2019 Fall – Journey to the west: from Singapore to Canada

2019Fall/BMTH100/120 Mathematics of Finance, Humber College

After teaching part-time at Seneca College for almost three years, I decided it’s time to move on due to the commute: we moved to where UTM is, and I find it very challenging to travel to Seneca on a regular basis. Usually, one-way travel takes me at least one hour, and being stuck in traffic along 401 makes it worse than it already is. I did enjoy my teaching at Seneca very much, and my teaching there reminds me a lot of my previous institution in Singapore: Singapore Polytechnic. Even the structure of the buildings on Newnham campus is almost the same with SP: all the buildings are connected through bridges and tunnels. My guess is at both places, the building structure is to accommodate the harsh weather: Canada’s winter is too cold for people to walk outdoor; while Singapore is too hot to walk outside.

I’m fortunate to start teaching at Humber College right away: this semester I’m teaching a course that I used to teach: Mathematics of Finance. For those who are interested in taking a look at what we do, here are the slides. A major learning objective for this course is to teach students how to understand a real-life scenario/story and translate it into mathematical language. After that the can use a financial calculator to find the solutions. Most of my students agree that this course, surprisingly, is not so much about mathematics, but rather about comprehending the stories.

2019Fall/MAT135: Differential Calculus

If you are currently taking this course with me, you can find all the course slides here: MAT135 Differential Calculus

The clicker questions we use in class can be found here:

Below are a few GeoGebra activities that we did in class.

Even/Odd functions: In this app, students can visualize even/odd functions and explore the symmetries embedded in these functions.
Function transformations: In this app, students can explore how different types of function transformations affect the graph of a function.
Inverse trigonometric functions: In this app, students can see how the graphs of inverse sine/cosine/tangent are related to the original functions and see the reason for the choice of domains of these functions geometrically.
Limits of functions: In this app, students can explore the limits to two given functions: $f(x) = \frac{x^2-1}{x-1}$ and $f(x) = \frac{x-1}{x^2-1}$ , and visualize removable discontinuity, vertical asymptote and horizontal asymptote.
The derivative of a Function as Slope of Tangent Line: In this app, students can explore what is a tangent line to a curve at a point, and how the slope of the tangent lines changes when a point is travelling along a given curve.
Derivative as a function: Students get to explore what happens to the derivative function based on a given one and they are related to each other geometrically. They can learn how to identify which curve is $f(x)$ and which one is $f^\prime(x)$ .

2019Fall/MAT102: Introduction to Mathematical Proofs

This is not my first time teaching this course, but the level of excitement and nervousness doesn’t seem to go down at all at the beginning of this semester. I’m fortunate to have a whole class of students who engage fully during the lectures so far and make the teaching so enjoyable.

If you’re a current student enrolling in this course, or just want to take a look at what’s happening in class, you can find all the slides here:

https://drive.google.com/open?id=1i2ltPgAfRQs6rf2FSY0yRMKXDvmwzSUs

This week we were talking about logic symbols and how quantifiers work, and how by changing the order of quantifies, we can tell completely different stories. Here’s one example we did in class:

$(\forall x \in \mathbb R)(\exists y \in \mathbb R)(y \geq x)$

$(\exists y \in \mathbb R) (\forall x \in \mathbb R) (y \geq x)$

While the first statement is saying “for any real number x, we can always find a y such that $y \geq x$ ” which is a true statement, because we can simply make $y =x$ , the second statement is saying “we can find a real number y which is greater than or equal to all real numbers” which is a false statement. This is equivalent to say real numbers have an upper bound.

Can you tell the difference here?