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David Semitekol

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Where do you use math in your profession?

One of the most difficult challenges that math teachers face today is motivating their students. This becomes more difficult when faced with the all famous question: "What am I going to use this for?"

Help me with some real world examples of modern day math. Please let me know your profession and what type of math you use to share with our students.

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Thank you everyone so much for the contributions! They are great and I wasn't expecting such a turn out. My goal is to gain enough examples and to use them at the start of each lecture. I'm hoping that these examples in the beginning of class will spark the student's interest for the reaming of the lecture and to show that that we really do use math.

There is a difference between having to learn something and wanting to learn something. When we have to learn it we just try to get through it. When we want to learn it, this is when we make breakthroughs. Stimulate the interest in students so that they want to learn math and we increase our probability in someone discovering the next breakthrough.

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    Feb 14 2012: Here are some examples:

    * Fourier analysis of waves: Jean Baptiste Fourier discovered that any repeating waveform is mathematically equivalent to a series of sinusoids (sine and cosine waves) added together at different amplitudes, phase shifts, and harmonic (integer-multiple) frequencies. When you look at a graphical equailizer on a stereo system and see the individual bargraphs showing how much of each frequency comprises the sound, you are seeing the results of a Fourier transform function applied to that wave. Fourier transforms work for *all* waves, not just pressure waves (sound). In machine vibration analysis, for example, technicians and engineers use Fourier tranforms to decompose a vibration waveform into its different harmonic frequencies, those decomposed signals holding clues about the health of the machine.

    * Charles Proteus Steinmetz applied the notation of imaginary (vs. real) numbers to the solution of alternating-current electric circuits near the turn of the last century. His mathematical contribution to the then most empirical subject of electrical engineering revolutionized the field. As it turns out, complex numbers work wonderfully well to represent electrical signals (there are those waves again!) changing in time. Technicians and engineers in the electrical industries use Steinmetz's principles continually to calculate voltage and current quantities in power systems.

    * The calculus principles of integration and differentiation are widely used in automatic control systems. Differentiation is used to calculate the rapidity of some variable's change, for the purpose of damping rapid changes. Integral is used to calculate how much control action is necessary to bring a variable back to its "setpoint" (target value), by integrating the error (variable-setpoint) over time. Technicians and engineers "tune" control systems by adjusting the coefficient multipliers of the differentiation and integration functions to achieve stable control.

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