This London Mathematical Society Popular Lecture is an introduction to the mathematical theory of knots, starting with the Reidemeister moves on a knot diagram and the crossing number of a knot. A table of the prime knots with small crossing numbers is given, and some of their properties discussed. Then the Jones polynomial of a knot is defined, and an explicit example calculated. The lecture finishes with an open research question about the Jones polynomial. [(CC) BY-NC-SA 2.0 UK]

Knots

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This video quiz contains three questions on Maclaurin series followed by answers and, then, detailed solutions. Two of the questions contain ways to check your answer.  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Maclaurin series quiz

This screen capture video contains integrals for you to calculate using trigonometric changes of variables. Full solutions are provided.  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Trigonometric change of variable quiz

This screen capture video contains integrals for you to calculate using partial fraction decompositions of the integrands. Full solutions are provided.  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Partial fraction integral quiz

This screen capture video discusses the notation and interpretation of multiple integration. A simple example of a double integral is calculated to demonstrate the geometric interpretation of such integrals.   [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Multiple integrals

This screen contains two worked examples of the calculation of multiple (double) integrals.In one the order of integration is changed.  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Knots

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