Category Archives: Math Thoughts

Succeeding in First-Year Calculus: My guides to MAT135 and MAT137

Last year I wrote a guide for students taking the University of Toronto’s big (2000 student) first year calculus class MAT135. It was so successful that I wrote another guide to MAT137, the more specialized first year calculus class. Let me share them with you: “How to Succeed in MAT135.” “How to Succeed in MAT137.” […]

Posted in Math Thoughts | Tagged , , , , , , | Comments closed

Delta-Epsilon Magic

In my second year of undergrad I had a formative experience with Delta-Epsilon proofs that stuck with me for a long time. Last week I was able to provide a similar experience for some first year calculus students.

Also posted in Full Article | Tagged , , , , , | Comments closed

Van der Waerden’s Theorem is false for $\omega_1$

One of my main research problems involves something I think is related to arithmetic progressions in $\Z$. After learning a nice proof of Van der Waerden’s Theorem, and sharing it with colleagues, Daniel Soukup asked a nice question about Van der Waerden’s Theorem on $\omega_1$. We answered it, and the example was sufficiently nice that […]

Posted in Math Thoughts | Tagged , , , , , | Comments closed

Secret Santa 4: The Surprise

After a long hiatus (7 months!) I am finally back to writing. This week I revisited an old problem that Sam Coskey told me a couple of years ago. Some of you will remember this “Secret Santa problem”, which I wrote about before. The problem is: Sam’s Problem. Is it possible for two people to […]

Posted in Math Thoughts | Tagged , , , | Comments closed

Math Anxiety

A study was done at the University of Chicago looking at whether math can cause physical pain. (The rather laughable title of the article is “Doing Math Really Does Make Your Head Hurt, Says Science”. Here‘s the actual published study.) The idea is that for people with high levels of math anxiety, just knowing that […]

Posted in Math Thoughts | Tagged , | Comments closed

Perceptions about Mathematics

“When someone asks you what you do as a mathematician, they take the most advanced training they have in mathematics and assume that you do a much harder version of that.” This is a paraphrase of something I will attribute to Leo Goldmakher. The idea is that if someone has only ever taken high-school math, […]

Posted in Math Thoughts | Tagged , | Comments closed

Is Algebra Necessary? – Andrew Hacker

Today on The Sunday Edition, on CBC Radio 1, host Michael Enright interviewed Andrew Hacker, about his controversial views on mathematics education. Basically, he thinks that demanding that all high school students master Algebra is “an onerous stumbling block for all kinds of students”. Listening to the interview this morning made me angry. I don’t […]

Posted in Math Thoughts | Tagged , , | Comments closed

Every Day I’m Simulating

  Have you ever tried to explain/inflict forcing on your non-set theory friends? Let me tell you it is hard. In my ongoing effort to try to explain everything to everyone here is my attempt at explaining the idea of forcing, without explaining forcing. First, I direct you to this post which explains the simulation […]

Posted in Math Thoughts | Tagged , , | Comments closed