*x^2+b*x+c=0. I uploaded the rendered image "Quadratics_Solutions.gif" to this blog post. One popular Web 2.0 service, the online collaboration tool Zoho Writer has a LaTeX Equation Editor. According to the Zoho P H We O T Ogot S a lot of requests Blog: "As you may know, a significant % of our users are students.
from this user segment to build an Equation Editor into Zoho Writer. And Zoho Writer has it now." The tool that Zoho added is LaTeX, a document markup language developed in the
Live
1980's. If you host a blog or web page, you can use equation rendering plug-ins or cgi programs such as Yourequations.com or MathTex to embed equations into your online content. This topic is also being discussed at Mathematics24x7.ning.com and on the Math, Math Education, Math Culture group at LinkedIn.com. 3 comments
Tags: math, mathematics, science, education, web2.0, maths
Representing Scale in Mathematics The conception of scale and its representation and exploration are critical mathematical skills. Analogies are commonly used. A transistor is two thousand times smaller than a human hair. Antarctic ice is as deep as Smallest_Transistor_1999
a dozen football fields. Analogies are not always
helpful, and it should not be necessary to repeat them every time that science or technology is discussed. Exponential or Scientific Notation or powers of ten provide a convenient representation of distance, time, money and other measurements. We use words like "trillion" in Finance and "nanometer" in Physics, as symbols for powers of ten, to help us reason about the very large and the very small. Exponential notation is used on a scientific calculator. Sometimes powers of two are used, as in defining a Kilobyte of memory, or repeatedly folding a sheet of paper in half. An understanding of scale helps us to understand science. For example, travelling to Mars would be much harder than travelling to the International Space Station. Both are in space, but Mars is about one million times further away. Zooming, as used in photography, is a transformation that helps us to appreciate different scales. It is the dynamic version of the relationship with the real world that we infer when looking at a model car or the map of a country. Scaling relates to the concept of similar triangles in geometry. M.C. Escher used one scaling transformation, now known as the Droste Effect, in his mathematical prints. Zooming is an essential tool in navigating computer media and makes graphical content more accessible by letting us adjust the scale to match our visual acuity.The space simulation software Celestia provides an "exponential zoom feature that lets you explore space across a huge range of scales". Fractals show self-similarity at many scales, and graphical presentations let you zoom in to theoretically limitless depth, as shown on this video, Baroque Mandelbrot Zoom on Youtube. In summary, representations of scale include: exponential notation or powers of ten, maps and models, zooming out to explore simulations of space, or zooming in to explore the structure of fractals. This post was my response to a discussion Multiple Representations, with math teachers on mathematics24x7.ning.com. Transistor image is from the linked 1999 BBC article. Post a comment
Tags: math, mathematics, science, space, astronomy, education, fractal, maths …
Heartening Success of Nesin Mathematics Village Jun 30, 2009
Post a comment
The Nesin Mathematics Village, or Nesin Matematik Koyu, in Turkey arose from controversial beginnings. I first read the story "Mathematics under arrest" of its controversial beginnings in 2007, when Professor Ali Nesin was unfairly charged as a criminal for operating an unauthorised summer school. Closure of the school by authorities in 2007 was condemned by mathematicians around the world, including Alexandre Borovik, of Manchester, England. I recalled that story while contemplating what it means to be a mathematician and the waste that occurs when authorities deny mathematicians that role, as in the case of Chen Jinrun, when criticised by rebels during the Communist Revolution in China. A quick search of the web shows that Professor Ali Nesin's small school has grown into a heartening success, an educational village dedicated to giving young people the opportunity to focus on mathematics. "Nesin Mathematics Village, random faces" by Alexandre Borovik shows that the village is thriving, and includes a photo of the founder, Ali Nesin. A maths undergraduate in England tells more of the story, in "Nesin Mathematics Village in Turkey", and shows interest in beginning something similar. Post a comment
