University of Virginia
Taylor and I
We are looking for passionate students to join our diverse community of scholars, researchers, and artists. Answer this question, which corresponds to the school/program you selected above, in a half page or roughly 250 words. College of Arts and Sciences - What work of art, music, science, mathematics, or literature has surprised, unsettled, or challenged you, and in what way?
I got lost.
Learning Calculus BC had been a somewhat predictable process of applying rules and formulas, until I met Taylor series. A quirky combination of X, N, derivatives, and factorials, it overwhelmed me with such a bombastic look.
Yes, I heard of its annual domination of the last question in free response. Yes, I did see a repeating pattern in it, but what exactly is Taylor series and how do those fancy concepts such as LagrangeError Bound relate to it?”
The mystery of Taylor series engaged me so deeply that I had turned myself into an ambitious detector searching for any possible clue.
I divided my task into two parts: extensive clue-searching and direct investigation. By browsing through miscellaneous websites, I realized its duality as both a series and a polynomial, and discovered a crucial point I missed before: it is actually an approximation of a function. In this way,“error bound” naturally made sense. Additionally, I worked and reflected on practice problems. Through drawing association between Taylor series and familiar concepts such as properties of derivatives, I gradually destructed this monster into easy pieces. The new perspective and increasing familiarity debunked the seemingly imposing look of Taylor...
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