Norman Brenner


Professorial Lecturer
Department of Computer Science
The George Washington University



Contact Information

Norman Brenner
Department of Computer Science
The George Washington University

800 22nd Street NW, Suite 400
Washington, DC 20052

phone: office (202) 994-6080, cell (301) 980-6374


Office Hours

Mon   6:00 pm - 7:00 pm
Tue  6:00 pm - 7:00 pm
Other times by appointment

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Teaching Activities

This term I am teaching Introduction to Computers & the Internet (CS1021), Introduction to Webpage Design & Javascript (CS1023); next term, I may add Discrete Structures (CS1311).

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Fundamentally, I am interested in rules-based systems. Besides computer programming, I enjoy learning the structure of human languages, and have studied (more often dabbled in) about 150 of them. I like phonology and its representation in spelling, and well-designed computer languages and operating systems.

Some things I am thinking about now:

  • Comparison of website building techniques between ASP and the newer ASP.NET, and also between VB6 and the newer VB.NET and C#
  • Helping the GWU Tourism Department build a data base of international aid projects
  • A discussion of ease of use in programming languages, and excoriation of  “inhuman factors”
  • Examination of the use of Information Technology in legal firms
  • A discussion of the Duke of Wellington as a master manager—winning battles with superior administrative talent
  • Building my favorite programming language, APL, in the MSIL language of Microsoft’s new .NET framework
  • Analysis of a simplified three body gravitational system (Sun, Neptune, Pluto), confirming the orbit-orbit resonance of the latter planets; I plan to redo my hand calculations using Mathematica ®.
  • A pedagogical presentation of solutions to the problem of summing powers of consecutive integers, comparing Bernoulli’s solution with Stirling’s and Faulhaber’s.
  • Learning the structure of several dozen important spoken languages, and learning a few well (Basque, Chinese, Georgian, (Ancient) Greek, Lakhota, Quechua, Polish, Tamil, Wolof)
  • Proposal of practical (i.e. typable/readable/consistent/accurate) orthographies for languages such as Cantonese, Italian, Lakhota, Maya, Swahili, Thai
  • Teaching a survey course on all the languages of the world, emphasizing the common features of phonology and grammar
  • Designing a website to teach a language, whether human or computer, in an optimal pedagogical manner; the human language version would include audio clips, and both would include copious well-chosen examples
  • A Fast Fourier transform of disk-stored data by matrix transposition


I am always on the look-out for new and interesting ideas in linguistics, programming languages, military history and dinosaurs as living organisms. From time to time, I give lectures on linguistic topics for the student organization Global Languages Network.  Send me email at with your thoughts!  

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Publications and Preprints

PhD Thesis

·        A 3-D Model for the Spin-Orbit Resonance of the Planet Mercury, Massachusetts Institute of Technology, Department of Earth and Planetary Sciences


Refereed Proceedings

·        “APL on a Multiprocessor Architecture”, APL ’82 Conference Proceedings, Association for Computing Machinery

·        “A Powerful But Simple Editor for APL”, APL ’83 Conference Proceedings, Association for Computing Machinery, 195—200

·        “Extending APL for Pattern Matching”, APL ’83 Conference Proceedings, Association for Computing Machinery

·        “Editing APL Objects with CMS XEDIT”, APL ’84 Conference Proceedings, Association for Computing Machinery

·        “VLSI Circuit Design Using APL with Fortran Subroutines”, APL ’84 Conference Proceedings, Association for Computing Machinery


Refereed Journals

·        Algorithm 467: Matrix Transposition in Place”, Communications of the ACM, 1972.

·        “Fast Fourier Transposition With Minimum Multiplications”, IEEE Audio & Signal Processing, 1976 (with C. Rader)


Book Chapters

·        “The Fast Fourier Transform”, chapter 6.2 of  Methods of Experimental Physics; Vol. 12, Astrophysics, Part C: Radio Observations, Academic Press, 1976

·        “Contour Mapping”, chapter 6.3.1 of  Methods of Experimental Physics; op.cit.