Tags: math, mathematics, school, education, turkey, maths, matematik …
Mathematicians or Mathematics Enthusiasts? Jun 30, 2009
Post a comment
Wikipedia defines that "A mathematician is a person whose primary area of study and/or research is the field of mathematics.” Although I use some mathematics in my work, and the subjects that I teach have some mathematical content, I do not call myself a Mathematician. As academics, we must be careful not to misrepresent our expertise. In my blog post The Agile Mathematician Chen Jingrun, I began with the disclaimer "I am not familiar with his work" lest I misrepresent myself as being a mathematician. Conversely, we should not be hasty in denying that title to someone who claims it, like the rebel leaders who misjudged Chen Jingrun. What are the circumstances in which a teacher, technologist or amateur may use that title? The Wikipedia definition may be too limited, and it is not definitive, as Wikipedia may be edited at will. Everyone is a mathematician (with a small "m") at least some of the time. But the title Mathematician is not like the title Motorist for someone who drives a car. It implies that the holder is advancing the field or at least striving to do so. Old mathematicians die and young ones take their place, so teachers are advancing mathematics, even if they do not publish papers. I won’t press this matter any further, but will focus on using mathematics, rather than discussing the meaning of words. For now I will say that I am a Mathematics Enthusiast. This post is also on mathematics24x7, with comments. Post a comment
Tags: math, mathematics, teacher, education, amateur, research, maths, profession
…
Thinking Upstream About Ideas and Human Rights Jun 27, 2009
Post a comment
My other blog Thinking Upstream, about ideas and human rights, is based on online news of some of the bloggers and journalists who remain unjustly imprisoned in several countries. As one blogger among many, I hope to draw attention to the WithoutArticle19
people mentioned, urging that we each seek peaceful
ways to secure their freedom. They have been hurt by authoritarianism and its cruel repression, and by those who execute that repression or gain from it. I have no experience of the countries mentioned, but am convinced of the accuracy of the news, by the variety of reputable publications, to which I refer in the hyper-links of my posts. I blog about human rights because: all freedoms and rights are fragile, and at risk of being lost, if we are even a little careless. Thinking Upstream is now a PDF file on Scribd.com for easy offline reading, even in places where Friendster is blocked. I used Google Translate to machine-translate it into various languages, also in PDF format on Scribd.com.Thinking Upstream is at: http://cmcallister.blog.friendster.com/. Your comments are welcome. The image refers to United Nations' Article 19, and contains photos of victims of repression. Post a comment
Tags: internet, blogger, freedom, human rights, journalist, article 19
Boosting Motivation For Learning Mathematics Jun 25, 2009
Post a comment
In the discussion, On teaching math successfully, on the LinkedIn.com forum, Math, Math Education, Math Culture; Dan, a math teacher at a community college, asks "... how to motivate students to learn math?" I replied: Dan, there are two branches of your question on this Mandelbrot_Set
forum, but I think that we can handle that. David's
reply on the other branch made me laugh, as he joked about bad teaching practices that we can see in others but not in ourselves. He was joking about their value as teaching methods? Can we appeal to heroes, like Chen Jingrun or Grigory Perelman? Or are they in a different league from most of us who merely use mathematics, rather than creating it? One student rebuked me, in the group All Science Professionals on Hi5.com for suggesting some famous scientists as role models, saying that he would find his own way as a scientist, and I think he will be right. Mathematics is crucial to many subjects, and I
have been attempting to promote it on my Vox blog and in unlikely places like the Hi5 (Mathematics group) and Friendster (Mirimatics group) social networks. Mathematics is created, and we cannot predict what it will be like until it happens, so there is a sense of adventure. The visible originality of the Mandelbrot set (1978) is a good example of a recent mathematical discovery. The unconventional role models whom I mentioned, discovery of the unknown (even as a spectator), the mere usefulness of mathematics; these certainly motivate me. Feedback is important. How will you know if you succeed in boosting your students' motivation? If you have a website, that is a tool that you could use to show off your interest in mathematics. (The above image of the Mandelbrot set is the first of a fascinating sequence of images at Wikimedia.org.) Post a comment
