Department of Mathematics
Directory
Ralph Howard
Title: | Professor |
Department: | Mathematics College of Arts and Sciences |
Email: | howard@math.sc.edu |
Phone: | 803-777-7471 |
Office: | LeConte 352 |
Resources: | My Website |
Research Interests
Differential and integral geometry and its applications to other fields such as mathematical relativity, convexity, and, most recently, number theory.
Education
- Ph.D. California Institute of Technology (1982)
- M.S. California State University, Northridge (1974)
- B.A. California State University, Northridge (1973)
Experience
- Professor, University of South Carolina (1999 – present)
- Associate Professor, University of South Carolina (1988 – 1999)
- Assistant Professor, University of South Carolina (1984–1988)
- Research Associate, Michigan State University (1982–1984)
- Visiting Assistant Professor, Duke University (Fall 1987)
- Visiting Associate Professor, Royal Institute of Technology, Stockholm (Fall 1993 & Spring 1994)
Courses Taught
- MATH 122: Calculus for Business Administration and Social Sciences
- MATH 172: Mathematical Modeling for the Life Sciences
- MATH 174: Discrete Mathematics for Computer Science
- MATH 141: Calculus I
- MATH 142: Calculus II
- MATH 241: Vector Calculus
- MATH 242: Elementary Differential Equations
- MATH 250: Honors Vector Calculus
- MATH 300: Transition to Advanced Mathematics
- MATH 520: Ordinary Differential Equations
- MATH 521: Boundary Value Problems and Partial Differential Equations
- MATH 511: Probability
- MATH 523: Mathematical Modeling of Population Biology
- MATH 524: Nonlinear Optimization
- MATH 527: Numerical Analysis
- MATH 531: Foundations of Geometry
- MATH 546: Algebraic Structures I
- MATH 532: Modern Geometry
- MATH 550: Vector Analysis
- MATH 551: Introduction to Differential Geometry
- MATH 552: Applied Complex Variables
- MATH 554: Analysis I
- MATH 555: Analysis II
- MATH 574: Discrete Mathematics I
- MATH 580: Elementary Number Theory
- MATH 700: Graduate Linear Algebra
- MATH 701: Algebra I
- MATH 705: Analysis III
- MATH 723: Advanced Differential Equations
- MATH 726: Numerical Analysis I
- MATH 727: Numerical Analysis II
- MATH 732: Algebraic Topology I
- MATH 733: Algebraic Topology II
- MATH 734: Differential Geometry
- MATH 738: Differential Topology
- MATH 739: Complex Geometry II
- MATH 748: The Symmetric Group and its Representations
- MATH 748: Groups and Graph
Selected Publications
- Mohammad Ghomi and Ralph Howard
Total diameter and area of closed submanifolds. Mathematische Annalen
363 (2015), no. 3-4, 985–999. - Mohammad Ghomi and Ralph Howard
Tangent cones and regularity of real hypersurfaces. Journal für die Reine und
Angewandte Mathematik. [Crelle's Journal] Math. 697 (2014), 221–247. - Ralph Howard
Convex bodies of constant width and constant brightness. Advances in Mathematics
204 (2006), no. 1, 241–261. - Aaron Abrams, Jason Cantarellai Joseph H. G, Fu, Mohammad Ghomi, and Ralph Howard
Circles minimize most knot energies. Topology 42 (2003), no. 2, 381–394 - P. T. Chruściel, E. Delay, G. J. Galloway, and R. Howard
Regularity of horizons and the area theorem. Annales Henri Poincaré. A Journal of
Theoretical and Mathematical Physics 2 (2001), no. 1, 109–178. - Lars Andersson and Ralph Howard
Comparison and rigidity theorems in semi-Riemannian geometry. Communications in
Analysis and Geometry 6 (1998), no. 4, 819–877. - Ralph Howard
The kinematic formula in Riemannian homogeneous spaces. Memoirs of the American
Mathematical Society 106 (1993), no. 509, vi+69 pp. - Ralph Howard and Anton Schep
Norms of positive operators on \(L^p\)-spaces. Proceedings of the American Mathematical
Society 109 (1990), no. 1, 135–146.