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Transcript

The brackets

FLOOR

ROUND

CEILING

Dr David K Butler (Maths Learning Centre)

Nearest Integer

Least Integer Above

Greatest Integer Below

Proof

Derangements

First, count the number of derangements...

Arrangements of 5 things

Arrangements of 3 things

Derangements

Arrangements where

nothing is in its original place.

"!" - Factorial

Arrangements of 4 things

Derangements

Now show it's the nearest integer...

Derivatives of integer powers

The number e

Taylor polynomials

Taylor series

School of Maths

Undergraduate Seminar

9th September 2014

Taylor's theorem

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