About Me

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 Associate 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!

Dynamical Systems

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.

Mathematics Education

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.

Publications

• • Andrews-Larson, C.
  • Siefken, J.
  • Simha, R.
  Report on a US-Canadian Faculty Survey on Undergraduate Linear Algebra: Could Linear Algebra Be an Alternate First Collegiate Math Course? Notices of the AMS, May 2022
• • Siefken, J.
  Onboarding Instructors into an Active Learning Class MAA Math Values Blog, October 2021
• • Siefken, J.
  Linear Algebra: MAT223 Workbook introductory linear algebra textbook designed for active learning
• • Gonschorowski, J. S.
  • Quas, A.
  • Siefken, J.
  Support Stability of Maximizing Measures for Shifts of Finite Type Journal of Ergodic Theory and Dynamical Systems, October 2019
• • Calkins, S.
  • Grannan, S.
  • Siefken, J.
  Using Peer-Assisted Reflection in Math to Foster Critical Thinking and Communication Skills PRIMUS, June 2019
• • Evans, L.
  • Siefken, J.
  • et al.
  Multivariable Calculus in-progress multivariable calculus textbook
• • Siefken, J.
  Registration Delay and Student Performance Journal of the Scholarship of Teaching and Learning, April 2017
• • Siefken, J.
  A Minimal Subsystem of the Kari-Culik Tilings Journal of Ergodic Theory and Dynamical Systems, July 2016
• • Siefken, J.
  A Minimal Subsystem of the Kari-Culik Tilings (2015) PhD Thesis.
• • Siefken, J.
  The Gas Station Problem Notes from the Margin, Volume VIII, 2014
• • Epple, D.
  • Siefken, J.
  Collapse a Sturmian and Fibonacci Game The American Math Monthly
• • Quas, A.
  • Siefken, J.
  Ergodic Optimization of Super-continuous Functions in the Shift Journal of Ergodic Theory and Dynamical Systems, Volume 32, Issue 6, December 2012, pp 2071–2082.
• • Siefken, J.
  Ergodic Optimization in the Shift (2010) Masters Thesis.
• • Brugger, M.
  • Burton, R.
  • Siefken, J.
  The LA Book (2008) Honors Thesis.

Resources

I've seen some incredible things throughout my travels, and I've collected a few.

Teaching Resources

• The Mathematical Association of America's Instructional Practices Guide has over 100 pages of teaching tips. It is written so that sections can be read in isolation—you can flip through it randomly. Here is a direct link to the pdf.
• The TIMES project's Inquiry Oriented Linear Algebra website
• The IMAGEmath project introduces real analysis and metric spaces via image denoising, differential equations through heat diffusion, and linear algebra through x-ray tomography.
• The Primary Historical Sources project aims to provide excerpts from primary historical sources that are suitable for use in introductory mathematics classes.

Software

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.

• PreTeXt React

  PreTeXt React is a ReactJS frontend to the PreTeXt project, which enables authors to specify textbook source in XML and have it easily converted for display on the web, in print, in braille, etc..

  PreTeXt React will eventually become the default PreTeXt frontend for the HTML view.

• Canvas Quiz Stats

  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

  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.

• UToronto Toolkit (UTK)

  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

• Latex Beautifier

  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

  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

  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

  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.

• Scantron to Spreadsheet

  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.

• Sturmian Sequence Visualizer

  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!

Courses

I am on sabbatical for the 2023/2024 academic year.

Previous Courses

• Calculus with Proofs 2022/2023, MAT137
• Chaos, Dynamics, and Fractals Spring 2020, 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.

• Linear Algebra Fall 2018, Spring 2019, Fall 2019, Spring 2020, Fall 2020, Spring 2021, Fall 2021, Spring 2022, Fall 2022, Spring 2023, MAT223

  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.

• Linear Algebra Fall 2017, Spring 2018, MAT223
• Calculus I Fall 2017, MAT135
• Linear Algebra for ISP Spring 2017, Math 281-3

  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.

• Differential Equations for ISP Winter 2017, Math 281-2

  Math 281-2 is the second term in a year-long math sequence for students in Northwestern's Integrated Sciences Program.

• Multivariable Calculus Winter 2017, Math 230

  Math 230 is a one-term Multivariable calculus class covering differentiation but not integration.

• Multi-variable Calculus for ISP Fall 2016, Math 281-1

  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.

• Linear Algebra Fall 2016, Math 240

  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.

• Multivariable Calculus Spring 2016, Math 230

  Math 230 is a one-term Multivariable calculus class covering differentiation but not integration.

• Linear Algebra for ISP Spring 2016, Math 281-3

  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.

• Probability and Stochastic Processes Winter 2016, Math 310-2

  Math 310-2 is the second term in the introductory probability sequence at Northwestern University. You can find my notes here.

• Differential Equations for ISP Winter 2016, Math 281-2

  Math 281-2 is the second term in a year-long math sequence for students in Northwestern's Integrated Sciences Program.

• Multi-variable Calculus for ISP Fall 2015, Math 281-1

  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.

• Linear Algebra Spring 2015, Math 211

  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 Introduction to Linear Algebra for Science and Engineering by Norman and Wolczuk. These worksheets are available here.

  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.

• Linear Algebra for Engineers Fall 2013, Math 110

  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 Linear Algebra: A Modern Introduction by David Poole. These worksheets are available here.

• Calculus I Summer 2012, Math 100

  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 Calculus Early Transcendentals by Edwards and Penny. I also created conceptual clicker questions for use during class. A sample can be found here.

• Linear Algebra Summer 2011, Math 211

  A traditional lecture, nothing special here.

Contact

You may contact me by mailing siefkenj at math.toronto.edu