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Sugata Adhya
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  • Kolkata, West Bengal
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Topology

{ {f Є C(X) : | g – f | ≤ u } : g Є C(X) & u is a positive unit of C(X) } forms a base for some top. on C(X). Corresponding to this top. how to show that  multiplication is cont. on (C(X))2? Moreover if U denotes the set of all units in C(X) how…Continue

Started May 16, 2012

Convergence
2 Replies

What does the sentence mean: "Convergence in this topology (uniform norm topology) is uniform convergence of the functions" ? (Gillman, Jerison : Rings of Continuous Functions) Does it mean whenever a sequence of functions on the said space…Continue

Started this discussion. Last reply by E Krishnan Apr 4, 2012.

Uniform Norm Topology & m-topology
1 Reply

I would like to read some detailed disscussion on Uniform Norm Topology & m-topology. Can anyone suggest some standard texts/lecture notes? ("GILLMAN/JERISON: Rings of Continuous. Functions" was found to be a little bit compact for me.)Continue

Tags: m-topology, Topology, Norm, Uniform

Started this discussion. Last reply by Amber Habib Apr 14, 2012.

Topology
3 Replies

Let (X, d) be a compact metric space. Suppose that f: X ---> X is a function such that d(f(x), f(y)) < d(x, y) for x ≠ y; x, y Є X. Then show that there exists x' Є X such that f(x') = x'.Continue

Started this discussion. Last reply by Amber Habib Apr 14, 2012.

 

Sugata Adhya

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Profession
Student
What interests you most in Math Education
Algebra, Mathematical Analysis, Programming
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Mathematics is something that I do poorly yet passionately.
Pure mathematics is, in its way, the poetry of logical ideas. ~ Albert Einstein

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Sugata Adhya's Blog

Raising the Grade on Teacher, Student Performance BY Bill Gates

Speaking at the annual convention of the American Federation of Teachers recently, Bill talked about the importance of developing more effective ways to measure teaching excellence and share best practices to improve education in the classroom.

When you think about it, teaching is one of the most difficult, complex professions there is. You have to be able to make a subject clear, and interesting. You have to calm the disruptive kids, challenge the advanced kids,…

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Posted on June 22, 2011 at 9:02pm

Does mathematics need a philosophy BY Timothy Gowers

Introduction


There is a philosophical doctrine known as bialetheism, with, apparently, many adherents in Australia, who take the view that there can be true contradictions. I do not wish to defend this view, but nevertheless in the next 45 minutes I will be arguing, sincerely, that mathematics both does and does not need a philosophy. Of course, the apparent contradiction can in my case be resolved in a boringly conventional way: the statement "Mathematics needs philosophy" has…

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Posted on June 21, 2011 at 11:08am

Why 5, 8 and 24 Are the Strangest Numbers in the Universe BY Michael Moyer (Scientific American)

In the May 2011 issue of Scientific American mathematician John Baez co-authors "The Strangest Numbers in String Theory," an article about the octonions, an eight-dimensional number system that was discovered in the mid–19th century but that has been largely ignored until quite recently. As the name of the article implies, interest in the octonions has been rekindled…

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Posted on June 18, 2011 at 7:26am

On multiple choice questions in mathematics BY Terence Tao

Now that the project to upgrade my old multiple choice applet to a more modern and collaborative format is underway (see this server-side demo and this javascript/wiki demo, as well as the …

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Posted on June 16, 2011 at 6:25pm

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