Mathematics A to Z: Part 2

Last summer, Nebus Research had a fun series on the definitions of 26 different mathematical terms, one for each letter of the alphabet. Here are the words from F to J:

F is for fallacy, or a mathematical argument can includes incorrect reasoning.

G is for graph, as in graph theory (as opposed to an ordinary x-y Cartesian graph.

H is for hypersphere, which is the generalization of a circle or sphere into n-dimensional space. As a student, one of my favorite formulas was the one for the volume of a hypersphere in \mathbb{R}^n:

V_n = \displaystyle \frac{\pi^{n/2}}{\Gamma(1 + n/2)}

I is for into, a possible characteristic of a function f : A \to B.

J is for jump discontinuity, of the concepts that shouldn’t be brand-new to students at the start of a calculus class but often is.

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  1. I suspect the thing fascinating and annoying about fallacies is that they don’t have anything to do with whether the conclusion is true or false, or whether the premises have anything to do with reality. A logical fallacy is wholly a matter of how the argument is structured. It can be semantically nonsense and sound, or can be correct (and even convincing!) in its conclusions but logically void. It’s tricky to think of the validity of an argument as being independent of the rightness of its premises or conclusions.

  1. Mean Green Math Likes Me | nebusresearch

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