I am sure that the title of the post is going to confuse many readers, but for lack of a better title please be content with it. Rest assured that the post itself is quite unambiguous. We would like to throw some light on the a special kind of ambiguity which we find in mathematical systems (here mainly in algebra).
A Taste of Modern Algebra: Remainder Theorem for Polynomials
Introduction
In high school curriculum we are taught the "Remainder Theorem" as one of the important results of Algebra. The theorem and its proof are quite simple, but the practical application and theoretical ramifications of this result are quite interesting. To recall, the theorem is stated as follows:Remainder Theorem: If $ f(x) = a_{0}x^{n} + a_{1}x^{n - 1} + \cdots + a_{n - 1}x + a_{n}$ is a polynomial with real coefficients then the remainder obtained on dividing $ f(x)$ by $ (x - a)$ is $ f(a)$.
By
Paramanand Singh
Friday, August 5, 2011
Continuous Functions on a Closed Interval: Uniform Continuity
Uniform Continuity vs. Continuity
We have discussed some very useful properties of continuous functions in the last few posts. In the current post we will focus on another property called "uniform continuity". To understand what this is all about it first makes sense to reiterate the meaning of usual concept of continuity as we have seen earlier.
By
Paramanand Singh
Thursday, June 9, 2011
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