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, …].
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
