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Let me start by saying that there isn't necessarily a very good selection of answers to this question.

I am teaching some very basic mathematics (see below for module content) to a group of Computing Students who will not fail this class. I am trying to teach the material as well as I can. For example, all of our arithmetic of fractions will be born out of the definition that $\frac{1}{n}$ is a number that when multiplied by $n\neq 0$ gives one... and one is the number that when multiplied by any number gives the same number: $1\times m=m$.

So I am happy with that side of things.

  • I am just wondering is there any point in adding in applications to computing (specifically computing)? Are there any good examples?

I do not have a computing background and am happy explaining to them why they should be adept at all of this stuff.

Three good examples I have are units of data for conversion of units, a crude way of drawing lines on a pixel screen for coordinate geometry and Moore's Law for curve fitting.

Module Outline

The Fundamentals of Arithmetic with Applications --- The arithmetic of fractions. Decimal notation and calculations. Instruction on how to use a calculator. Ratio and proportion. Percentages. Tax calculations, simple and compound interest. Mensuration to include problems involving basic trigonometry. Approximation, error estimation, absolute, relative and relative percentage error. The calculation of statistical measures of location and dispersion to include arithmetic mean, median, mode, range, quartiles and standard deviation.

Basic Algebra --- The laws of algebra expressed literally and illustrated both numerically and geometrically. Algebraic manipulation and simplification to include the factorisation of reducible quadratics. Transposition of formulae. Function notation with particular emphasis on functions of one variable.

Indices and Logarithms --- Indices with a discussion of scientific notation and orders of magnitude. Conversion of units. Logarithms and their use in the solution of indicial (exponential) equations. Discussion of the number e and natural logarithms.

Graphs --- Graphs of quantities which are in direction proportion and indirect proportion. Graphs of simple linear, exponential and logarithmic functions. Reduction of non-linear relations to linear form to allow for the estimation of parameters.

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  • $\begingroup$ Your examples make computing much more interesting and relevant than it would otherwise be (at least to non-professional" types). In this regard, your course might be a lot more memorable than most other courses in the same field, insofar as people might remember your examples five, ten, or more years later. Keep up the good work. $\endgroup$ – Tom Au Aug 29 '14 at 13:54
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Since you mentioned Moore's Law...

You could make a nice unit on exponential explosion. You could tell the story of the Persian prince and grains of wheat, nicely described in this Wikipedia page. Even better, look at Chapter 2 ("The Persian Chessboard") of Carl Sagan's book,

Sagan, Carl. Billions & Billions: Thoughts on Life and Death at the Brink of the Millennium. Random House LLC, 2011.

You can find PDFs of the book on the web, e.g., here.

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  • $\begingroup$ Thank you very much for these suggestions. $\endgroup$ – JP McCarthy Sep 3 '14 at 7:47
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You might note that some systems of measurement are mixed-base number systems, and that more complicated unit conversion is essentially changing between mixed bases. For example, converting a quantity expressed in meters and centimeters can be expressed in a sum of yards and inches, or even yards, feet, and inches. Currency conversion to currencies not on a decimal system is challenging until one adopts a general formula for conversion of mixed base representations. Writing a general purpose algorithm that converts between two mixed base systems can then be applied to these and other situations.

Gerhard "Making Simple What's Mixed Up" Paseman, 2015.01.29

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  • $\begingroup$ Thank you for this suggestion. J.P. "Often Amused by your Monikers" McCarthy $\endgroup$ – JP McCarthy Jan 29 '15 at 19:59

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