Spring 2024
Speaker: Darren A. Narayan, Professor of mathematics at RIT
March 28 (Thursday), Physics 128, 4:30-5:30pm (Tea at 3pm Physics 101)
Title: Fibonacci Determination
Abstract: This presentation will include a surprising connection between matrix determinants and the Fibonacci sequence. It will include an eventful storyline from the initial discovery to eventual publication. The talk is appropriate for both faculty and students.
Spring 2023
Speaker: Grant Sanderson, 3Blue1Brown
February 23 (Thursday), LSRC B101 (Love Auditorium), 6pm-8pm
Title: Quantum computing and colliding blocks
Abstract: Grant’s lecture expanded on his 2019 video on the number of collisions produced between two blocks on a frictionless surface tending to compute pi, and the application of such findings to the realm of quantum computing. Like how his channel endeavors to simplify the mathematical problem with a change in perspective, Grant gave an enlightened view on how velocities of the colliding blocks can be modeled by slicing a line through a circle in a velocity phase diagram, with each curve representing a conservation law of energy or momentum. The sliced line, representing the movement of the blocks, would periodically hit the boundary of the circle in a manner such that the intersecting points would be spaced out evenly by an arbitrary angle 2θ due to inscribed angle geometry. In light of this fact, Grant ultimately simplified the problem into a basic question: how many times we must add 2 θ to itself before it surpasses 2𝜋? In the case where θ = 0.001, the answer to that question, which is 3141, would have the same first digits as pi. Yet what Grant concluded from the talk was not simply the proof to this interesting observation. He emphasized upon the lesson of what phase space allows us to do: by representing the relevant state of a system into a single point in abstract space, we can translate the problem of what may be a sophisticated dynamics problem into a simplified geometrical one.
After the talk, the attendees were able to ask a diverse range of questions in an in-depth 45-minute Q&A session. The questions varied from Grant’s initial motive for his 3Blue1Brown channel to the scope of topics he will focus on for future videos that are to be uploaded. For those who wanted to have longer, personal conversations with Grant, a group of selected students were able to have dinner with him later in the night. The student feedback from the talk were optimistic, with many viewing the opportunity to see in-person one of the pioneering YouTubers in mathematics education to be phenomenal. With the unparalleled achievement it has made, DUMU continues to devote itself to organizing and providing resources to students interested in mathematics outside the classroom. Stay tuned for what DUMU has to offer in the future.
Spring 2019
Speaker: Michael Harris, Professor of Mathematics at Columbia University
March 28 (Thursday), LSRC B101 (Love Auditorium), 4:30-5:30pm (Tea at 3pm Physics 101)
Title: Mechanical Mathematician
Abstract: A mathematical claim is only accepted as valid if it is accompanied by a proof. Ideally, a proof should be a deduction from accepted principles that meets two requirements: on the one hand, it must strictly follow the rules of logical reasoning, but on the other hand, it should clarify why the claim had to be valid in the first place. When these two criteria come into conflict, the first takes priority. Some deductions, however, are so long or complex that they cannot be checked for errors by human beings. The success in designing computer systems to provide mechanical verification of the proofs of some famous theorems has led some mathematicians to suggest that all future proofs be written in computer readable code. A few mathematicians have gone so far as to predict that artificial intelligence will make human mathematicians obsolete.
Is mathematics a means to an end that can be achieved as well, or better, by a competent machine as by a human being? If so, what is that end, and why should we trust machines over humans? Or is mathematics rather an end in itself, pursued for its intrinsic human value? If so, what could that value be, and can it ever be shared with machines?
Fall 2018
Speaker: Rachel Levy, Deputy Executive Director of MAA and Professor at Harvey Mudd College
December 3, 2018 (Monday), Physics 128, 4:30-5:30pm (Tea at 3pm Physics 101)
Title: Mathematical Modeling from Kindergarten to Industry
Abstract: Mathematical Modeling is taking off at all levels of mathematics education. The kinds of math modeling problems students can solve have direct and meaningful connections to the world around us. Modeling helps people engage in data science and mathematical tools that can be of value in any career. Creativity can be inspired by modeling because problems require genuine choices and have multiple solutions. Through modeling problems, teachers, students and families can develop new relationships with the mathematics in the K-12 curriculum.
I work at the Mathematical Association of America, where our mission is to advance the understanding of mathematics and its impact on the world. We have programs like MAA PIC Math that prepare university faculty to engage their students in industrial problems. We also run the AMC mathematics contests that introduce middle, high school and college students to challenging mathematical problem solving.
In my research, I have explored whether students as young as Kindergarten can engage in mathematical modeling in ways that resonate with the ways my undergraduates at Harvey Mudd College engaged in industry-based problems. This means going beyond assignments where models are presented as finished products to mathematical modeling projects that ask a big messy important question and leave it to the modelers to develop and justify a useful solution.
In this talk I will share with you some surprising insights from four years following elementary school mathematical modelers and discuss how observing their teachers improved my own practice as a mathematical modeling educator and researcher.