·        “Ruled-Surface Mapping”, chapter 6.3.2 of  Methods of Experimental Physics; op.cit.

·        “Gray-Scale Mapping”, chapter 6.3.3 of  Methods of Experimental Physics; op.cit.

·        “Fast Fourier Transform For Number of  Data Not a Power of Two”, IBM Collection of Numerical Algorithms, 1973.

·        Several Non-numerical Algorithms in APL, APL Handbook of Mathematical Techniques, IBM, 1983.


Technical Reports

·        Three Fortran Programs Implementing the Fast Fourier Transform, Lincoln Laboratory Technical Report.

·        Rapidly Bit Reversing Data for the Fast Fourier Transform, Lincoln Laboratory Technical Report.

·        Programs for Performing the FFT, SHARE Program Library, #360D.13.4.001, .002, .003, .005.



·        "Toward a Model of Cultural Values and Norms: A Confirmatory Factor Analysis", Norman Brenner & Steve McGuire (GWU Mgt. Sci.); presented at 18th Annual Washington Consortium of Schools of Business Research Forum, April 2003


Patent Disclosures

·        Fast Fourier Transform for a Small Computer Without Hardware Multiplication, IBM Patent Disclosures, 1972.


Research in Progress

·        "Agile Project Management:  An Experiment in the Efficacy of Network-based vs. Hierarchical Management Structures", Fred.  Sencindiver (GWU Mgt Sci) & Norman Brenner


·        "Global Attitudes to Ideal Job", Steve McGuire (U Calif), Norman Brenner, Vanessa Perry (GWU Marketing Dept.), Vikas Jain (GWU Marketing)


·        "The Duke of Wellington As A Human Resources Manager", to be submitted to Investor's Daily


·         Mismanagement at Waterloo:  A Lesson for Senior Management”, to be submitted to Investor’s Daily


·        "Sum of Integer Powers--A Pedagogical Review of Methods and Results" , to be submitted to American Mathematical Monthly


·        “A Failure of Inheritance: Extending the Treeview Object in Visual Basic .Net”, to be submitted to TOPLAS


·        "Unifying Two Modes of Object Type Definition" , to be submitted to TOPLAS


·        "Notes on Advanced Features of the HP 49g+/50g Pocket Calculator" , to be submitted to


·        "A Simple Model Which Predicts the Orbit-Orbit Resonance of Neptune and Pluto", to be submitted to Astronomical Journal


·        Minimal encoding of moves in a chess game”, to be submitted to Chess Bulletin


·        A Grammar of Lakhota [with practical romanization]”, adapted from Handbook of North American Indians, Vol. 17


·        Lessons in the Shanghai Vernacular [with practical romanization]”, adapted from a website by Benjamin X. Ao


·        A brief history of programming languages”, submitted to Segue Technologies house blog


·        Languages of the World, Ranked by Importance”, to be submitted to Language


·        Diacritic-free Romanization For Several Languages, Including Notes on the Conventional Idiocies of Standard Spelling Systems”, to be submitted to Language


·        Tom Lehrer’s classic song The Elements, updated”, to be submitted to Mr. Lehrer


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·         "Database of International Aid Projects for Sustainable Tourism", Sheryl Spivack (GWU Tourism Dept), Shaun Mann (Tourism), Z.  Rozga (Tourism), Norman Brenner  Preliminary database of international donor projects


·         "SAVE database ", Z.  Rozga (GWU Tourism Dept.), Norman Brenner  Preliminary SAVE database



·         B.A. from Central High School, Philadelphia PA

·         A.B. (Mathematics) from Princeton University, Princeton NJ

·         M.A. (Applied Mathematics) from Harvard University, Cambridge MA

·         Ph,D. (Earth and Planetary Sciences) from Massachusetts Institute of Technology, Cambridge MA

·         Winner of First MIT Spelling Bee  Campus newspaper (The Tech)

·         Married to Krystyna Boron, living in Bethesda MD; two sons, Daniel and Lucas


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Page last updated  2009 October 18; 2012 January 16; 2013 February 16; 2014 January 2; 2014 February 5; 2015 March 5