FOr Students

You can find schedules, syllabi, links, etc. on Moodle.

PatrickJMT on youtube works out examples from algebra, trig, calculus, linear algebra, etc. 

philosophy

Equip students with rigorous tools, problem-solving strategies and technology to reveal mathematics and patterns hidden in their unique lived experiences, empowering them to meaningfully engage with, critically analyze and creatively shape their world.

statement

My teaching philosophy centers on empowerment. I want students to go beyond being able to solve contrived and abstract problems assigned to them from a textbook—I want them to see mathematics as a powerful tool and creative medium to discover and engage with the hidden structures lying underneath just about everything in their lives, from their favorite hobbies to the technology on their smart phones to the invisible forces governing nature, behavior and art. Although the content itself is important, I focus heavily on helping students hone their mathematical thinking skills: being able to question assumptions, construct logical arguments, poke holes in their own or other’s arguments, articulate underlying patterns and structures, and use those structures to gain a deeper understanding of their world. 

To put this into practice requires several steps. First, it’s important to address the preconceived notions and negative emotions surrounding math. I emphasize from the very beginning that learning how to do math is like learning how to play an instrument or a sport—it requires making mistakes in front of others and getting good feedback. It requires trust, not just in me and others to support their bumpy journey to mastery but also in their own abilities. This is baked into the class structure through students working in class on worksheets alone or together, putting their solutions and proofs up on the board for critique during class, and opportunities to redo homework, quizzes and exams after receiving feedback. I also make a point to nurture creativity in different approaches to solving a problem or writing a proof. I try to understand their unique way of thinking and encourage them to pursue their own path as long as it is mathematically correct. This empowers students to believe in themselves, but also to see mathematics as fun, creative and even beautiful when they discover a particularly elegant proof. 

This must start on a foundation—like in art, it helps to learn how to use the tools and study and copy masterpieces before jumping into their own creative endeavors. I strive to give students a good foundation first, using active lecture that alternates between me explaining ideas and students asking questions and applying the concepts on worksheets, with additional questions that probe their understanding in a more nuanced way. We deconstruct famous proofs, examine problem solving strategies and look for possible mistakes with a critical eye. I also show them how to use technology for visualization to further aid their understanding and to move beyond tedious computation. 

Along the way, they see numerous examples of how to apply the mathematics to their everyday lives. In Linear Algebra, this happens at the end every chapter, where they see how to recognize situations with underlying linear structures and apply their learning to solving relevant and interesting problems, from analyzing social networks to solving complex chemical equations to solving puzzles in video games. They begin to see that linear algebra is quite literally everywhere, and can be used in a wide variety of ways. They begin to see it as a versatile tool—a system of linear equations used to find an equilibrium point can also be seen as a matrix equation to transform systems over time. In Geometry, they not only learn about a non-Euclidean geometry called projective geometry, they also see why it was developed in the first place by understanding its deep history and connection to linear perspective drawing. 

At the end of both Linear Algebra and Geometry, I assign projects. They can do whatever they want as long as they apply what they learned in class, and students have been emboldened to go places I would never have thought to go—into their research in quantum chemistry, how to rank Pokemon, and analyzing differences in chord progressions over various periods of music history. I see that they are empowered by the end of the semester to apply their newfound knowledge and skills to their personal interests. When they bring their passions, they not only gain new tools to understand their worlds but enrich the worldviews of the entire class. These projects have sometimes turned into research projects that continued after the end of class funded by my endowed chair budget, resulting in conference presentations, papers submitted for publication and in one situation, an award-winning publication (Carl B. Allendoerfer Award for expository excellence in Mathematics Magazine for “A New Perspective on Finding the Viewpoint”, with SU student Robert Lehr ‘15). I am overjoyed when I see students become so engaged with the material that they want to continue pursuing it beyond the end of the semester.

classes taught

Awards

2026 recipient of the Teaching Award for Tenured Faculty, Southwestern University

2007 recipient of the B.F. Bryant Prize for Excellence in Teaching for Graduate Students in the Department of Mathematics, Vanderbilt University

Nomination for the 2026 Teaching Award:

"I would be honoured to nominate Dr. Futamura for a teaching award for her exceptional dedication to her students. Dr. Futamura has an impressive ability to make challenging material very approachable. When I took her calculus course, I had never even taken a precalculus class and was intimidated by the subject, but her well-structured lessons allowed me to gain an understanding. She uses a variety of teaching approaches, namely group work and discussions, practice problems and online resources. One of the qualities that really sets her apart is that she goes through problems with us, not for us. This kind of teaching encourages us to think critically and shows us how to tackle complex problems. She also uses humor and creative memory techniques to simplify these concepts, making them easy to understand. Beyond her skills as a teacher, Dr. F creates a welcoming classroom environment for her students. She is always approachable, never rejects questions, and makes a genuine effort to get to know her students. Her enthusiasm for math and teaching is refreshing and I believe she is well-deserving of recognition."