# Teresa Downard

### Instructor

### Educational & Professional Experience

- Co-designer of the new math QSR GUR MATH 160 "Mathematics and Art" - Offered every spring!
- Newsletter Editor and Designer for the Special Interest Group on Mathematics and the Arts of the Mathematical Association of America SIGMAA-ARTS
- Regularly exhibit mathematical art in the Bridges Conference and Joint Math Meetings Art Exhibits.
**More info below...**

"Lie Tree" 2013 - A painting about my graduate project on Lie Algebras and Lie Groups - a topic at the intersection of algebra and geometry where we can understand symmetric surfaces by looking at their tangent spaces. Much of the mystery of a Lie group like the cylinder is revealed by the tangent space at the identity, this reminds me of how the lushness, beauty, and essential characteristics of a tree are exhibited by growth from a certain point. This piece features a tulip tree and a selection of Lie subgroups.

"Freehand" 2016 - A drawing about my work on similarity constructions for polygons drawn by hand. All the transformations depend primarily on bilateral symmetry and reflections.

**MATH & ART COURSE DEVELOPMENT**

We developed this class to encourage creative problem solving, to get people thinking in ways they've never thought before, and to make a class that would be super fun to take and teach. Here's the most recent syllabus for the Math and Art Class SyllabusM160.pdf This year I'm going to try to have more engagement and follow up with the homework so I'll be making some changes in that department...

Here is a link to the library guide for the course created by librarian Peter Smith and myself http://libguides.wwu.edu/c.php?g=458139&p=4488460

Dina (who is now at University of Victoria) and I talked at a variety of conferences when we were developing the Math and Art class, culminating in this talk at the Joint Math Meetings in 2015 called "Folding, imagining, and constructing a math and art class." This is the Beamer presentation JMMFoldingConstructMathArtClass.pdf** **and my notes for the talk JMMscrpt.docx

To get feedback on the course and share the accomplishments of the students, I gave a follow-up talk at the Joint Math Meetings 2018 in San Diego called "Problem Solving and Creativity". Here are the slides ProblemSolvingCreativity.pdf, I'll try to post the script soon.

**SIGMAA-ARTS NEWSLETTER**

Here is the 2016 Newsletter I designed for the group of mathematical artists SIGMAA-ARTS Newsletter2016.pdf I wanted to come up with a template for the layout in Latex that used a tessellated background that could change each year, use the MAA logo, and to figure out a design for the title. The title uses the Greek letter capital Sigma and Typographer Caps as an example of things both beautiful and well thought-out. The mini-pages used for text over the background was tricky!

Here is the 2017 Newsletter Newsletter2017.pdf This year I implemented an area where members could share their work and do some self-promotion. The newsletter is also published online at the SIGMAA-ARTS website at http://sigmaa.maa.org/arts/ .

**SIMILARITY FOR DESIGN**

In the last couple years I've been working on applying modern mathematical ideas on similarity to a system for making similar polygons that is useful for artists and designers. Here are some of my materials from the Bridges Conference at the University of Jyväskylä in Finland in 2016:

*Similarity Drawn Freehand* - A paper published in the Bridges Conference Proceedings https://archive.bridgesmathart.org/2016/bridges2016-667.html

My slides for the workshop SimilarityFreehand.pdf and a handout that goes with it if you want to give it a try... Handout.pdf

I've submitted a paper called *Reflections on Similarity* to Leonardo https://www.leonardo.info/about to share the idea with other artists and designers who are interested in mathematics and the sciences.

**DEPARTMENT CONTRIBUTIONS**

I designed and painted this logo for the Math Department facebook page. Some of the design elements include the oak doors to Bond Hall lit up at night, the mountains and the sea that represent where we live, the paths and stairs that represent the journey and progress, Western's colors of blue and white, and if you zoom out you can see the big white "e" that stands for the mathematical constant that you see on the Math Department T-shirts. The font for MATHEMATICS at the top is based on Latex's uppercase calligraphy math font mathcal.

I work with a group of other teachers on curriculum reform in our core classes at Western. Here is our poster PosterMathFocusGroup.pdf from the 2017 Slesnick STEM Education Symposium about the work on Math 112. I designed the layout and art to symbolize student-centered learning that fits a variety of different learning styles.

Here is the poster for an introductory talk My talk for Western's Association of Mathematics (WAM) undergrad math club on similarity constructions.

**ART EXHIBITS**

These are links to some of my mathematical artwork shown at international mathematical art exhibits. My regular (non-math related) artwork is primarily in pen and ink nature drawings and paintings involving portraiture. I actually don't have any examples of my nature drawings because I usually sell those or give them as gifts and don't take pictures. I kind of like them being a temporary or one-time piece of artwork out in the world.

http://gallery.bridgesmathart.org/exhibitions/2012-bridges-conference/tdownard

http://gallery.bridgesmathart.org/exhibitions/2014-joint-mathematics-meetings/teresadownard

http://gallery.bridgesmathart.org/exhibitions/2014-bridges-conference/teresadownard

http://gallery.bridgesmathart.org/exhibitions/2015-joint-mathematics-meetings/teresadownard

http://gallery.bridgesmathart.org/exhibitions/2016-joint-mathematics-meetings/teresadownard

http://gallery.bridgesmathart.org/exhibitions/2016-bridges-conference/teresadownard

http://gallery.bridgesmathart.org/exhibitions/2018-joint-mathematics-meetings/teresadownard

*Leaning Lace *2010

### Research Interests

I study visual problem solving, the applications of mathematics to art and design, and the visualization of abstract mathematical structures found in modern mathematics.

How can mathematical ideas be visualized so they are both beautiful, meaningful, and useful? Can we both create art out of the math and create math out of the art? How can mathematical ideas be communicated and manipulated visually? How do we blend creative and logical thinking?

Lately I've been learning about Projective Geometry and Graphs on Surfaces. I was thinking about similarity and perspective drawing before, and now I'm trying to understand planarity criterion in projective space!

### Biography

As a teacher my goal is to figure out what will enable my students to learn the material well and be successful in the course and long term. I'm constantly revising my curriculum materials and strategies. My favorite thing about teaching is seeing all the different approaches to problems and concepts that students come up with and also writing good problems. I encourage an interactive class where students are trying to figure things out, are talking with each other, and working together outside of class. I tend to focus on the conceptual or the "why" during class and try to use examples that illustrate the key points and common pitfalls. I'm known for my Projects which are outside of class assessments with deep and rewarding problems.

As a person I love the woods, drawing, reading, playing music, knitting, my tea or coffee, spending time with my family, and making stuff by hand.