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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
Ralph Howard

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.

Challenge the conventional. Create the exceptional. No Limits.

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