An oddly intuitive method to finding the distance between two skew lines in 3 space.

We begin by considering two lines. Namely, $latex f(t): x = 1 + 2t, y = 2 - 3t, z = 3 + 4t$ and $latex h(s): x = -1 + 3s, y = 3-s, z = -5 + 5s$. I now plot these two lines in 3 space in order [...]

By | November 6th, 2017|0 Comments

Basics of Vector Representation

Not so long ago, I started reading some linear algebra, just out of interest. I was uncertain about whether or not I would understand the concepts, or if it would be worth it to go through all the trouble. I can now say that it was worth it. Honestly, it [...]

By | October 25th, 2017|2 Comments

The Probability Lifesaver – by Steven J. Miller, a review

NB. I was sent this book as a review copy. In addition, I lent this book to a student studying statistics, as I thought that it would be more interesting for them to let me know how much they get out of it. This is the review by Singalakha Menziwa, [...]

By | October 20th, 2017|0 Comments

The Mathematics of Various Entertaining Subjects, Volume 2- edited by Jennifer Beineke and Jason Rosenhouse, a review

NB. I was sent this book as a review copy. From Princeton University Press I tell my first year students that whether or not they will use their first year maths directly in the future, taking a course in mathematics is like going to a gym for your [...]

By | October 15th, 2017|2 Comments

Missing lectures after writing a challenging test – thoughts from a recent MAM1000W student

The following is by one of the current undergraduate tutors for MAM1000W, Nthabiseng Machethe, who has been providing me with extremely useful feedback and her thoughts on the course from the perspective of a recent student of it. She wrote this to me after a lot of students were disappointed [...]

By | October 1st, 2017|1 Comment

The Seduction of Curves – by Allan McRobie, a review

NB. I was sent this book as a review copy. From Princeton University Press This is a beautiful book, it is a thought-provoking books and it is an informative book.  It really is the intersection of mathematics, nature and art, and explores the three themes via the language [...]

By | October 1st, 2017|0 Comments

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|1 Comment

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
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