Collegemathematics

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How to prove the Pythagorean Theorem
The Pythagorean Theorem plays an essential role in many facets of math from Euclidean Geometry to complex numbers to trigonometry. Today we’ll explore one of its many proofs.
How to approach initial value word problems
We’ve all been there: on a homework set or in an exam, you turn to the final page and, to your dismay, it’s a wall of text. The dreaded Word Problem. Some of the words are useful, but some of them are meant to distract. Let’s look at a strategy for answering initial value word problems.
An introduction to enumeration using generating functions
In the year 1202, Italian mathematician Leonardo Fibonacci published the extremely influential Liber Abaci (Book of Calculations). The book's most significant contribution was to bring to Europe the Hindu-Arabic number system that we all use today. But it also contained a curious thought experiment about the reproductive patterns of rabbits, which ...
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