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Mathematical Musings | Nick Wasserman

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Understanding Sample Standard Deviation 

The formula to compute the standard deviation from a sample of data looks complex - ugly even. But understanding the the notion of variation (e.g., standard deviation) is fundamental to statistical thinking. At its core, the computation for sample standard deviation is very sensible (like so many other complex-appearing mathematical formulas, e.g., the distance …

Posted 39 months ago by

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Assumptions in Geometric Probability  ☆

Geometric probability makes use of measurement to determine probabilities. For example, the probability of hitting a bullseye could be found by computing the ratio of the area of the bullseye (4π in^2) and the area of the entire dart board (64π in^2), which is 4/64 = 0.0625; or the probability of breaking a stick randomly …

Posted 51 months ago by

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Functions, Bijections, and Combinatorics  ☆

At times, studying general definitions of functions and particular classifications of functions (e.g., bijective, surjective) can seem tedious. As a secondary teacher, the functions we consider nearly always map real numbers to real numbers, which can make it difficult to be motivated to push past this into the abstract. While bijections have implications for infinite …

Posted 59 months ago by

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A Mathematical Group  ☆

While many future mathematics teachers may never step foot in an abstract algebra course, those that do are often initially presented with the axiomatic definition of a group (closure, associativity, identity element, inverse elements) and then presented with some common examples of group tables - frequently small finite sets - to illustrate the impact of …

Posted 63 months ago by

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