# 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 |

#### Education

#### 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.

#### Research

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.