Faculty Profile

		Sam Nelson, Ph.D. Assistant Professor E-mail: snelson@cmc.edu Phone: (909) 607-8979 Campus Address: Adams Hall 200 Departments: Mathematics Web Site
		Office Hours Tuesday 10:00 AM - 12:00 PM Thursday 10:00 AM - 12:00 PM Current Course Schedule Math 31-5 MWF- 2:45 PM - 4:00 PM  RHN 103 Math 50 MW- 8:35 AM - 9:50 AM  RHS 105

Educational Background

Ph.D., Louisiana State University; M.S., Louisiana State University; B.S., University of Wyoming

Teaching Interests

• Calculus, Discrete Mathematics, Introductory Pure Mathematics, Linear algebra, Abstract algebra, Topology, Algebraic topology, Geometry

Research Interests

• Low-dimensional topology, knot theory, algebraic topology

Selected Professional Activities

• Reviewer for Zentralblatt
• Organizer for special sessions on Algebraic Structures in Knot Theory at AMS meetings in Baton Rouge, Claremont, Washington D.C. and Riverside
• Undergraduate research (see www.esotericka.org/students.html)

Selected Research and Publications

• "The Combinatorial Revolution in Knot Theory" (to appear in Notices of the AMS)
• Enhancements of counting invariants: the column group
• Semiquandles and flat virtual knots
• On rack polynomials
• Link invariants from finite Coxeter racks
• Link invariants from finite racks
• The 2-generalized knot group determines the knot
• Generalized quandle polynomials
• Virtual Yang-Baxter cocycle invariants
• On bilinear biquandles
• On symplectic quandles
• A polynomial invariant of finite quandles
• Symbolic computation with finite biquandles
• An isomorphism theorem for Alexander biquandles
• Quandles and Linking Number
• Matrices and Finite Biquandles
• Non-classicality and quandle difference invariants
• Matrices and finite Alexander quandles
• Symbolic computation with finite quandles
• On the Orbit Decomposition of Finite Quandles
• Matrices and Finite Quandles
• Alexander quandles of order 16
• Signed ordered knotlike quandle presentations
• On Generalized Knot Groups
• Virtual Crossing Realization
• Classification of Finite Alexander Quandles
• The Betti numbers of some finite racks
• Unknotting virtual knots with Gauss diagram forbidden moves