Nikolai A. Krylov

My education and experience:
B.S. and M.S. in Mathematics, St. Petersburg State University, St. Petersburg, Russia 1993
Ph.D. in Mathematics, University of Illinois at Chicago, Chicago IL 2002

I joined the faculty of Siena College in 2005 after a 3-year visiting instructor position at International University Bremen (now known as Jacobs University Bremen) in Germany.

My Siena Experience

My Teaching Philosophy

I strongly believe that a good teacher has to understand and respect students in order to facilitate active learning and to reach every person in the class.

What I Love About Siena

I have a passion for mathematics and I love teaching it. Siena’s small learning community emphasizing dynamic faculty-student interaction creates a unique social environment where I find ample opportunities for my personal professional growth as a teacher and as a mathematician.

My Favorite Courses to Teach

Multivariable calculus (MATH 210), Foundations of Mathematics (MATH 301), Introduction to Number Theory (MATH 340), Differential Geometry (MATH 425), Topology (MATH 460), and Independent Study in Mathematics (MATH 499).

My Professional Experience

Articles & Book Reviews

• Permutations with a distinct divisor property.
  International Electronic Journal of Algebra, vol. 29
  2021
• Complete generalized Fibonacci sequences modulo primes
  Moscow Journal of Combinatorics and Number Theory, vol. 9
  2020
• On the subgroup generated by solutions of Pell's equation
  Journal of Number Theory, vol. 194
  January, 2019
• A BASIS OF THE GROUP OF PRIMITIVE ALMOST PYTHAGOREAN TRIPLES
  Journal of Algebra, Number Theory: Advances and Applications, vol. 16
  2016
• A congruence property of irreducible Laguerre polynomials in two variables
  INTEGERS (Electronic Journal of Combinatorial Number Theory), vol. 16
  2016
• The group of primitive almost Pythagorean triples
  INVOLVE Journal, vol. 6
  2013
• Dynamics of folds in the plane
  College Mathematics Journal, vol. 42
  2011
• Folding Noneuclidean Strips of Paper
  Mathematics Magazine, vol. 84
  2011
• Angle Contraction between geodesics
  Journal of Dynamical Systems and geometric Theories, vol. 8
  2010
• Zeta[n] via hyperbolic functions
  INVOLVE Journal, vol. 3
  2010
• Pseudo-isotopy classes of diffeomorphisms of the unknotted pairs (Sn+2, Sn) and (S2p+2, Sp x Sp)
  Illinois Journal of Mathematics, vol. 51
  2007
• Relative mapping class group of the trivial and the tangent disk bundles over the sphere
  Pure and Applied Mathematics Quarterly, vol. 3
  2007
• Kernel of the variation operator and periodicity of open books
  Topology and its Applications, vol. 148
  2005
• On the Jacobi group and the mapping class group of S3 × S3
  Transactions of the American Mathematical Society, vol. 355
  2003

Awards & Distinctions

• Almost Pythagorean Triples and Quadratic Numbers 

  
  Category: Research
  SiENA COLLEGE, 2016
•  Group structure on the set of solutions of a certain quadratic Diophantine equation.
  Category: Research
  SIENA COLLEGE, 2015
•  Connected derivatives of a polynomial.
  Category: Research
  SIENA COLLEGE, 2014
•  Generators of the Group of Primitive Almost Pythagorean Triples.
  Category: Research
  SIENA COLLEGE, 2013
•  The Groups of Almost Pythagorean Triples.
  Category: Research
  SIENA COLLEGE, 2011
•  Knots as disjoint segments on surface plane models.
  Category: Research
  SIENA COLLEGE, 2010
•  Multiple integrals and values of the Riemann's zeta function.
  Category: Research
  SIENA COLLEGE, 2009
• Convergence between two lines and the triangle at infinity.
  Category: Research
  SIENA COLLEGE, 2008
• Student Research Fellowship
  Category: Other
  University Fellowship, University of Illinois at Chicago, 2000
• Student Research Fellowship
  Category: Other
  University Fellowship, University of Illinois at Chicago, 1999
• B.S. Diploma with Honors
  Category: Other
  St. Petersburg State University, Russia, 1993

Presentations

• Multivariable Laguerre polynomials vs. classical Laguerre polynomials
  2017
  Skidmore College Mathematics Colloquium, Saratoga Springs, New York
• On the subgroup generated by solutions of Pell's equation and elements of order 2 in the corresponding quotient group
  2017
  AMS/MAA Joint Meetings, Atlanta, Georgia
• Algebraic groups of solutions of two Diophantine equations a2 + mb2 = c2 and x2 - my2 = 1
  2016
  Siena Mathematics Colloquium, Loudonville, New York
• On the subgroup generated by solutions of Pell's equation and elements of order 2 in the corresponding quotient group
  2016
  Meeting of the Seaway Section of the Mathematical Association of America, Rochester, New York
• Multivariable Laguerre polynomials irreducible over the rationals
  2015
  Conversations in mathematics at RIT, Rochester, New York
• A basis of the group of primitive almost Pythagorean triples
  2014
  AMS/MAA Joint Meetings, Baltimore, Maryland
• A congruence property of irreducible Laguerre polynomials in two variables
  2014
  MAA Seaway Section Meeting, Alfred, New York
• What happened when we tried to find the half-derivative of a polynomial
  2014
  Siena College Mathematics Colloquium, Loudonville, New York
• Bachet's equation: From Diophantus to modern times
  2012
  Siena College Mathematics Colloquium, Loudonville, New York
• What do Pythagorean triangles and daisies have in common?
  2011
  Siena College Mathematics Colloquium, Loudonville, New York
• Dynamics of simple folds in a plane
  2009
  Siena College Mathematics Colloquium, Loudonville, New York
• Dynamics of simple folds in a plane
  2008
  AMS central section fall meeting, Middletown, Connecticut
• On extension of diffeomorphisms of an n-manifold M embedded into (n+2)-sphere
  2007
  Topology Research Seminar at Dartmouth College, Dartmouth, New Hampshire
• The relative mapping class group of the tangent disk bundle over the standard n-sphere
  2007
  MAA Seaway Section Meeting, Oneonta, New York
• Pseudo-isotopy classes of diffeomorphisms of the unknotted pairs (Sn+2, S^n) and (S2p+2, Sp x Sp)
  2006
  AMS central section spring meeting, Durham, New Hampshire
• Relative mapping class group of Sp x Dq
  2005
  American Mathematical Society and Mathematical Association of America Annual Meeting, Atlanta, Georgia
• Periodicity of open books via mapping class groups
  2004
  Mathematics Seminar at University of Goettingen Mathematics Institute, Goettingen, Germany
• On the relative mapping class groups and manifolds with simple open book decompositions
  2003
  Joint India AMS Mathematics Meeting, Bangalore, India
• On the Jacobi group and the mapping class group of Sk x Sk
  2002
  International University Bremen Mathematics Colloquium, Bremen, Germany
• On the Jacobi group and the mapping class group of S3 x S3
  2001
  AMS central section spring meeting, Irvine, California