Henry's Math.it
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# Henry's Math.it

Fields of mathematics I'm studying and mastering for my high school's CE class
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## Complex numbers: angles and polar coordinates

Henry Mullins's insight:

This is a little difficult to follow, but it thoroughly explains the multiplication of points in the complex plane.

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## Inverting 3x3 part 2: Determinant and Adjugate of a Matrix

Finishing up our 3x3 matrix inversion
Henry Mullins's insight:

Again, this is hellish and I do not suggest you do it ever

Eeeeeevvvvvveeeerrrr

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## Birthday Probability Problem

Learn more: http://www.khanacademy.org/video?v=9G0w61pZPig The probability that at least 2 people in a room of 30 share the same birthday.
Henry Mullins's insight:

He makes at least one mistake in the video, but it doesn't affect the outcome. This is, as he says, a neat problem and a neat result.

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## Permutations

Henry Mullins's insight:

Basic permutations

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## Wolfram|Alpha: Computational Knowledge Engine

Wolfram|Alpha is more than a search engine.
Henry Mullins's insight:

This website is -the- website to go to for pretty much everything math-related.

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## xkcd • View topic - permutations of a set with non-unique elements

Henry Mullins's insight:

This was a page I came across while looking for how to calculate the permutations of a set with non-unique values. It's apparently incredibly difficult to generalize.

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## Determinant - Wikipedia, the free encyclopedia

In linear algebra, the determinant is a value associated with a square matrix. It can be computed from the entries of the matrix by a specific arithmetic expression, while other ways to determine its value exist as well. The determinant provides important information when the matrix is that of the coefficients of a system of linear equations, or when it corresponds to a linear transformation of a vector space: in the first case the system has a unique solution exactly when the determinant is nonzero; when the determinant is zero there are either no solutions or many solutions. In the second case that same condition means that the transformation has an inverse operation. A geometric interpretation can be given to the value of the determinant of a square matrix with real entries: the absolute value of the determinant gives the scale factor by which area or volume (or a higher dimensional analogue) is multiplied under the associated linear transformation, while its sign indicates whether the transformation preserves orientation. Thus a 2 × 2 matrix with determinant −2, when applied to a region of the plane with finite area, will transform that region into one with twice the area, while reversing its orientation.

Determinants occur throughout mathematics. The use of determinants in calculus includes the Jacobian determinant in the substitution rule for integrals of functions of several variables. They are used to define the characteristic polynomial of a matrix that is an essential tool in eigenvalue problems in linear algebra. In some cases they are used just as a compact notation for expressions that would otherwise be unwieldy to write down.

The determinant of a matrix A is denoted det(A), det A, or |A|.[1] In the case where the matrix entries are written out in full, the determinant is denoted by surrounding the matrix entries by vertical bars instead of the brackets or parentheses of the matrix. For instance, the determinant of the matrix

Henry Mullins's insight:

Believe it or not, this wikipedia article explains the much simpler way to find the determinant of a 3×3 matrix before you even hit the table of contents. Multiplying the frst row by its cofactors is annoying and confusing and doesn't work for anything but 3×3's anyway.

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## Inverting 3x3 part 1: Calculating Matrix of Minors and Cofactor Matrix

Beginning our quest to invert a 3x3 matrix. We calculate the matrix of minors and the cofactor matrix.
Henry Mullins's insight:

Yay higher quality
Anyway, if I wanted to be the worst math teacher ever and torture all my students, I'd have them do this by hand

This is within two standard deviations of the holocaust

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## Combinations

Henry Mullins's insight:

Basic combinations

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## Standard Deviation and Variance

Henry Mullins's insight:

A good reference for standard deviation and variance.

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## Combinations and Permutations

Henry Mullins's insight:

Pretty much the most helpful page I ran across when doing anything with combinations or permutations.

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