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
\(R(\alpha, N)\):