Tags: teaching, math, mathematics, science, education, maths
The Agile Mathematician Chen Jingrun Jun 10, 2009
Post a comment
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 not made public until 1973. His work continues to be relevant to recent research in number theory. Mathematician Jason Dyer reports on "Carnival of Mathematics #43" in the blog "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 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 select the angle when you jump out of the window!" As reported in How Chinese's idols
have changed: On February 17 1978, People's Daily and Guangming Daily introduced Xu Chi's article "Goldbach Conjecture" from People's literature. This was the day when hundreds of millions of Chinese learned of Chen Jingrun, who was honored as China's "jewel in the mathematical crown". Post a comment
Tags: math, mathematics, china, theory, prime, maths, number, conjecture …
Century Old Topology Problem Solved in 2006 Jun 8, 2009
Post a comment
In case you missed the solution of the century old Poincaré conjecture in 2006, I'll repost a link to the New York Times article "Elusive Proof, Elusive Prover: A New Mathematical Mystery". 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 "Solution of the Poincaré conjecture", for nonmathematician, explaining the problem with Grigori_Perelman
doughnuts, balls, a cigar and even mozzarella cheese that is stretched to represent Ricci flow,
the method of solution. For further reading, there is a repository of original material here "Notes and commentary on Perelman's Ricci flow papers". The New Yorker covers the story of the Poincaré conjecture in the article Manifold Destiny, August, 2006. Photo of Grigory Perelman Courtesy International Congress of Mathematicians Press Office. Post a comment
Tags: mathematics, geometry, topology, poincare, perelman
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Math Accessibility Online - An Open Discussion 2 hours ago
5 comments
The open discussion document Math Accessibility Online (PDF file on Scribd.com) is about support for mathematics, and more specifically algebra and calculus, on Web 2.0 and social networking sites. If you wish to add your opinion to it or modify it, please email your request to me at: colin dot [email protected] (Substitute a period or dot for the "dot" word in my email address). Then, I will give you write access to the original on Google Docs. Alternatively, email your mathematical opinion to me, and I will paste it into the document along with your name. I have also added a public wiki, http://onlinemathematicsaccess.wikispaces.com/, where you may record your opinion about Math Accessibility Online. I wish to thank Maria Droujkova for organising the 22nd July online meeting at Mathfuture on this topic. I prepared this document and wiki, because I am unable to attend her online meeting. 5 comments
Tags: math, mathematics, science, education, collaboration, maths, algebra, calculus …
ABO
Colin Malay View m
Comm lecture in this opinio busine way.
Se
New Mathematics Problem Solving Group 4 days ago
Post a comment
You are welcome to join the new "Math Problem Solving" group at Mathematics24x7.ning.com. Rashmi Kathuria, creator of the Mathematics24x7 social
Links Bo
Id
M
Li
No
network, has kindly permitted me to add the discussion group. The social network has 145 members including maths teachers and maths enthusiasts. I'm sure that some of them will
MY G
be happy to join you in discussing and solving maths problems. Pose your maths problems there, or add comments that lead towards a solution or understanding. Embed equations in your text as images, if they improve the presentation of your discussion. Mathematics24x7 has diverse blog posts and topics about teaching mathematics at all stages. Although I am not a mathematician, I have added three problems to get the discussion started: Algebra and Graph Theory Combine Resistors to Achieve Minimum Current and save the planet! Based on Ohm's Law, Kirchhoff's Rules and 10% tolerance resistors. Geometry and Algebra of Irrational Numbers
NEIG
Largest Semicircle Inscribable in a Unit Square or Corn Circles 101. From the topic "maxima & minima" on a Mathematics forum on Orkut.com Algebra and Differential Calculus. Problem of Monkey Climbing a Chain Can you solve it faster than the monkey?
Explor family
From the Friendster group "ELITE MATH CIRCLE". The Combine Resistors problem is my own design. The other two problems are borrowed from maths groups on Friendster.com and Orkut.com, and have hyperlinks to those groups for reference.
TAG
borne
Problems may range from Kindergarten to Postgraduate level and may cover any subject
edu
involving mathematics. Discussions on Ning.com social networks support images
mat
embedded within the text, which is useful for algebra. You may render equations as
mat
images, using an on line equation editor, and upload them into your discussion.
mat nort
Post a comment education …
Tags: electronics, math, mathematics, science, geometry, teacher, physics,
geome
nw200
sara
seasi
Editing Equations on Web 2.0 Sites Jul 7, 2009
softwa
3 comments
Support for equation
ARC
editing is a weakness of all Web 2.0 sites that I have Quadratic_Solutions
encountered. Students and lecturers of science and
mathematics need to use equations and formulae to develop their work. The blackboard or whiteboard is convenient in the classroom, but academics also need to share their work
Jul
Jun
Ma
Ap
Ma
online. Social networks and Web 2.0 sites are the ideal forum for sharing, but they are not
200
geared for academic use. Programmers of FORTRAN, ALGOL and C already have a
200
solution; they have been expressing equations in plain text for half a century. It is common
SUB
to see x-squared written as x^2, and the square root of x as x^.5, (x to the power of one half), but many people would not be familiar with that shorthand. Some Web 2.0 sites
Su po
support HTML markup when editing posts and comments, and provide format controls like
Power
Bold and Italics on the toolbar. Academic discussions would be considerably improved if
Theme Gardn
Web 2.0 sites would add just three buttons: Superscript, Subscript and Greek letters to the editing toolbar. Some social networks, such as LinkedIn.com and Friendster.com do not
Us
support any HTML editing. The Hi5.com social network supports HTML in discussions, but you need to code it by hand, or with HTML editing software such as Kompozer, and paste it into the edit box. Most blogs let you attach an image to your post, so a solution is to use an online equation editor, as at CodeCogs or Thornahawk, to generate an image of your equation. For example, the expression "\frac{-b\pm{\sqrt[]{(b^2 - 4*a*c)}}}{2a}" renders the formula for solutions to the quadratic equation a*x^2+b*x+c=0. I uploaded the rendered image "Quadratics_Solutions.gif" to this blog post. One popular Web 2.0 service, the online collaboration tool Zoho Writer has a LaTeX Equation Editor. According to the Zoho P H We O T Ogot S a lot of requests Blog: "As you may know, a significant % of our users are students.
from this user segment to build an Equation Editor into Zoho Writer. And Zoho Writer has it now." The tool that Zoho added is LaTeX, a document markup language developed in the
Live
1980's. If you host a blog or web page, you can use equation rendering plug-ins or cgi programs such as Yourequations.com or MathTex to embed equations into your online content. This topic is also being discussed at Mathematics24x7.ning.com and on the Math, Math Education, Math Culture group at LinkedIn.com. 3 comments
Tags: math, mathematics, science, education, web2.0, maths
Representing Scale in Mathematics The conception of scale and its representation and exploration are critical mathematical skills. Analogies are commonly used. A transistor is two thousand times smaller than a human hair. Antarctic ice is as deep as Smallest_Transistor_1999
a dozen football fields. Analogies are not always
helpful, and it should not be necessary to repeat them every time that science or technology is discussed. Exponential or Scientific Notation or powers of ten provide a convenient representation of distance, time, money and other measurements. We use words like "trillion" in Finance and "nanometer" in Physics, as symbols for powers of ten, to help us reason about the very large and the very small. Exponential notation is used on a scientific calculator. Sometimes powers of two are used, as in defining a Kilobyte of memory, or repeatedly folding a sheet of paper in half. An understanding of scale helps us to understand science. For example, travelling to Mars would be much harder than travelling to the International Space Station. Both are in space, but Mars is about one million times further away. Zooming, as used in photography, is a transformation that helps us to appreciate different scales. It is the