2017 2/3rds numbers game

This is the fourth year that I've played the 2/3rds numbers game with my first year maths class. I'm always interested to see how, knowing previous results will affect this year's results. Of course I am sure that a great deal depends on exactly how I explain the game, and [...]

By | September 22nd, 2017|0 Comments

Some more volume visualisations

Here is an animation which may help you imaging a shape which has a circular base, with parallel slices perpendicular to the base being equilateral triangles:   The same thing, where the slices are squares.   And here is the region in the (x,y) plane between $latex y=\sqrt{x}$, the x-axis [...]

By | September 14th, 2017|1 Comment

Guidelines for visualising and calculating volumes of revolution

I have seen some people try to blindly use the formulae for volumes of revolution by cylindrical cross-sections and by cylindrical shells, and I thought that I would write a guide as to how I would recommend tackling such problems, as generally just using the formulae will lead you down [...]

By | September 13th, 2017|0 Comments

Using integration to calculate the volume of a solid with a known cross-sectional area.

Hi there again, I have not written a post in while, here goes my second post. I would like us to discuss one of the important applications of integration. We have seen how integration can be used to solve the area problem, in this post we are going to see [...]

By | September 7th, 2017|0 Comments

Introduction to trigonometric substitution

I have decided to start writing some posts here, and this is my first post. I would like to introduce trig substitution by presenting an example that you have seen before. Trig substitution is one of the techniques of integration, it's like u substitution, except that you use a trig [...]

By | August 27th, 2017|2 Comments

Riemann sums to definite integral conversion

In the most recent tutorial there is a question about converting a Riemann sum to a definite integral, and it seems to be tripping up quite a few students. I wanted to run through one of the calculations in detail so you can see how to answer such a question. [...]

By | August 23rd, 2017|0 Comments

Philosophy of Mathematics, by Øystein Linnebo – A review, by Henri Laurie

From http://press.princeton.edu/titles/11024.html This book was sent to me by the publisher as a review copy. PHILOSOPHY OF MATHEMATICS OR PHILOSOPHY FOR MATHEMATICS? By Henri Laurie. Review of Øystein Linnebo's "Philosophy of Mathematics", Princeton University Press, 2017. (This one is impressionistic; I hope to present a more conventional summary-of-contents [...]

By | August 21st, 2017|3 Comments

Some sum identities

During tutorials last week, a number of students asked how to understand identities that are used in the calculation of various Riemann sums and their limits. These identities are:   $latex \sum_{i=1}^n 1=n$ $latex \sum_{i=1}^n i=\frac{n(n+1)}{2}$ $latex \sum_{i=1}^n i^2=\frac{n(n+1)(2n+1)}{6}$ $latex \sum_{i=1}^n i^3=\left(\frac{n(n+1)}{2}\right)^2$   Let's go through these one by one. [...]

By | August 20th, 2017|0 Comments

MAM1000W 2017 semester 2, lecture 1 (part ii)

The distance problem If I want to know how far I walked during an hour, I can ask how far I walked in the first five minutes, and how far I walked in the second five minutes, and how far I walked in the third five minutes, etc. and add [...]

By | August 13th, 2017|0 Comments

MAM1000W 2017 semester 2, lecture 1 (part i)

I wanted to put up a little summary of some of the most important things to remember from the end of last semester. There was a sudden input of new concepts, so let's put some of them down here to get a clear reminder of what we need to know. [...]

By | August 13th, 2017|0 Comments
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