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Tag archives for Algebra

Cauchy-Schwarz inequality

10
Jun
posted by                filed under Mathematics
Cauchy-Schwarz inequality
Proof – 1 The form of the inequality suggests that if we can somehow construct a quadratic equation where some condition can be imposed on its discriminant, we may be able to generate the required inequality. Consider the function f (x) given by f (x) = (a1x – b1)2 + (a2x – b2)2 + ….. + (anx – bn)2 Obviously, Note that f ...more»
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Euler’s formula

30
Apr
posted by                filed under Mathematics
Euler’s formula
Most of us are familiar with Euler’s (miraculous) formula: However, how many of us have actually given much thought to why this should hold true? Even more fundamental is the question that what meaning should be attached to raising a real number like e to a complex power iθ. Many math authors will propose this formula as a definition. That’s very ...more»
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What’s the difference between permutations and combinations?

10
Apr
posted by                filed under Mathematics
What’s the difference between permutations and combinations?
One math topic that students find most confusing is Permutations and Combinations, and the biggest problem students face is not realizing the difference between a situation which involves permutations and one which involves combinations. Although for many people it takes time to understand this distinction, here's  an article that explains on a simple level the difference between the two concepts ...more»
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