Wednesday, October 29, 2008

Sturm's Theorem: An Initial Lemma

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Here's a major problem that Jacques Charles Francois Sturm solved: Find the number of real roots of an algebraic equation with real coe...
1 comment:
Monday, October 27, 2008

Jacques Charles Francois Sturm

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Jacques Charles Francois Sturm was born on September 29, 1803 in Geneva, Switzerland. His father was a math teacher. When Sturm was 16, hi...
2 comments:
Saturday, October 25, 2008

Ruffini's Proof: Field Extensions

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In today's blog, I will present Paolo Ruffini's proof that if n ≥ 5 and F is a splitting field, then F/k is not a radical tower....

Pierre Laurent Wantzel

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Pierre Larent Wantzel was born on June 5, 1814 in Paris, France. His father was a professor of applied mathematics at the Ecole speciale du...
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Wednesday, October 22, 2008

Abel's Proof: Field Extensions: Step 1: Proof

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The content in today's blog is taken from the essay by Michael I. Rosen entitled "Niels Hendrik Abel and Equations of the Fifth Deg...
Monday, October 20, 2008

Abel's Proof: Field Extensions: Step 1: Lemmas

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The content in today's blog is taken from the essay by Michael I. Rosen entitled "Niels Hendrik Abel and Equations of the Fifth Deg...
Sunday, October 19, 2008

Abel-Ruffini Proof: Field Extensions

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When Niels Abel prepared his impossibility proof , he used the vocabulary of the mathematics of his time. As a result of his work and the ...
Saturday, October 04, 2008

Abel's Proof: Aftermath

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Niels Abel submitted his impossibility proof for the quintic equation in 1824. Because of lack of funds, he was forced to condense his pr...