# Elena Nogina

Professor

Mathematics

EMAIL: enogina@bmcc.cuny.edu

Office: N-598G

Office Hours: TH: 2:40-5:40 PM

Phone: +1 (212) 220-1360

Dr. Elena Y. Nogina has authored more than seventy papers in mathematical logic and computability theory. Her results in recursive topology are included in monographs on constructive mathematics.

For many years Dr. Nogina was a tenured professor at Moscow University, which was one of the world’s leading research centers in Mathematics. She also held a research position at the Computing Center of the USSR Academy of Sciences, as well as visiting professorships at the University of Montpellier, France, and at the University of Amsterdam, the Netherlands.

Since moving to the United States, Dr. Nogina has been teaching mathematics at CUNY, first at Lehman College and then at BMCC. She has been actively involved in mentoring students. Her current research interests include modal logics of provability and proofs, and their applications in the mathematical theory of knowledge and game theory. Since her appointment to BMCC in 2004, Dr. Nogina has been the recipient of fifteen research and in-service grants, including one from the National Science Foundation. She was a visiting scholar at the University of Bern, Switzerland, and Cornell University.

For a number of years Dr. Nogina was the Mathematics Panel Chair of the University Committee on Research Awards. Since 2009, Dr. Nogina has been an elected member of the Departmental Personnel and Budget Committee.

## Expertise

Computability Theory

## Degrees

- Ph.D. in Mathematics, from Moscow University and the USSR Academy of Sciences. Ph.D. Thesis “On Effectively Topological Spaces.”,

## Courses Taught

- This course is the first algebra course offered at the College. It includes such topics as algebraic representation, signed numbers, operations with polynomials, factoring, the solution of linear equations, the coordinate system, the solution of simultaneous linear equations of two variables, and graphing. This course is designed to prepare students for the CUNY Freshman Skills Assessment Test required for transfer to the upper division of CUNY, as well as for more advanced math courses. If a student passes MAT 12, the student should not register for MAT 51, since MAT 12 combines MAT 8 and MAT 51.

Students who passed MAT 12, MAT 14, MAT 41, MAT 51, MAT 56, MAT 160, MAT 161, MAT 56.5, MAT 150.5 cannot take MAT 161.5.

Course Syllabus - This course includes the study of several mathematical systems. The role of mathematics in modern culture, the role of postulational thinking in all of mathematics, and the scientific method are discussed. The course considers topics such as: the nature of axioms, truth and validity; the concept of number; the concept of set; scales of notation; and groups and fields.

Prerequisites: MAT 12, MAT 14, MAT 41, MAT 51 or MAT 161.5

Course Syllabus - This course covers computations and measurements essential in the health science professional fields. Topics include: units and measurements, ratios, solutions and dosages.

Prerequisites: MAT 12, MAT 14, MAT 41, MAT 51 or MAT 161.5

Course Syllabus - This course covers fundamental mathematical topics associated with computer information systems, including: numeration systems; sets and logic; Boolean algebra, functions, and elementary switching theory; combinatorics; mathematical induction; permutations; combinations; binomial coefficients; and distributions.

Prerequisite: MAT 12 or MAT 51; and MAT 56 or MAT 56.5 or MAT 206.5.

Course Syllabus - This course covers basic algebraic and trigonometric skills, algebraic equations, and functions. Topics include: mathematical induction, complex numbers, and the binomial theorem.

Prerequisite: MAT 56 or MAT 56.5

Course Syllabus - This is an integrated course in analytic geometry and calculus, applied to functions of a single variable. It covers a study of rectangular coordinates in the plane, equations of conic sections, functions, limits, continuity, related rates, differentiation of algebraic and transcendental functions, Rolle's Theorem, the Mean Value Theorem, maxima and minima, and integration.
Prerequisite: MAT 206 or MAT 206.5

Course Syllabus - This course provides an introduction to the concepts of formal integration. It covers the differentiation and integration of algebraic, trigonometric, and transcendental functions. Topics include the definite integral, the antiderivative, areas, volumes, and the improper integral.
Prerequisite: MAT 301

Course Syllabus - This course is an extension of the concepts of differentiation and integration to functions of two or more variables. Topics include partial differentiation, multiple integration, Taylor series, polar coordinates and the calculus of vectors in one or two dimensions.
Prerequisite: MAT 302

Course Syllabus - This course covers matrices, determinants, systems of linear equations, vector spaces, eigenvalues and eigenvectors, Boolean algebra, switching circuits, Boolean functions, minimal forms, Karnaugh maps.
Prerequisite: MAT 302, or permission of the department

Course Syllabus - This course covers the standard material comprising an introduction to group and ring theory: set theory and mappings; groups, normal subgroups, and quotient groups; Sylow's Theorem; rings, ideals, and quotient rings, Euclidean rings, polynomial rings.
Corequisite: MAT 315

Course Syllabus

## Research and Projects

- Proof Theory. Justifcation Logic: Theory, Applications, Topological Models. Game Theory

## Publications

- Since 2005:
- On completeness of epistemic theories. The Bulletin of Symbolic Logic, vol. 24, No. 2, 2018 (joint with S. Artemov).
- On completeness of epistemic theories. 2017 European Summer Meeting of the Association for Symbolic Logic (Logic Colloquium’17), Stockholm University, Abstracts, 2017 (joint with S. Artemov).
- Provability. Explicit proofs. Reflection. The Bulletin of Symbolic Logic, vol. 22, No. 3, 2016.
- On Explicit-Implicit Reflection Principles. The Bulletin of Symbolic Logic, vol. 21, No. 1, 2015.
- On Logic of Formal Provability and Explicit Proofs. arXiv:1405.2559, pp. 1-15, 2014.
- On a Hierarchy of Reflection Principles in Peano Arithmetic. arXiv:1405.2558, pp. 1-13, 2014.
- Symmetric Logic of Proofs and Provability. 2010 Spring AMS Eastern Sectional Meeting May 22-23, 2010 New Jersey Institute of Technology, Newark, NJ, 2010.
- Logic of Strong Provability and Explicit Proofs. The Bulletin of Symbolic Logic, v. 15, no.1, 2009.
- The Topology of Justification. Logic and Logical Philosophy, v. 17, no.1-2, pp. 59-71, the Nicolaus Copernicus University Press, 2008 (joint with S. Artemov).
- Topological Semantics of Justification Logic. Lecture Notes in Computer Science, v. 5010, pp. 30-39, Springer, 2008 (joint with S. Artemov).
- Epistemic Completeness of GLA. The Bulletin of Symbolic Logic, v. 13, no. 3, 2007.
- On Logic of Proofs and Provability. The Bulletin of Symbolic Logic, v. 12, no. 2, 2006.
- Introducing Justification into Epistemic Logic. Journal of Logic and Computation, Oxford University Press, v. 15, pp. 1059-1073, 2005 (joint with S. Artemov).,
- On Epistemic Logic with Justification. Theoretical Aspects of Rationality and Knowledge. Proceedings of TARK 2005, Singapore, pp. 279-294, 2005 (joint with S. Artemov).
- E. Nogina , Basic epistemic logics with justifications. Technical Report TR-2005004, CUNY Ph.D. Program in Computer Science, pp. 1-17, 2005 (joint with S. Artemov).

INVITED LECTURES and TALKS (since 2005):

- Shanin 100
**—**Conference of The*Euler*International Mathematical Institute, St. Petersburg, May 2019. - Conference Operations, Sets and Types (OST18), University of Bern, Switzerland, March 2018.
- 2015 European Summer Meeting of the Association for Symbolic Logic (Logic Colloquium’15) Helsinki, Finland, August 2015.
- The conference Proof Theory, Modal Logic and Reflection, ITAM, Mexico-City, October 2014.
- The Computational Logic Seminar, CUNY Graduate Center, November 2013.
- Academia Sinica, Taipei, Taiwan. October, 2013.
- National Chung Cheng University, Taiwan. October 2013.
- Kobe University, Japan. March 2013.
- Nihon University, Tokyo, Japan. March 2013
- Symposium on Proof Theory and Constructivism, University of Leeds, UK, July 2009 (joint with S. Artemov).
- International Workshop on Topological Methods in Logic, Tbilisi, Georgia, June 2008 (joint with S. Artemov).
- Swiss — South-African Workshop on Logic and Information, University of Bern, Switzerland, January 2007.
- The University of Paris 12, France, May 2006 (joint with S. Artemov).
- The University of Athens, January 2006 (joint with S. Artemov).
- Universita degli Studi di Siena, Dipartimento di Scienze Matematiche e Informatiche 4 R. Magari, July 2005 (joint with S. Artemov).
- Ludwig Maximilian University, Munich, January 2005 (joint with S. Artemov).
- The London Logic Forum, King s College London, January 2005 (joint with S. Artemov).

## Honors, Awards and Affiliations

- 2008-2011, National Science Foundation Award, Division of Computing and Communication Foundations, co-PI
- 2010-2011 and 2015-2016, BMCC Faculty Publications Program awards
- 2004-2005 and 2006-2007, CUNY Community College Collaborative Incentive Research Grants, PI
- 2005-2011, six PSC-CUNY Research Awards, PI
- 2010-2014, four PSC-CUNY in-service awards, the Mathematics Panel Chair of the University Committee on Research Awards