COL Gary W. Krahn

Professor and Head for the Department of Mathematical Sciences.
Office: 238 Thayer Hall - phone:(845) 938-5285.  DSN 688
Email:

• Biography
• Course taught
• Education
• Student Research Projects
• Research Interests
• Publications
• Presentation

Education:

• Doctor of Philosophy, Applied Mathematics, Naval Postgraduate School, 1994
• Master of Science, Applied Mathematics, Naval Postgraduate School, 1985
• Bachelor of Science, Engineering, United States Military Academy, 1977

Courses Taught: 

Differential Calculus, Integral Calculus, Multivariable Calculus, Mathematical Modeling, Discrete Mathematics, Discrete Structures, Abstract Algebra, Foundations of Higher Mathematics, Probability and Statistics, Graph Theory and Combinatorics, Discrete Dynamical Systems, Advance Linear Algebra

Recent Student Research Projects

  Independent Research in Stochastic Modeling for Army Personnel Planning
  Independent Research in Coding Theory - Generating Pseudo Random Sequences
  Independent Research in Linear Shift Registers - Combinatoric Structure
  Independent Research in Graph Theory - Traversal of particular edges
  Independent Research in Graph Theory - Counting Traversals within a Graph
  Independent Research in Number Theory - Josephus Numbers
  Independent Research in Abstract Algebra - Rubics Cube Analysis
  Independent Research in Game Theory - Master Mind Algorithm
  Independent Research in Shift-and-Add Pairs for linear sequences

Publications

 “Theory of Two-Dimensional Transformations” (with Y. Kanayama), IEEE Journal of Robotics and Automation, 1998. 

“2-Cycles Along Graphs and Digraphs,” Proceeding of the Third Annual U.S. Army Research Laboratory Technical Symposium, 1995, pp. 1 - 29.

“A Generalization of de Bruijn Sequences,” Transactions of the 3rd ARL Technical Symposium, November 1995.

“Two Dimensional Transformations and its Application to Vehicle Motion Control and Analysis” (with Y. Kanayama), IEEE International Conference on Robotics and Automation, 1993, pp. 13-18.

“Structural Properties of Shift-and-Add Pairs” (with H. Fredricksen), Transactions of the Seventh Army Conference on Applied Mathematics and Computing, 1989, pp. 193-203.

“A Randomness Property of m-sequences” (with H. Fredricksen), Transactions of the Fifth Army Conference on Applied Mathematics and Computing, 1988, pp. 643-647.

Research Interests

• Utility of information on the battlefield.

• Analyze binary sequences of length 2n that are not de Bruijn, however, possess sufficient structure so that every distinct binary n-tuple can be systematically “combed” out of the sequence -i.e., every n-tuple can be found appearing at the successive positions in a subsequence. This work has direct applications in digital communications and secure data transmissions.

• Analyze the classical Pebbling Problem on Graphs and Digraphs.  This work has direct applications to the strategic placement of military  personnel and equipment.

• Analyze the paths along a directed connected graph that visit each arc exactly twice. This procedure has produced sequences with remarkable randomness properties. This has digital communication applications.

• Utilize the structure of algebraic systems to create more efficient robotic path planning algorithms. Currently, this work is being applied on a Robot at the Naval Postgraduate School.

Brief Biography

Created and born in San Diego, California in 1955.  Departed San Diego in 1973 with few ideas and no direction. (Little has changed)  Those casual days in Southern California came to an abrupt end upon entering the U.S. Military Academy at West Point. With a vision and new insights on leadership, graduation arrived in June 1977.  Quickly passing through Ft. Sill and Ft Knox, the next five years were spent as an  artilleryman at Ft. Ord, California - the home of the 7th Infantry Division.  After completing the Officer Armor Advance Course at Ft Knox KY, it was a blessing returning to Monterey California to attend the Naval Postgraduate School.  Prof. Hal Fredricksen worked very hard and eventually was able to hand me an MS in Applied Mathematics.  Following graduate school, the next year was spent in S. Korea as the Battalion Operations Officers for 2/17 FA supporting the DMZ mission.  In 1986, the Department of Mathematical Sciences, USMA became home.  It was a joy attempting to inspire cadets to see the beauty of calculus, the utility of differential equations, the purpose of math modeling, and the power of discrete mathematics during this four year tour.  After a year at Leavenworth in CGSC, I returned to the Naval Postgraduate School to earn a Ph.D.  Under the gentle hand of Hal Fredricksen, the Ph.D. in Applied Mathematics was completed.  In 1994, I returned to the Department of Mathematical Sciences to once again become a member of the USMA /D-math family.  I continue to teach and be taught.   

As the Director of the Probability and Statistics program I quickly learned that the numbers were against me.  Therefore, I was asked to become the Director of the Discrete Dynamical Systems program, but failed to be discrete!  I was transferred into the position of Deputy Head and it only took a few years before Chris Arney, the Department Head, had to make a decision to either fire me or to move on in order to keep his sanity.  Chris departed on Christmas Day in the year 2000, at which time I became the Department Head. 

Return to USMA home page, D/Math home page, or the  Math Faculty home page. 

Last updated: Monday May 08, 2006
Updated by: COL Gary Krahn