dynamic version of the relationship with the real world that we infer when looking at a model car or the map of a country. Scaling relates to the concept of similar triangles in geometry. M.C. Escher used one scaling transformation, now known as the Droste Effect, in his mathematical prints. Zooming is an essential tool in navigating computer media and makes graphical content more accessible by letting us adjust the scale to match our visual acuity.The space simulation software Celestia provides an "exponential zoom feature that lets you explore space across a huge range of scales". Fractals show self-similarity at many scales, and graphical presentations let you zoom in to theoretically limitless depth, as shown on this video, Baroque Mandelbrot Zoom on Youtube. In summary, representations of scale include: exponential notation or powers of ten, maps and models, zooming out to explore simulations of space, or zooming in to explore the structure of fractals. This post was my response to a discussion Multiple Representations, with math teachers on mathematics24x7.ning.com. Transistor image is from the linked 1999 BBC article. Post a comment
Tags: math, mathematics, science, space, astronomy, education, fractal, maths …
Heartening Success of Nesin Mathematics Village Jun 30, 2009
Post a comment
The Nesin Mathematics Village, or Nesin Matematik Koyu, in Turkey arose from controversial beginnings. I first read the story "Mathematics under arrest" of its controversial beginnings in 2007, when Professor Ali Nesin was unfairly charged as a criminal for operating an unauthorised summer school. Closure of the school by authorities in 2007 was condemned by mathematicians around the world, including Alexandre Borovik, of Manchester, England. I recalled that story while contemplating what it means to be a mathematician and the waste that occurs when authorities deny mathematicians that role, as in the case of Chen Jinrun, when criticised by rebels during the Communist Revolution in China. A quick search of the web shows that Professor Ali Nesin's small school has grown into a heartening success, an educational village dedicated to giving young people the opportunity to focus on mathematics. "Nesin Mathematics Village, random faces" by Alexandre Borovik shows that the village is thriving, and includes a photo of the founder, Ali Nesin. A maths undergraduate in England tells more of the story, in "Nesin Mathematics Village in Turkey", and shows interest in beginning something similar. Post a comment
Tags: math, mathematics, school, education, turkey, maths, matematik …
Mathematicians or Mathematics Enthusiasts? Jun 30, 2009
Post a comment
Wikipedia defines that "A mathematician is a person whose primary area of study and/or research is the field of mathematics.” Although I use some mathematics in my work, and the subjects that I teach have some mathematical content, I do not call myself a Mathematician. As academics, we must be careful not to misrepresent our expertise. In my blog post The Agile Mathematician Chen Jingrun, I began with the disclaimer "I am not familiar with his work" lest I misrepresent myself as being a mathematician. Conversely, we should not be hasty in denying that title to someone who claims it, like the rebel leaders who misjudged Chen Jingrun. What are the circumstances in which a teacher, technologist or amateur may use that title? The Wikipedia definition may be too limited, and it is not definitive, as Wikipedia may be edited at will. Everyone is a mathematician (with a small "m") at least some of the time. But the title Mathematician is not like the title Motorist for someone who drives a car. It implies that the holder is advancing the field or at least striving to do so. Old mathematicians die and young ones take their place, so teachers are advancing mathematics, even if they do not publish papers. I won’t press this matter any further, but will focus on using mathematics, rather than discussing the meaning of words. For now I will say that I am a Mathematics Enthusiast. This post is also on mathematics24x7, with comments. Post a comment
Tags: math, mathematics, teacher, education, amateur, research, maths, profession
…
Thinking Upstream About Ideas and Human Rights Jun 27, 2009
Post a comment
My other blog Thinking Upstream, about ideas and human rights, is based on online news of some of the bloggers and journalists who remain unjustly imprisoned in several countries. As one blogger among many, I hope to draw attention to the WithoutArticle19
people mentioned, urging that we each seek peaceful
