On this page is a summary of my teaching experience with links to relevant blog posts as they appear. I’ve split it up roughly by topic.
| Pre-College Math |
Discrete Math, Non-Major Courses, and Transitional Courses |
| Calculus | Linear Algebra |
| Logic | Other Upper Level Math |
Pre-College Math
I have tutored at both the grade school and high school levels.
Blog posts:
- Fun with the Pythagorean theorem.
Discrete Math, Non-Major Courses, and Transitional Courses
- Dartmouth Math 10, Introductory Statistics: Spring 10
- Dartmouth Math 19/CS 19, Discrete Math for Computer Science: Fall 10
- University of Florida MHF 3202, Sets and Logic: Fall 06
- Notre Dame Math 104, Finite Mathematics: Summer and Fall 01, Spring and Fall 02
Blog posts:
- Many links to resources for teaching statistics.
- Handouts for writing proofs and using induction.
- Proof traits, kinds, tips, and warnings, as well as examples (good and bad).
- A test question about functions on finite sets, injectivity, and surjectivity (no answer).
- An explanation of reflexivity, symmetry, and transitivity.
- A quiz question about a transitive function (with answer).
- A list of common themes and methods in counting.
- A two-question quiz about counting and probability (no answers).
- A math writing problem about assembly line malfunctions, using probability (partial answer).
- A three-problem quiz about logical implication (no answers).
- Thoughts on mathematical versus natural language and teaching the difference.
- The Excel reference I made for my introductory statistics students.
- Thoughts and a quiz question on presenting risks honestly.
- Regression: a test question about the regression effect (with answer), and warnings about regression and correlation in general.
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Calculus
- Dartmouth Math 8, Calculus II: Fall 07, Winter 08, Fall 08, Fall 11
- Dartmouth Math 12, as Vector Calculus: Winter 06
- Dartmouth Math 12, as Calculus Plus: Fall 08
- Dartmouth Math 13, Vector Calculus: Winter 09 (starting about halfway through)
- Penn State Math 140, Engineering Calc I: Spring 05
- Penn State Math 141, Engineering Calc II: Fall 04
- Notre Dame Math 125, Engineering Calculus I: Spring 04
Blog posts:
- Handouts for various calculus topics. One more handout and some links.
- Comments on limits.
- A visual explanation of the chain rule.
- Related rates, optimization, and telling them apart.
- A lot about equations of lines and planes, though not the equations themselves.
- Parametrization of curves and related topics.
- Enumeration and discussion of techniques of integration.
- Non-power-series series topics: heavy-handed examples (includes sequences), working with factorial, a table and flowchart of series convergence tests, and assorted musings.
- Examples of finding power series via geometric series using integrals and derivatives.
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Linear Algebra
- Dartmouth Math 22, Linear Algebra: Spring 07
- Dartmouth Math 24, Honors Linear Algebra: Spring 06, Winter 12
Blog posts:
- Slides for short presentations of linear algebra applications; slides and other resources for a longer presentation.
- Handouts for writing proofs and using induction. For more on proofs, pop back up to the discrete math section.
- A proof of the equivalence of nonzero determinant and matrix inverse.
- Unusual definitions for potential vector spaces, with which to test your understanding of the axioms (no answers).
- A proof that a vector space with more than one element is infinite.
- Examples of matrices with some combination of diagonalizability or invertibility.
- A list of statements whose proof uses linearity to translate between domain and codomain.
- Slightly ridiculous analogies about linear independence, spanning, and coordinate vectors.
- Miscellaneous comments on vectors.
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Logic
- Dartmouth Math 29, Computability Theory: Spring 07 (as reading course), Spring 09, Spring 11
- Dartmouth Math 39, Logic: Fall 07
- Dartmouth Math 89, Seminar in Logic (Set Theory): Winter 12
- Dartmouth Math 119, Topics in Logic (graduate course): Spring 06
I wrote my own book for computability theory, with two goals: one was to be more like a graduate computability theory book in topics and tone, rather than a computer science book, and the other was to be completely self-contained, as Math 29 has no prerequisites. You can find it at the AMS or on Amazon.
Blog posts:
- For basic logic, pop back up to the discrete math section; the logic and proof category may also be of interest (strong overlap there with linear algebra).
- I compiled links to many Turing machine simulators, though I never used them in class.