Fall 2017
Speaker: L. Mahadevan, Professor at School of Engieering and Applied Mathematics, Harvard University
December 6, 2017 (Wednesday), French 2231, 4:30-5:30pm (Tea at 3pm Physics 101)
Title: Morphogenesis: geometry, physics and biology
Abstract: A century after the publication of D'Arcy Thompson's classic On growth and form his vision has finally begun to permeate into the fabric of modern biology. Within this framework, I will show how a combination of biological and physical experiments, mathematical models and computations allow us to begin unraveling the physical basis for morphogenesis in the context of examples such as shoots, leaves, guts and brains.
Spring 2017
Speaker: Francis Su, Professor at Department of Mathematics, Harvey Mudd College
February 13, 2017 (Monday), Physics 128, 4:30-5:30pm (Tea at 3pm Physics 101)
Title: Voting in Agreeable Societies
Abstract: When does a candidate have the approval of a majority? How does the geometry of the political spectrum influence the outcome? What does mathematics have to say about how people behave? When mathematical objects have a social interpretation, the associated results have social applications. We will show how some classical mathematics can be used to understand voting in "agreeable" societies. This talk also features research with undergraduates.
Speaker: Henry Segerman, Professor at Department of Mathematics, Oklahoma State University
April 18, 2017 (Tuesday), Physics 130, 4:30-5:30pm (Tea at 4pm Physics 101)
Title: 3D Shadows: Casting light on the fourth dimension
Abstract: Our brains have evolved in a three-dimensional environment, and so we are very good at visualising two- and three-dimensional objects. But what about four-dimensional objects? The best we can really do is to look at three-dimensional "shadows". Just as a shadow of a three-dimensional object squishes it into the two-dimensional plane, we can squish a four-dimensional shape into three-dimensional space, where we can then make a sculpture of it. If the four-dimensional object isn't too complicated and we choose a good way to squish it, then we can get a very good sense of what it is like. We will explore the sphere in four-dimensional space, the four-dimensional polytopes (which are the four-dimensional versions of the three-dimensional polyhedra), and various 3D printed sculptures, puzzles, and virtual reality experiences that have come from thinking about these things. I talk about these topics and much more in my new book, "Visualizing Mathematics with 3D Printing"
Fall 2016
Speaker: Chris Wiggins, Professor at Department of Applied Physics and Applied Mathematics, Columbia University
September 20, 2016 (Tuesday), Physics 128, 4:30-5:30pm (Tea at 4pm Physics 101)
Title: Data Science @ The New York Times
Abstract: TBA
Speaker: Eugenia Cheng, Author and Scientist In Residence at School of the Art Institute of Chicago
October 13, 2016 (Thursday), Physics 128, 4:30-5:30pm (Tea at 4pm Physics 101)
Title: How to Bake π, Making abstract mathematics palatable
Abstract: Mathematics can be tasty! It is a way of thinking, and not just about numbers. Through unexpectedly connected examples from music, juggling, and baking, I will show that math can be made fun and intriguing for all, through hands-on activities, examples that everyone can relate to, and funny stories. I'll present surprisingly high-level mathematics, including some advanced abstract algebra usually only seen by math majors and graduate students. There will be a distinct emphasis on edible examples.
Spring 2016
Speaker: Tadashi Tokeida, Professor at Department of Mathematics, Stanford University
April 15, 2016 (Friday), Physics 128, 4:30-5:30pm (Tea at 4pm Physics 101)
Title: A world from a sheet of paper
Abstract: Take a sheet of paper. By folding, stacking, crumpling, tearing, we will tour a rich diversity of phenomena, from geometry and magic tricks to elasticity and the traditional Japanese art of origami. Much of the lecture consists of actual table-top demos, which you can try with family and friends. So then, take a sheet of paper.
Speaker: Mark Goresky, Member at School of Mathematics, Institute for Advanced Study
April 21, 2016 (Thursday), Physics 128, 4:30-5:30pm (Tea at 4pm Physics 101)
Title: A glamorous Hollywood star, a renegade composer, and the mathematical development of spread spectrum communications
Abstract: During World War II Hedy Lamarr, a striking Hollywood actress, together with George Antheil, a radical composer, invented and patented a secret signaling system for the remote control of torpedoes. The ideas in this patent have since developed into one of the ingredients in modern digital wireless communications. The unlikely biography of these two characters, along with some of the more modern developments in wireless communications will be described.
Fall 2015
Speaker: Bruce C. Berndt, Professor at Department of Mathematics, University of Illinois at Urbana-Champaign
October 22, 2015 (Thursday), Gross Hall 107, 4:30-5;30pm (Tea at 4pm at Physics 101)
Title: Ramanujan's Life, His Earlier Notebooks and His Lost Notebook
Abstract: Ramanujan was born in southern India in 1887 and died there in 1920 at the age of 32. He had only one year of college, but his mathematical discoveries, made mostly in isolation, have made him one of the 20th and 21st centuries' most influential mathematicians. An account of Ramanujan's life will be presented. Most of Ramanujan's mathematical discoveries were recorded without proofs in notebooks, and a description and history of these notebooks will be provided. In 1976, George Andrews found Ramanujan's "lost notebook" in the library at Trinity College, Cambridge. A history and description of this lost notebook will also be provided. The lecture will be accompanied by photographs of Ramanujan, his home, his school, his notebooks, and those influential in his life, including his mother and wife Janaki.