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MATH 5411 3.00AF (Fall 2016)
Analysis for Teachers
Real analysis is the part of mathematics that includes calculus. Understanding analysis better will add context and depth to one's ability to teach calculus. In particular, there are a large number of interesting topics that one can explore, that rely on ideas from analysis. For example:
- Fractals and fractal dimension
- Chaos and iteration
- Fourier series
- Approximation theory and computer graphics
Beyond real analysis is complex analysis, which is needed if one wants to really understand iteration (eg the Mandelbrot set lives in the complex plane).
It turns out that the standard way we teach calculus is not at all how calculus was discovered. Instead we follow an approach that only evolved in the 19th century, long after calculus had been invented. It is a highly evolved approach, that makes sense only with a great deal of hindsight. No wonder our students often fail to find it natural and intuitive.
The approach we'll take is that of exploration and problem solving. We won't
try to develop a comprehensive body of theory. Rather, we'll pick a number
of elementary-sounding topics or projects from either real or complex analysis,
that lead naturally to a deeper understanding analytic ideas. Sometimes this
will involve analytic arguments and proofs, and sometimes computer
explorations. We'll also try to understand a bit of the history of analysis.
In particular, we'll try to understand what pitfalls mathematicians stumbled
across, that led to the 19th century approach to calculus that we all
Note that in earlier years, Analysis for Teachers was offered as a 6 credit course, but it is now 3 credits.
Basic familiarity with calculus. Some experience coding would be
helpful too. It is not assumed that people have studied undergraduate
M 6-9pm in S525 Ross (changed from Vanier College 114)
By appointment. Just send me an e-mail and I can arrange to be available
either before or after class. Other days of the week are often possible
- 30% Assignments
- 30% Mathematics project - research a mathematics topic based on
analysis. Evaluation will be based on a class presentation, and
a more detailed written report.
- 30% Pedagogy project - reflect on how some aspect of analysis could
be incorporated into your teaching practice, or built into an
enrichment activity. Evaluation will be based on a class presentation
and a written report.
- 10% Class participation