**Problem of the Week**

**Number Theory Conf.**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

people:grads:kelley:teaching_portfolio

Most of what follows is a collection of quizzes that I wrote for my classes. While they are not perfect, there are parts of them that I think worked well. Note that the course coordinator wrote the tests and chose most of the homework (which was online and graded automatically). Occasionally, I also assigned additional handwritten homework.

In the likely event that the following list is too long, I recommend looking at quizzes 1 and 2 (and a couple other random quizzes). Note that “rref” stands for reduced row echelon form.

Quiz 1, Quiz 2, Quiz 3, Quiz 4, Quiz 5, Quiz 6, Quiz 7, Quiz 8, Quiz 9, Quiz 11, Quiz 14, Quiz 15

Notation for quizzes 9, 11, and 15:

- $K_X(u)$ is the coordinate vector of $u$ written in terms of basis $X$. For example, if $X = \{v_1, v_2, v_3\}$ and $u = 4v_1 - 5v_3$, then $K_X(u) = [4, 0, -5]$ (written as a column vector).
- ${}_Y T_X$ is the matrix of the linear transformation $T$ where the input is written in terms of basis $X$ and the output is written in terms of basis $Y$. Here is what I mean: Let $T: U \to V$ be a linear transformation. Suppose $X$ and $Y$ are bases of $U$ and $V$ respectively. Then ${}_Y T_X$ is the unique matrix with the property that for all $u \in U$, we have ${}_Y T_X K_X(u) = K_Y(T(u))$.

Here is the programming project that the class did.

*My reasons for the assignment:* For applications, understanding definite integrals is crucial. Also, some of them can only be calculated by use of a computer (or tables/tedious calculations). Hence, I wanted to make sure that my students (a) understood definite integrals, and (b) were comfortable with the fact that a computer can easily compute certain definite integrals. Also, one thing I like about group work is that more challenging assignments can be tackled by a group than by an individual. Further, it is important to learn how to work well on a team.

*Notes on the challenge problems:* The first challenge problem at the end was *not* very well thought out, especially the “hint.” Certainly there is a much better way of obtaining upper and lower bounds than the method I had in mind. One thing I like about the third challenge problem is that a popular online computational engine could not compute it, saying “Standard computation time exceeded…”

Quiz 2, Quiz 4, Quiz 7, Quiz 11

I try to include as many things as is reasonable in a quiz. For example, problem 4(b) in quiz 2 tests several basic properties of logarithms. Normally, each problem has fewer ingredients, but a somewhat tricky logarithms question seemed appropriate for a calculus class.

A more typical quiz where I try to include a lot is quiz 4. In lectures, I try to emphasize the different growth rates of different functions. Hence, I want my students to eventually be able to efficiently “figure out” problems 3 and 4 (from quiz 4). In those problems, the lesson is that exponential functions grow much faster than polynomials. Similarly, polynomials grow much faster than logarithms.

The bonus problems at the end of quiz 12 begin with the paragraph preceding problem 5. Also, on quiz 10 problem 1, I gave full credit if they wrote a definition that works for continuous functions $f$. (I have since specifically added that hypothesis in the problem.)

At the beginning of the semester, I gave this review quiz (for no points).

Also, feel free to browse my previous courses. The quiz study guides are at the “Old Announcements.” Some were detailed, and some weren't.

Here are some of my student evaluations.

people/grads/kelley/teaching_portfolio.txt · Last modified: 2017/02/04 19:52 by kelley

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