# MATH 5411 3.00AF (Fall 2016)Analysis for Teachers Course Outline

### Description:

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
• Inequalities
• 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 follow nowadays.

Note that in earlier years, Analysis for Teachers was offered as a 6 credit course, but it is now 3 credits.

### Prerequisites:

Basic familiarity with calculus. Some experience coding would be helpful too. It is not assumed that people have studied undergraduate real analysis.

### Course Webpage:

www.math.yorku.ca/~salt/courses/5411f16/5411.html

Tom Salisbury

### Course meetings:

M 6-9pm in S525 Ross (changed from Vanier College 114)

### Office hours:

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 too.