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Mathematics is a powerful but dangerous tool in a presentation. A single equation can contain a significant amount of information; however, is that information necessary, or can it be displayed in different ways? Attempting to impress the audience with equation after equation will quickly put the audience to sleep. It is better for the speaker to show the effects of the equation.
For example, in presenting a best-fitting line to set of data, one could display the equation y = 3.52t + 5.26; however, would a chart not present the information more quickly? There are circumstances where the coefficient 3.52 may be significant, for example, if the data is expected to grow at a rate of 2.7 ± 0.6, then the specific value 3.52 becomes significant.
As another example, solutions to a differential equation may be exceptionally complex: the solution to y(2)(t) + t2y(1)(t) + y(t) = 1, y(0) = y(1)(0) = 0 contains a product of an exponential function and the Heun triconfluent function, however, more useful is the image showing the solution, as shown in Figure 1.
Figure 1. A solution to a 2nd-order initial-value problem.
Large equations tend not to be memorable, and matrix entries even less so. Large equations may be presented either as part of the background or it can be presented as part of a summary of the details; however, do not derive equations—if the audience is interested, they will either read your report or ask you afterward.
The most common typeface used for mathematical equations are Times New Roman and Computer Modern (and its derivatives). These are both typefaces with serifs and a high degree of contrast. While neither of these characteristics is appropriate for viewing text at a distance, their use is almost universal.
In general, a typeface is comprised of a family of related fonts which, most basically, are differentiated by the presence or absence of emphases such as boldface and italics. We will use the terms regular, italic, bold, and bold-italic to describe the resulting fonts. Common usage has lead to the following rules for how various mathematical elements are displayed:
| Element | Font | Example |
|---|---|---|
| Numbers | regular | 1, −5, 3.141592654 |
| Variables | italic | x y z |
| Units | regular | 3 m, n km/h |
| Functions | regular | f(x), sin(t) |
| Matrices and Vectors | bold | Ax = b |
Combinations should be appropriate: ∇f(x) defines the gradient (a vector) of a scalar function f which has a vector x as an argument whereas the Laplacian would be denoted as ∇2f(x).
Unfortunately, this requires its own heading: if you must use the multiplication symbol (for example, in a cross product), do not use a 'x' or 'x', but rather, use the symbol × (×). The appearance of 3 x f(x) will be viewed as confusing and unprofessional. Do not use an Arial "x", either, as the bars are not perpendicular to each other and the ends of the bars are cut horizontally, as is shown in Figure 2.
Figure 2. An Arial 'x', a Times New Roman 'x', and a multiplication symbol.
Simple mathematical equations can be created in PowerPoint by writing the equation and changing the font appropriately and following a few rules:
For more complex mathematical expressions, use the Microsoft Equation Editor: select Insert→Object... and from the list select Microsoft Equation 3.0. This puts you into a mathematics editor which allows you to create very complex expressions with relative ease. To give an example, Figure 3 demonstrates how the approximation of the sum by using an integral may be generated using Microsoft Equation 3.0.
Figure 3. Creating an expression using Microsoft Equation 3.0.
The editor includes numerous palettes which include both mathematical symbols and more complex objects and groupings. For example, by selecting parentheses around an object (from the lower-left palette), the height of the parentheses will dynamically change to match the largest vertical object contained within the parentheses.