Fall 2023 Projects

• Falculty Mentors: Jarod Alper, Andy Heald, James Morrow
• Graduate student mentors: Herman Chau, Vasily Ilin, Leopold Mayer
• Undergraduate TA: Zilu (Luca) Li
• Student participants: Anthony Xing, Benjamin Li, Chengyu Gong, Christie Yang, George King, Nathan Louie, Qiguang Yan, Sarah Mathison, Xinyan Li, Yanzhe (Steven) Zhong, Yu He Zhang, Zhongrui An

Projects:

• Continued Fraction Expansion for e
  • The continued fraction expansion of e is [1, 0, 1, 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, …].
  • Members: Xinyan Li, Leopold Mayer, Christie Yang
  • GitHub code


• Witt's Cancellation Theorem
  • Thm: Let ⟨-,-⟩ be a symmetric bilinear form (i.e. ⟨x,y⟩ = ⟨y,x⟩ for all x,y ∈ V). Suppose that there is form-preserving map g: U → U' where U, U' ⊂ V are subspaces. Then there is a form-preserving map f: V → V extending g.
  • Cor: U ⊕ V ≅ W ⊕ V ⟹ U ≅ W.
  • Members: Andy Heald, Nathan Louie, Sarah Mathison, Qiguang Yan


• Random Graphs
  • Goal: Build a random graph G(n,p) with n = # of nodes with p = probability of an edge. Show that the expected number E(# edges in G(n,p)) of edges in a random graph G(n,p) is (n choose 2)p.
  • Related goals: compute other expected numbers, e.g. number of triangles in a random graph.
  • Members: Zhongrui An, Hermann Chau, Vasily Ilin, George King, Benjamin Li, Yu He Zhang
  • GitHub code


• Formalizing Math 300
  • Goals:
    • Formalize the exercises (and possibly results) in the Math 300 textbook by Conroy--Taggart: An Introduction to Mathematical Reasoning.
    • Write a Lean guide for students taking Math 300
  • Members: Yanzhe (Steven) Zhong, Anthony Xing, Luca Li, Chengyu (Kenneth) Gong
  • GitHub code