Valentina S. Harizanov

Office
: Government Hall (2115 G Street), Room 220
Phone
: 202–994–6595
e-mail:
harizanv@gwu.edu
Professor of Mathematics
Columbian College  of Arts and Sciences
, GWU
Curriculum Vitae pdf

Office hours:
Tu 2:05–3:05pm; Th 11:40am–12:40pm
at other times by appointment
any time by e-mail

Teaching
Current Courses
Recent Courses
Other Courses Taught at GW
Teaching Evaluations
GW Logic Seminar
Doctoral Students

Research
Research Interests
Research Publications in Refereed Journals
Recent and Future Meetings
Books
Selected Conference Presentations
Selected Invited Lectures
Special Lectures at GWU
Other
Graduate Education
Professional Affiliations
Translations
Invited Book Reviews
Current GW Administrative Assignments
Web Pages of Recent Co-Authors

Research Interests

Most of my research is in computable (recursive) algebra and model theory (see Harizanov's Handbook of Recursive Mathematics chapter), and in computability (recursion) theory, which are subfields of mathematical logic (see Crossley's  2005 tutorial). Computability theory is the mathematical theory of algorithms. (See computability theory home page.) Problems which can be solved algorithmically are called decidable. Undecidable problems can be more precisely classified by considering generalized algorithms, which require external knowledge. Turing degrees provide an important measure of the level of such knowledge needed. Computable model theory explores algorithmic properties of objects and constructions arising within mathematics. I am especially interested in computability theoretic complexity of relations (see Hirschfeldt's Bulletin of Symbolic Logic paper) and structures (see Harizanov's Bulletin of Symbolic Logic paper), including their Turing degrees. I am also interested in natural language semantics, philosophy of mathematics, and theoretical computer science (in particular, frequency computations, inductive inference and algorithmic learning theory, and quantum computing). My research has been supported by the NSF research grants DMS-0502499 (2005–07) and DMS-0704256 (2007–09), as well as by the NSF binational research grants for collaboration with Russia/Kazakhstan (2000–09).

Recent and Future Meetings (Organizer or Speaker)

Current Courses

Fall 2007 Spring 2008
-Math 33  Multivariable Calculus
-Math 272  Graduate Topics: Algorithms and Mathematics
-Graduate Reading and Research
-Dissertation Research
-Math 170  Computational Complexity
-Math 195  Undergraduate Reading and Research
-Graduate Reading and Research
-Dissertation Research


Recent Courses

Fall 2006 Spring 2007
-Math 801  Dean's Seminar for Freshmen: Mathematics of the Infinite
-Math 272  Graduate Topics: Set Theory
-Graduate Reading and Research
-Dissertation Research
-Math 801  Dean's Seminar for Freshmen: Turing machines, Chomsky languages, digital and quantum computing
-Math 272  Graduate Topics: Algorithmic Methods
-Math 195  Undergraduate Reading and Research
-Graduate Reading and Research
-Dissertation Research

Fall 2005 Spring 2006
-Math 103  Computability Theory, including Writing in the disciplines version
-Math 195  Undergraduate Reading and Research
-Math 272  Graduate Topics: Model Theory and Algorithmic Model Theory
                 Math 272 Mini Conference
-Math 295  Graduate Reading and Research
-Math 399  Dissertation Research
-Math 801  Dean's Seminar for Freshmen: Is Reason Computable?
                 Special Events
-Math 295  Graduate Reading and Research
-Math 399  Dissertation Research



Courses Taught at GW

Introductory Undergraduate: College algebra; General mathematics; Mathematical ideas;
    Precalculus; Calculus with precalculus;
    Calculus for the social and management sciences; Finite mathematics for the social and management sciences;
    Single variable calculus I
; Single variable calculus II, Multivariable calculus
Advanced Undegraduate:  Introduction to mathematical logic; Introduction to automata theory (Statistics Department);
    Axiomatic set theory; Computability theory (including writing in the disciplines version); Computational complexity

Graduate:  Mathematical logic; Graduate topics: Incompleteness of formal systems. Turing degrees;
    Graduate topics: NP-completeness. Multi-valued logic;  
Graduate topics: Effective model theory;
    Graduate topics: Independence results in set theory;  
Graduate topics: Recursion theory: hierarchies, oracles and degrees;
    Graduate topics: Models, algorithms, and applications;  
Graduate topics: The forcing method;
    Graduate topics: Computable model theory;  
Graduate topics: Frequency computations. Computable algebra;
    Graduate topics: Algorithmic learning. G
ödel incompleteness;
    Graduate topics: Computability theory and applications to  structures;  
Graduate topics: Ordinals, definability, and computability;
   
Graduate topics: Model theory and algorithmic model theory; Graduate topics: Set theory;
    Graduate topics: Algorithmic methodsGraduate topics: Algorithms and mathematics
Special Courses: Mathematical theory of languages III for the University Honors Program;
    Set theory for the Summer Program for Women in Mathematics;

    Dean's Seminar for Freshmen: Mathematical logic, language, and learning;
    Dean's Seminar for Freshmen: Is reason computable?;
    Dean's Seminar for Freshmen: Mathematics of the infinite;
    Dean's Seminar for Freshmen: Turing machines, Chomsky languages, digital and quantum computing;                 
    Computational complexity for the Computational Sciences Master's Program

Teaching Evaluations

Graduate Education

    Ph.D. 1987, University of Wisconsin-MadisonMathematics
        Dissertation advisor: Terry Millar
        Dissertation: Degree Spectrum of a Recursive Relation on a Recursive Structure, 95 pp.
    M.A. 1984, University of Wisconsin-Madison, Mathematics
    M.S. 1981, University of Belgrade, Mathematics
        Master's thesis: Generalized Quantifiers, 69 pp. (in Serbian)

GW Logic Seminar

Spring 2008 Fall 2004
Fall 2007 Spring 2004
Spring 2007 Fall 2003
Fall 2006 Spring 2003
Spring 2006 Fall 2002
Fall 2005 Spring 2002
Spring 2005 Fall 2001

Books

algorithmic

Selected Research Publications in Refereed Journals and Volumes

Invited Book Reviews

  • Computable Structures and Hyperarithmetical Hierarchy by C.J. Ash and J. Knight,” V. Harizanov, Bulletin of Symbolic Logic 3, 2001, pp. 383–385.
  • Countable Boolean Algebras and Decidability by S. Goncharov,” V. Harizanov, Journal of Symbolic Logic 63, 1998, pp. 1188–1190.
  • “V. Matiyasevich, Hilbert’s Tenth Problem,” V. Harizanov,  Modern Logic (International Journal for the History of Mathematical Logic, Set Theory, and Foundations of Mathematics) 5, 1995, pp. 345–355.
  • “Douglas Hofstadter” (a review of Gödel, Escher, Bach), V. Harizanov GW Forum, Spring, 1988, pp. 46–48.
  • Translations

    Selected Conference Presentations

    Selected Invited Lectures at Other Universities

    Special Presentations at George Washington

    Doctoral Students

    Professional Affiliations

    Recent GW Administrative Assignments

    Math Department

    College of Arts and Sciences

    University

    Web Pages of Recent Co-Authors