Freshman Advising Seminar: Symmetry

The human perceptual apparatus seems to make repeated use a few general principles to make sense of the world. A big one is symmetry. Animal bodies generally exhibit bilateral symmetry, for example; when they don't (as with a flounder, for example, or owls' ears) we notice. Everyone will separate a perfect circle from any less symmetric doodle, and a sphere from any less symmetric blob. The concept of symmetry has been clarified and generalized by mathematicians, perhaps beginning with Plato and his solids. Different types of symmetry are distinguished from each other and studied using the abstraction captured in the concept of a "group." This seminar will consider the phenomenon of symmetry, and how it enters into art and music as well as mathematics and physics. Students will take turns leading discussions of a range of topics over the term, using resources mainly available on the web, and contribute to a document recording these discussions.

We will scour the web and the MIT library for information about selected topics arising from unpacking the concept of symmetry, and come together weekly to discuss what we've discovered. Each week a pair of students will serve as discussion leaders, in collaboration with the faculty organizer. We will schedule a time to discuss the material with you beforehand. No "Psets" and no "Exams"!

But there will be a deliverable: We will create a manuscript together documenting what we have found, using Overleaf, a tool for collaborative creation of documents in LaTex. Here's a link to this document, available only to members of the class. I'm very excited to see how it develops. Many hands make light work!

The regular class meetings will occur on Wednesdays from 3:00 to 5:00 PM Eastern US time, in 2-255.

A couple of useful resources:

  • The Office of the First Year website has a great deal of useful information and a great many useful links. You name it, they can help you: specially designed for you as a first year student.
  • S3 is the standard office offering support of all sorts for all MIT undergraduates. If for some reason you have to miss an exam for example, the first step is normally a visit to S3. It's a very student-oriented office.

    Associate Advisor: Paige Dote,


    Elizabeth Athaide,
    Howard Beck,
    Nico Bulhof,
    Brandon Chen,
    Raul Hernandez,
    Isaac Lopez,
    Luis Modes,
    Syd Robinson,


    Date Leaders Topic Resources
    Wed Sep 8 Ensemble Symmetry, a general discussion
    Fri Sep 17 Raul and Luis Regular polyhedra and polytopes Symmetries of Platonic solids and 4-dimensional analogues
    Fri Sep 24 Nico and Syd Friezes and wallpapers Frieze patterns and Wallpaper patterns
    Fri Oct 1 Elizabeth and Isaac Hyperbolic geometry Escher, Wikipedia, and Encycla.
    Fri Oct 8 Howard and Brandon Hyperbolic isometries Encycla.
    Fri Oct 15 Elizabeth Symmetry in music
    Fri Oct 22 Nico and Raul Hyperbolic polygons Katok.
    Fri Oct 28 Luis and Isaac Hyperbolic tessellations Joyce , list.
    Fri Nov 5 Haynes Miller Homogeneous surfaces: Spherical, Flat, Hyperbolic
    Fri Nov 12 Howard and Brandon Groups Wikipedia
    Fri Nov 19 Syd and Elizabeth Symmetry of roots of polynomials Galois theory, Abel, Galois
    Fri Dec 3

    Professor Haynes Miller
    Department of Mathematics 2-478
    Massachusetts Institute of Technology
    Cambridge, MA 02139
    Zoom office: