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Maths, Undergraduate, Describing a Graph, Queen Mary, University of London

  1. Read the task in Box 1.
  2. Download each of the pdfs and read them. Keep these open so you can refer to them as you watch the video.
  3. Watch the video.

Step 1

The Task

The Mathematical Writing course at QMUL (http://www.maths.qmul.ac.uk/~fv/teaching/mw/ ) provides specific training on developing and presenting mathematical arguments. Through written explanation of mathematical concepts, the course aims to facilitate students’ understanding of fundamental mathematical ideas. This is particularly useful because at ‘A’ level students often use ‘templates’ or patterns to solve mathematical problems. While these templates may work in allowing students to solve a problem, they do not help with understanding. In the Mathematical Writing course, students engage with the underlying mathematical theory and learn the language of mathematics. Writing is used to help students consolidate, and perform a synthesis of, the material introduced in first year mathematics courses. It is also essential preparation for any student who wants to do a final year project.

In this task, the student is given a plot of a function. The question is: “Describe accurately the behaviour of the following function:”

The use of specialised terminology is necessary to identify the function's properties, and to communicate these properties clearly, concisely, and without ambiguity. This task has to be completed without using any mathematical symbols. In an appropriate context, having to express mathematics without symbols is a most useful exercise. It brings about the discipline needed to use symbols effectively, and it is invaluable for learning how to communicate to an audience of non-experts.

Download the question for describing a function.

Step 2

Texts

Describing a Function Text 1

1) it is a continuous even function, about y-axis, which has only one stationary point. From zero to plus infinity, the function increases steadily but approaches constant at infinity.

Describing a Function Text 2

This is a continuous, smooth function. It is piecewise monotonic. The function is even and therefore symmetric about the y-axis. It is bounded and not negative.

Describing a Function Text 3

This is a smooth even function, which is bounded. It vanishes at two points, one at a negative value and one at a positive value, and is negative strictly between these points. The function has the shape of an inverted Gaussian function.
Step 3

Step 4

Download the transcript for this video.

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