Thursday, March 23, 2006

Lennart Carleson wins the Abel Prize!

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Today, it was announced that Lennart Carleson has won the Abel Prize for 2006 for his work on harmonic analysis and the theory of smooth dy...
Saturday, March 11, 2006

Taylor Series

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The Taylor Series is one of the most useful results in all of mathematics. The method in all its generality was first presented by Brook Tay...
Friday, March 10, 2006

Taylor's Formula

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In today's blog, I will go over Taylor's Formula . This is a theorem that can be used to establish the Taylor Series and the MacLa...
7 comments:
Friday, February 24, 2006

Euler's Formula

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Today's proof for Euler's Formula is based on the Taylor's Series . Euler's Formula is the equation: e ix = cosx + isinx ...
4 comments:
Wednesday, February 22, 2006

Euler's Identity

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One of the simplest and most elegant equations is Euler's Identity : e πi + 1 = 0 . It states that Euler's number e (which is equa...
8 comments:
Friday, February 17, 2006

Cyclotomic Integers

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In Ernst Kummer's groundbreaking partial proof on Fermat's Last Theorem, he used cyclotomic integers . Cyclotomic integers are base...
6 comments:
Wednesday, February 15, 2006

Quadratic Reciprocity: Last Step

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In today's blog I continue the proof for the Principle of Quadratic Reciprocity . If you are not familiar with the concepts of quadrat...
Monday, February 13, 2006

Quadratic Reciprocity: Expanding on Gauss's Lemma

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In today's blog I continue the proof for the Principle of Quadratic Reciprocity . If you are not familiar with the concepts of quadrat...
1 comment:
Sunday, February 12, 2006

Euler's Criterion

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In today's blog I continue the proof for the Principle of Quadratic Reciprocity . If you are not familiar with the concepts of quadrat...
Saturday, February 11, 2006

Euler's Theorem

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In today's blog I continue the proof for the Principle of Quadratic Reciprocity . If you are not familiar with the concepts of quadrat...
Wednesday, February 08, 2006

Units for Modular Arithmetic

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In today's blog I continue the proof for the Principle of Quadratic Reciprocity . If you are not familiar with the concepts of quadrat...