# Tien Chih

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## Tien Chih, PhD

I am an Assistant Professor of Mathematics at Montana State University-Billings.

### Mathematics Professor.

• Phone: 406 629 2939
• Email:
• Office: LA 838

Montana State University-Billings
1500 University Drive
Billings, Montana, 59101, USA

### Education

• Ph.D in Mathematics, University of Montana, 2014
• M.A. in Mathematics, University of Montana, 2009
• B.A. in Mathematics, UH Hilo, 2007

### Personal

I grew up in Hilo, Hawaii where I graduated from Hilo High School. After briefly attending college in Chicago, I took a break from school and worked various odd jobs few years. Afterwards, I returned to Hilo where I attended the University of Hawaii at Hilo. I wasn't sure what I wanted to do with my life, but after a life changing class with Dr. Ramon Figueroa-Centeno, I decided that I wanted to be a Mathematician, and that I wanted to help other students find their love for Mathematics! After that I attended the University of Montana for graduate school where I earned a Doctorate in Mathematics. I held the position of Assistant Professor at Newberry College in South Carolina for three years before returning to Montana and joining the faculty of MSUB in 2017.

I enjoy cooking, gardening, biking, camping and spending time with my family!

## Curriculum Vitae

Here is a link to my full curriculum vitae

### Highlights and Honors

• 2022 Faculty Excellence Award. Award for excellence in teaching, research and service.
• 2021 Walter and Charlotte Pippenger Excellence in Innovation Award: Award for innovation in teaching and enhancing the student experience. Awarded for incorporating service learning for pre-service teachers through facilitations of Math Circles.
• 2021 Winston & Helen Cox Fellowship Award: Award for outstanding pre-tenure faculty member.
• 2020-2021 Center for Undergraduate Research in Mathematics Minigrant: Supervised a team of undergraduate scholars who produced results on automorphisms of graphs and x-homotopy.
• 2019 Montana Teaching Regents Scholar: Led a faculty cohort to develop experiential learning activities and other High Impact Practices in first year courses.
• 2018-Present Dolciani Mathematics Enhancement Grant: Supports a student Math Circle in Billings, MT for grades 4-8.

### Selected Invited Presentations

• "Report on CURM project: Homotopy of Graphs" Joint Mathematics Meetings, invited speaker, 2022.
• "Supporting Inquiry in Remote Teaching: Challenges depend on class size/format" CSU MathCouncil Colloquia: COMMIT-CaN, invited speaker, 2021.
• "IBL Practices for Online Classes" Greater Upstate NY IBL Consortium, invited panelist, 2020.
• "Homotopy in the Category of Graphs" Department of Mathematical Sciences Colloquium Series at theUniversity of Montana, invited speaker, 2019.

### Selected Publications

• "Circle on The Road" A workshop for new and experienced Math Circle leaders, co-organizer, 2021.
• "Talk Math With Your Friends" An online colloquium presenting fun, entry-level talks, co-organizer, 2020-present.
• "Journal of Math Circles" An open access, peer-reviewed journal publishing the scholarship of math outreach, associate editor, 2020-present.

## Teaching

"The “freedoms of mathematics” include the freedom to solve problems, to explore new directions, to open one’s imagination, and to land in a welcoming community." - Francis Su

I was fortunate that I returned to school to rediscover my love and passion for mathematics. This was in large part to the excellent faculty at UH Hilo, and in particular, my mentor Dr. Ramon Figueroa-Centeno. It was then that I made the decision to become a mathematician, and in particular, to become a teacher-scholar who helped other students redefine their relationship with mathematics. Unfortunately, math is not the most beloved subject amongst students, and so a lot of care and effort is needed to help them reforge a new positive relationship with the subject. Students frequently are turned off by math because they see themselves as "not a math person", or they don't see the relevance of mathematics to themselves. I now focus on student centered pedagogy, giving them ownership of their own learning. I center the view that everyone can grow to love, appreciate and excel at mathematics.

## Research

"I like crossing the imaginary boundaries people set up between different fields—it's very refreshing. There are lots of tools, and you don't know which one would work. It's about being optimistic and trying to connect things."-Maryam Mirzakhani

My current research focuses on taking ideas from classical homotopy in topology and extending them to graphs via $$\times$$-homotopy. One could just consider the homotopy of graphs as simplicial spaces, but this isn't very interesting! Instead we define homotopy categorically, with looped paths taking the place of the unit interval, and graph homomorphisms taking the place of continuous functions. In our first paper, my collaborator Dr. Laura Scull and I gave a concrete description on how the "continuous" motions of classical homotopy translate to "discrete" motions in graphs. The gif below depicts a homotopy between two functions.

One may suspect that results about classical homotopy would translate readily, but these are really very different settings. For example the product of two connected spaces is always connected, but the product of connected graphs need not be connected! So it isn't obvious that all classical homotopy results have analogues in $$\times$$-homotopy, and it's not clear how these analogues, when they exist, differ. This makes this an interesting line of research! We have several papers developing $$\times$$-homotopy, with more planned and on the way!

Our line of work is particularly suited for undergraduate scholars: the objects and functions are finite and concrete, the area is new so it is easy to pick unexplored topics, and while it is new research, one can look to established results in classical homotopy for inspiration and guidance.

Dr. Scull and I applied for and the Center for Undergraduate Research in Mathematics (CURM) mini-grant, which we recieved for the 20-21 academic year. I supervised a team of student scholars who examined the homotopies of automorphisms & endomorphisms of graphs. They gave a talk on their work in the Talk Math With Your Friends online seminar, and wrote a jupyter notebook visualizing their computations in an interactive way!

If you're interested in graphs, groups, shapes, enumeration, coding, or just playing around in a cool new setting, I would love to talk with you about collaboration! Please contact me if you are interested.

## Math Circle

"Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding." –William Paul Thurston

I am the founder of the MSU-Billings Math Circle, which as been ongoing for 4 years. We're happily supported by the Mathematical Association of America DMEG grant. We've had close to 100 students attend over the years, even through the pandemic. This program is free, and open to all students grades 4-8, teachers and parents. We play games, explore activities, work on puzzles, and work together to discover new and wonderful mathematics! We recruit MSUB students including pre-service teachers, for which I've recieved the Universities Pippenger Awars.

To expand the reach of Math Circles, I've become involved in the leadership and organization of Math Circles. I serve as the associate editor of the Journal of Math Circles, program coordinator of the MCTS SIGMAA, and was a co-organizer for the 2021 Circle on the Road workshop.