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Department of Mathematics


Ralph Howard

Title: Professor
Department: Mathematics
College of Arts and Sciences
Phone: 803-777-7471
Office: LeConte 352
Resources: My Website
Ralph Howard


Ph.D  California Institute of Technology   1977-1982
M.S.  California State University, Northridge  1973-1974
B.A.  California State University, Northridge  1970-1973


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.


Differential and integral geometry and its applications to other fields such as mathematical relativity, convexity, and, most recently, number theory.

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.

Challenge the conventional. Create the exceptional. No Limits.