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Fun tricks for everybody

Prerequisites

High-school maths, mainly arithmetic.

Curriculum

This course concentrates on a few interesting and fun examples of derivations of formulas and their geometrical interpretation.

Math: Fun tricks for everybody

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A detailed list of the lectures can be found in a PDF outline by clicking this panel.

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This course is completely free on Udemy. Click this panel to get to the download page.

Course Objectives & Outcomes

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Creative problem solving, with fun tricks and geometrical illustrations of the results.
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How to derive the formulas for partial sums for two very important examples of arithmetic progressions: 1+2+…+n and 1+3+5+…+(2n-1).
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How to derive some less known formulas, using cool computational tricks.
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You will learn (from an article) how to convert infinite periodic decimal expansions into fractions, by smart substitutions and solving linear equations.
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You will learn (from an article) about an interesting family of nested square roots and how to prove that some members of this family are… integers!
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How to derive the formula for the sum of squares of all natural numbers from 1 to n.
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How to derive the general formula for partial sums of geometric progressions; an important example of the sum of all the natural powers (from 1 to n) of 1/2.
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How to prove divisibility in some simple cases, using very basic (but fun) reasoning.
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You will learn (from an article) some basics about continued fractions (CF), and how to recognise irrational surds from their infinite periodic CF-expansions.