ways to secure their freedom. They have been hurt by authoritarianism and its cruel repression, and by those who execute that repression or gain from it. I have no experience of the countries mentioned, but am convinced of the accuracy of the news, by the variety of reputable publications, to which I refer in the hyper-links of my posts. I blog about human rights because: all freedoms and rights are fragile, and at risk of being lost, if we are even a little careless. Thinking Upstream is now a PDF file on Scribd.com for easy offline reading, even in places where Friendster is blocked. I used Google Translate to machine-translate it into various languages, also in PDF format on Scribd.com.Thinking Upstream is at: http://cmcallister.blog.friendster.com/. Your comments are welcome. The image refers to United Nations' Article 19, and contains photos of victims of repression. Post a comment
Tags: internet, blogger, freedom, human rights, journalist, article 19
Boosting Motivation For Learning Mathematics Jun 25, 2009
Post a comment
In the discussion, On teaching math successfully, on the LinkedIn.com forum, Math, Math Education, Math Culture; Dan, a math teacher at a community college, asks "... how to motivate students to learn math?" I replied: Dan, there are two branches of your question on this Mandelbrot_Set
forum, but I think that we can handle that. David's
reply on the other branch made me laugh, as he joked about bad teaching practices that we can see in others but not in ourselves. He was joking about their value as teaching methods? Can we appeal to heroes, like Chen Jingrun or Grigory Perelman? Or are they in a different league from most of us who merely use mathematics, rather than creating it? One student rebuked me, in the group All Science Professionals on Hi5.com for suggesting some famous scientists as role models, saying that he would find his own way as a scientist, and I think he will be right. Mathematics is crucial to many subjects, and I
have been attempting to promote it on my Vox blog and in unlikely places like the Hi5 (Mathematics group) and Friendster (Mirimatics group) social networks. Mathematics is created, and we cannot predict what it will be like until it happens, so there is a sense of adventure. The visible originality of the Mandelbrot set (1978) is a good example of a recent mathematical discovery. The unconventional role models whom I mentioned, discovery of the unknown (even as a spectator), the mere usefulness of mathematics; these certainly motivate me. Feedback is important. How will you know if you succeed in boosting your students' motivation? If you have a website, that is a tool that you could use to show off your interest in mathematics. (The above image of the Mandelbrot set is the first of a fascinating sequence of images at Wikimedia.org.) Post a comment
Tags: teaching, math, mathematics, science, education, maths
The Agile Mathematician Chen Jingrun Jun 10, 2009
Post a comment
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 not made public until 1973. His work continues to be relevant to recent research in number theory. Mathematician Jason Dyer reports on "Carnival of Mathematics #43" in the blog "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 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 select the angle when you jump out of the window!" As reported in How Chinese's idols
have changed: On February 17 1978, People's Daily and Guangming Daily introduced Xu Chi's article "Goldbach Conjecture" from People's literature. This was the day when hundreds of millions of Chinese learned of Chen Jingrun, who was honored as China's "jewel in the mathematical crown". 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 to the New York Times article "Elusive Proof, Elusive Prover: A New Mathematical Mystery". 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 "Solution of the Poincaré conjecture", for nonmathematician, explaining the problem with Grigori_Perelman
doughnuts, balls, a cigar and even mozzarella cheese that is stretched to represent Ricci flow,
the method of solution. For further reading, there is a repository of original material here "Notes and commentary on Perelman's Ricci flow papers". The New Yorker covers the story of the Poincaré conjecture in the article Manifold Destiny, August, 2006. Photo of Grigory Perelman Courtesy International Congress of Mathematicians Press Office. Post a comment
Tags: mathematics, geometry, topology, poincare, perelman
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