My name is Jason Siefken, and I am a professional mathematician who focuses on dynamical systems and mathematics education. I earned my PhD from the University of Victoria in 2015, spent some time as a postdoc at Northwestern University, and am now an Assistant Professor, Teaching Stream at the University of Toronto.
When I'm not coming up with new ways to push the boundaries of understanding, I enjoy hiking, rock climbing, computer programming, and fiddling with typography. I'm also a huge fan of cooking and love figuring out how to cook with ingredients I've never heard of before!
My mathematical research focuses on dynamical systems and ergodic theory. At its most general, a dynamical system is a set and a transformation that moves around points in the set—for example, think of the air molecules on earth (as set) and the wind as it blows them around (as a transformation).
The idea of a dynamical system is very general. It's too general to actually be useful, so mathematicians don't study dynamical systems in general. They study dynamical systems with specific properties. For example, a dynamical system is called mixing if any two points eventually end up close to each other. They may get far apart after that, but at some point they must get close.
Once properties such as mixing (or a very special property called ergodicity) get added to a dynamical system, suddenly you can start proving things about them. That's what I do.
My ultimate goal is to make the world a better place. Right now I'm working on that by teaching people (and sometimes computers) how to use mathematics to aid their thinking. This is hard! Though mathematics can be fun, it doesn't come naturally to most of us—unlike your tendency to pick up your mother tongue, you don't inevitably stumble into the conclusion that when approaching a problem the first thing you should do is write down everything you know. No, this is one of the many mathematical habits of mind that only comes through training.
If you want to see more about my philosophy of teaching, you can check out my Teaching Statement. Briefly summarized, I believe you learn by doing, being challenged, and forcing your brain to rewire itself. I am a big proponent of Active Learning, Inquiry Based Learning, and the Flipped Classroom (the list could go on and on). I am a 2016 MAA Project NeXT Fellow (go green dots!) and a TIMES Linear Algebra Fellow.
I've seen some incredible things throughout my travels, and I've collected a few.
I always strive to make my life (as well as those around me) easier by harnessing the power of the analytic engine to do the day's menial tasks. You can find a list of most of my projects on my Github page. Projects of particular relevance I've listed below.
Canvas Quiz Stats is a Greasemonkey extension that allows you to download per-student answers and quiz versions to randomized Canvas quizzes. It will also display all quiz questions and answers on a single page (overcoming Canvas's 25 question limit).
It currently has several URLs hardcoded to U of T's Canvas implementation, but should be easy to change.
TAPP is a program for sending TA contracts to TAs. It allows TAs to view, accept, and reject their offers online. This version of TAPP is a complete rewrite of the older TAPP-CP.
A collection of tools for course coordinators at the University of Toronto. UTK includes tools to help schedule TAs, instructor meetings, divide students into midterm rooms, etc.. github page
Reformat your latex code so that it looks nicer in your editor, and with proper indentation! (This is very much a work in progress.) github page
CourseMapper is a tool for curriculum design and planning. Developed in coordination with Teresa Dawson of the University of Victoria's Learning and Teaching Centre, CourseMapper is a web-based program with complete knowledge of a university's course offerings as well as course prerequsites. With CourseMapper, you may plan out a two to four year curriculum and be presented with a visual representation of the program in a flow-chart-like form. CourseMapper is also open-source software. An unbranded version suitable for tailoring to another university's course offerings can be found on my github page.
Graphit is a web interface for quickly creating and downloading as pdfs graphs of mathematical functions. The graphs are highly customizable, can be inserted into LaTeX documents, and best of all, the code used to generate them is embedded in each saved graph, so editing again later is easy!
Questionmaker is a little helper that outputs LaTeX/Beamer code for multiple choice clicker-style questions. It will autogenerate code for several layouts and will show you a nice preview of your question.
UVic scantron test results are emailed to you space-separated as the body of an email! This is not conducive to merging with your grading spreadsheet, which is where Scantron to Spreadsheet comes in. Given a list of IDs and the test summary data that was emailed to you, Scantron to Spreadsheet will merge the two producing a sorted list in the same order as your grade spreadsheet, suitable for copy-and-pasting.
I work with Sturmian sequences in my research. This webpage gives some properties of Sturmian sequences and provides some visualizations. It also includes a continued fraction calculator!
Linear Algebra Fall 2022, Spring 2023, MAT223
Calculus! Fall 2022, Spring 2023, MAT137
Chaos, Dynamics, and Fractals Spring 2023, MAT335
A third-year course on dynamical systems with an emphasis on (1) exploration of different type of dynamical systems and their behavior, (2) programming to simulate dynamical system, and (3) writing essays about technical topics for a lay audience.
Homeworks for this class were a mix of traditional written proofs and Python programming assignments in a scaffolded jupyter notebook. Homeworks are available here as well as the course notes.
As course coordinator for MAT223, redesigned the course after consulting with other departments about their needs. The course was conducted using a Think, Pair Share module with in-class questions designed by me and taken from the Inquiry Oriented Linear Algebra (IOLA) project. Resources are available here.
Math 281-3 is the third term in a year-long math sequence for students in Northwestern's Integrated Sciences Program. This course was conduced in an inquiry-oriented style using guided worksheets and resources from the Inquiry Oriented Linear Algebra (IOLA) project. Resources are available here.
Math 281-2 is the second term in a year-long math sequence for students in Northwestern's Integrated Sciences Program.
Math 230 is a one-term Multivariable calculus class covering differentiation but not integration.
Math 281-1 is the first term in a year-long math sequence for students in Northwestern's Integrated Sciences Program. Essentially, this course may be thought of as an honors section of Multi-variable calculus. Again, I used an inquiry-based approach based on guided worksheets available here.
Math 240 is a one-term linear algebra course. This class was conducted using a mix of the Inquiry Oriented Linear Algebra materials as worksheets I developed for previous linear algebra courses. This course also included problemsets based on the Peer-Assisted Reflection (PAR) model of Daniel Reinholz.
Math 230 is a one-term Multivariable calculus class covering differentiation but not integration.
Math 281-3 is the third term in a year-long math sequence for students in Northwestern's Integrated Sciences Program. This course was conduced in an inquiry-based style using guided worksheets available here.
Math 310-2 is the second term in the introductory probability sequence at Northwestern University. You can find my notes here.
Math 281-2 is the second term in a year-long math sequence for students in Northwestern's Integrated Sciences Program.
Math 281-1 is the first term in a year-long math sequence for students in Northwestern's Integrated Sciences Program. Essentially, this course may be thought of as an honors section of Multi-variable calculus. Again, I used an inquiry-based approach based on guided worksheets available here.
In Math 211, I used an inquiry-based approach to teaching
Linear Algebra. I improved worksheets that I'd previously used
for Math 110 and modified them to fit with the book
In this course I also emphasized communication. A prescribed half of the assignments were to be typed. The problems were less computational and more idea-based and a special emphasis was put on communication, including proper grammar, correct logical sequencing, and statements of all the needed definitions and theorems.
In Math 110, I used an inquiry-based approach to teaching
Linear Algebra. I constructed guided worksheets covering
the a first-semester course
following the textbook
In Math 100, I taught using a fully flipped classroom
in the style of Eric Mazur. I created a
Youtube
video playlists that covered each section of the textbook
A traditional lecture, nothing special here.
You may contact me by mailing siefkenj at math.toronto.edu