1. Exploring Computational Mathematics: Unfolding Polyhedra Brittany Terese Fasy, Duke University David Millman, UNC-Chapel Hill MathFest 2008

2. Standard Curriculum Undergraduate: Courses Quizzes and Exams Projects Senior Project Graduate: Research Presentations Papers Proposals Courses MathFest 2008

3. BRIDGING THE GAP An Undergraduate Research Course: MathFest 2008

4. Student Objectives Learn about Mathematical Research Understand an Open Problem Identify and Discuss Areas of Computational Mathematics Read an Academic Paper Present to Peers Write a Proposal Decide Upon an Area for Further Investigation MathFest 2008

5. Vertex Unfolding Vertex Unfolding of Simplicial Manifolds, E. Demaine, D. Eppstein, J. Erickson, G. Hart, and J. O’Rourke MathFest 2008

6. Course Components Lectures on Topic Areas Bi-Weekly Assignments Final Project Paper Presentation Future Investigation Proposal MathFest 2008

7. Topic 1: Computer Science Basic Programming Skills Data Structures Parsing and File I/O Debugging Tools and Technique Documentation Optional Inheritance and Templates Pointers MathFest 2008

8. Topic 2: Graph Theory Planar Graph Searching Graph Data Structures Euler Tour and Hamiltonian Cycle Optional: NP Complete Shortest Path Min Flow / Max Cut MathFest 2008

9. Topic 3: Topology Basis for a Topology Covering Set Homotopy Equivalence Fundamental Group Optional: Persistence Homology Mesh Generation MathFest 2008

10. Topic 4: Numerical Analysis Floating Point Numbers and Arithmetic Error Propagation Root Finding Convergence Optional: Matlab Solving ODEs Interpolation MathFest 2008

11. Topic 5: Computational Geometry Predicates (e.g. inCircle) Voronoi Diagrams Delaunay Triangulations Convex Hulls Triangle and Object Intersections Optional: Arrangements Range Queries MathFest 2008

12. Topic 6: Visualization Programming with OpenGL Matrix Transformations User Interactions and Callbacks Optional: Rendering Versus Ray Tracing Applications of Previous Topics MathFest 2008

13. Project Assignments 1. Computer Science Debugging Exercise Create Shape Object 2. Graph Theory Design & Create Graph Data Structure Create Planar Graph from Shape Object 3. Topology Euler Tour of Graph MathFest 2008

14. Project Assignments (continued) 4. Numerical Analysis Numerical Stability 5. Computational Geometry Compute Planar Coordinates 6. Visualization Visualize the Output Add User Interaction MathFest 2008

15. Presentations & Proposals Academic Papers for Each Topic Covered Group Presentations of Papers Proposal Writing for Project Extension MathFest 2008

16. Acknowledgements Olga Brezhneva Dave Coulliette Robert W. Vallin Jack Snoeyink MathFest 2008

17. QUESTIONS? MathFest 2008

18. How to Contact Us: brittany@cs.duke.edu dave@cs.unc.edu MathFest 2008