## Philosophy

My goal as a teacher is to affect change in students. I endeavour to be an enthusiastic guide and resource for their learning experience. Practically, this means: treating students with respect; encouraging interaction between myself and students; being prepared and engaged; making myself available for extra help; trying to explain concepts in such a way as to build students' intuition and conceptual understanding; and building students' proficiency through examples, quizzes, and assignments.

I have experience teaching undergraduate courses, running tutorials and labs, and coordinating and delivering outreach activities. I am technically saavy and can create novel and interactive online tools to complement and enhance classroom activities.

## Experience

 Instructor Dept. of Mathemathics, University of North Carolina, Chapel Hill NC. Differential equations and linear algebra (M383; upper level undergraduate class; class size: 35 students). Instructor Dept. of Mathemathical and Statistical Sciences, University of Alberta, Edmonton AB. Calculus II (M101; Winter 2008, class size: 80 students). Calculus I (M100; Fall 2007, class size: 90 students). Calculus II (M101; Fall 2006, class size: 90 students). TA Dept. of Mathemathical and Statistical Sciences, University of Alberta, Edmonton AB. Calculus I, II, and III (M113, M100, M101, M209). Differential Equations I (M201). Help sessions. Class sizes typically 30 students. TA Dept. of Mathemathics and Statistics, University of Calgary, Calgary AB. Calculus I, II, and III (M249, M251, M253, M349); Linear Algebra I (M211, M221); Introduction to Fourier Analysis (M415); Continuous tutorials. Class sizes ranging from 10 to 100 students.

## Outreach

### Integration as a Riemann sum

The Riemann integral given by $\int_a^b f(x) \,dx = \lim_{N \rightarrow \infty} \sum_{i=1}^N f(x_i) \Delta x_i.$ can be approximated by choosing a specific value for $$N$$ and a regular parition for the points $$x_i$$. The left, middle, and right Riemann sums can be succinctly written as $\int_a^b f(x) \,dx \approx R(\alpha, N) \equiv \Delta x \sum_{i=0}^{N-1} f\bigl(a + (i + \alpha) \Delta x\bigr), \qquad \Delta x = (b-a)/N$ for $$\alpha = 0, 0.5,$$ and $$1$$ respectively. For a specific example we consider the function $f(x) = 1 + \frac{8}{10} x^3$ drawn in red and integrate it from -1 to 1. The blue rectangles represent the terms of the (approximate) Riemann sum.

Using the controls below to increase/decrease the number of terms $$N$$ in the Riemann sum, and to alter the $$\alpha$$ parameter used to determine where the function is sampled within each cell, we can see a visual representation of the Riemann sum $$R(\alpha, N)$$ above.

 $$N$$: 10 $$\alpha$$: 0.0 $$R(\alpha, N)$$: