MATH 501 Analysis I |
3 Credits |
Lebesgue measure and integration on the line. Convergence
theorems. General measure and integration. Lp spaces.
Decomposition of measures. Radon Nikodym theorem. Product
measures and Fubini's theorem.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2023-2024 |
Analysis I |
3 |
Fall 2022-2023 |
Analysis I |
3 |
Fall 2021-2022 |
Analysis I |
3 |
Fall 2020-2021 |
Analysis I |
3 |
Fall 2019-2020 |
Analysis I |
3 |
Fall 2018-2019 |
Analysis I |
3 |
Fall 2017-2018 |
Analysis I |
3 |
Fall 2016-2017 |
Analysis I |
3 |
Fall 2015-2016 |
Analysis I |
3 |
Fall 2014-2015 |
Analysis I |
3 |
Fall 2013-2014 |
Analysis I |
3 |
Fall 2012-2013 |
Analysis I |
3 |
Fall 2011-2012 |
Analysis I |
3 |
Fall 2010-2011 |
Analysis I |
3 |
Fall 2009-2010 |
Analysis I |
3 |
Fall 2008-2009 |
Analysis I |
3 |
Fall 2007-2008 |
Analysis I |
3 |
Fall 2006-2007 |
Analysis I |
3 |
Fall 2005-2006 |
Analysis I |
3 |
Fall 2004-2005 |
Analysis I |
3 |
Fall 2003-2004 |
Analysis I |
3 |
Spring 2002-2003 |
Analysis I |
3 |
Fall 2001-2002 |
Analysis I |
3 |
Fall 1999-2000 |
Analysis I |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 502 Analysis II |
3 Credits |
Metric spaces and general topological spaces. Connectedness,
compactness, completeness and consequences. Baire
category theorem. Linear topological spaces.
Open mapping, closed graph theorems. Hahn Banach
theorem. Hilbert and Banach spaces.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2023-2024 |
Analysis II |
3 |
Spring 2022-2023 |
Analysis II |
3 |
Spring 2021-2022 |
Analysis II |
3 |
Spring 2020-2021 |
Analysis II |
3 |
Spring 2019-2020 |
Analysis II |
3 |
Spring 2018-2019 |
Analysis II |
3 |
Spring 2017-2018 |
Analysis II |
3 |
Spring 2016-2017 |
Analysis II |
3 |
Spring 2015-2016 |
Analysis II |
3 |
Spring 2013-2014 |
Analysis II |
3 |
Spring 2012-2013 |
Analysis II |
3 |
Spring 2009-2010 |
Analysis II |
3 |
Spring 2008-2009 |
Analysis II |
3 |
Spring 2005-2006 |
Analysis II |
3 |
Spring 2003-2004 |
Analysis II |
3 |
Fall 2001-2002 |
Analysis II |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 503 Functional Analysis and Applications |
3 Credits |
Examples of Hilbert and Banach spaces, geometry of the
Banach space. Linear functionals. Hahn Banach theorem, its
versions and applications. Convexity, Krein Milman theorem.
Applications of uniform boundedness principle,
closed graph and open mapping theorems. Fixed point
theorems (Banach, Brouwer, Schauder) and applications.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2007-2008 |
Functional Analysis and Applications |
3 |
Spring 2006-2007 |
Functional Analysis and Applications |
3 |
Spring 2004-2005 |
Functional Analysis and Applications |
3 |
Spring 2003-2004 |
Functional Analysis and Applications |
3 |
Spring 1999-2000 |
Functional Analysis and Applications |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 504 Banach Algebras and Spectral Theory |
3 Credits |
Basic Banach algebra theory. Commutative Banach algebras.
Commutative C* algebras and Gelfand representation theorem.
Spectral mapping theorem. Linear operators on a
Banach space. Compact operators. Spectral theory
for compact and normal operators. Fredholm theory.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2010-2011 |
Banach Algebras and Spectral Theory |
3 |
Spring 2005-2006 |
Banach Algebras and Spectral Theory |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 505 Complex Analysis |
3 Credits |
Analytic functions, Cauchy Riemann equations, conformal
mappings. Cauchy integral formula. Power series and Laurent
expansion. Residue theorem and its applications.
Infinite products and Weierstarss theorem. Global
properties of analytic functions, analytic continuation.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2021-2022 |
Complex Analysis |
3 |
Fall 2019-2020 |
Complex Analysis |
3 |
Spring 2017-2018 |
Complex Analysis |
3 |
Spring 2016-2017 |
Complex Analysis |
3 |
Fall 2015-2016 |
Complex Analysis |
3 |
Fall 2014-2015 |
Complex Analysis |
3 |
Spring 2012-2013 |
Complex Analysis |
3 |
Spring 2011-2012 |
Complex Analysis |
3 |
Spring 2010-2011 |
Complex Analysis |
3 |
Fall 2009-2010 |
Complex Analysis |
3 |
Fall 2008-2009 |
Complex Analysis |
3 |
Fall 2007-2008 |
Complex Analysis |
3 |
Fall 2005-2006 |
Complex Analysis |
3 |
Fall 2003-2004 |
Complex Analysis |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 506 Introduction to Fréchet Spaces |
3 Credits |
Locally convex topological spaces, duality theory,
inductive and projective limits of normed spaces,
Fréchet spaces and their duals, epimorphism
theorem, generalized Mittag-Leffler procedure.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2008-2009 |
Introduction to Fréchet Spaces |
3 |
|
Prerequisite: (MATH 501 - Masters - Min Grade D |
or MATH 501 - Doctorate - Min Grade D) |
and (MATH 502 - Masters - Min Grade D |
or MATH 502 - Doctorate - Min Grade D) |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 507 Topology |
3 Credits |
Fundamental concepts, subbasis, neighborhoods, continuous
functions, subspaces, product spaces and quotient
spaces, weak topologies and embedding theorem, convergence
by nets and filters, separation and countability,
compactness, local compactness and compactifications,
paracompactness, metrization, complete metric spaces and
Baire category theorem, connectedness
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2007-2008 |
Topology |
3 |
Fall 2006-2007 |
Topology |
3 |
Fall 2004-2005 |
Topology |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 508 Introduction to Complex Dynamics |
3 Credits |
Introduction to Riemann surfaces. Universal coverings
and Poincare metrics. Normal families. Iterated
holomorphic mappings. Fatou and Julia sets. Dynamics
on Riemann surfaces, hyperbolic and Euclidean
surfaces. Local fixed point theory. Periodic points.
Attracting and repelling cycles. Polynomial
dynamics. Mandelbrot sets and fractals.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2007-2008 |
Introduction to Complex Dynamics |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 509 Hardy Spaces and Operator Theory |
3 Credits |
Hardy Spaces, Hp Spaces, factorization of Hp functions,
Banach spaces, the Müntz-Szasz theorem,
singular inner functions, outer functions, composition
operators and their spectra, Toeplitz operators
and their spectra.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2010-2011 |
Hardy Spaces and Operator Theory |
3 |
Fall 2008-2009 |
Hardy Spaces and Operator Theory |
3 |
|
Prerequisite: MATH 505 - Doctorate - Min Grade D |
or MATH 505 - Masters - Min Grade D |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 510 Fréchet Spaces |
3 Credits |
Epimorphism theorem, examples and
applications, generalized Mittag-Leffler
procedure, the functor proj, the functor
ext and applications to the
structure theory of Fréchet Spaces
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2008-2009 |
Fréchet Spaces |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 511 Algebra I |
3 Credits |
Introduction to group theory. Isomorphism theorems.
Permutation groups and Cayley's theorem. Conjugacy
classes. Lagrange's theorem and the Sylow theorems.
principle ideal domains. Polynomial ring.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2023-2024 |
Algebra I |
3 |
Fall 2022-2023 |
Algebra I |
3 |
Fall 2021-2022 |
Algebra I |
3 |
Fall 2020-2021 |
Algebra I |
3 |
Fall 2019-2020 |
Algebra I |
3 |
Fall 2018-2019 |
Algebra I |
3 |
Fall 2017-2018 |
Algebra I |
3 |
Fall 2016-2017 |
Algebra I |
3 |
Fall 2015-2016 |
Algebra I |
3 |
Fall 2014-2015 |
Algebra I |
3 |
Fall 2013-2014 |
Algebra I |
3 |
Fall 2012-2013 |
Algebra I |
3 |
Fall 2011-2012 |
Algebra I |
3 |
Fall 2010-2011 |
Algebra I |
3 |
Fall 2009-2010 |
Algebra I |
3 |
Fall 2008-2009 |
Algebra I |
3 |
Fall 2007-2008 |
Algebra I |
3 |
Fall 2006-2007 |
Algebra I |
3 |
Fall 2005-2006 |
Algebra I |
3 |
Fall 2004-2005 |
Algebra I |
3 |
Fall 2003-2004 |
Algebra I |
3 |
Fall 2001-2002 |
Algebra I |
3 |
Fall 1999-2000 |
Algebra I |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 512 Algebra II |
3 Credits |
Modules. Fields, extension fields, Galois theory. Categories
and functors.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2023-2024 |
Algebra II |
3 |
Spring 2022-2023 |
Algebra II |
3 |
Spring 2021-2022 |
Algebra II |
3 |
Spring 2020-2021 |
Algebra II |
3 |
Spring 2019-2020 |
Algebra II |
3 |
Spring 2018-2019 |
Algebra II |
3 |
Spring 2017-2018 |
Algebra II |
3 |
Spring 2016-2017 |
Algebra II |
3 |
Spring 2015-2016 |
Algebra II |
3 |
Spring 2014-2015 |
Algebra II |
3 |
Spring 2013-2014 |
Algebra II |
3 |
Spring 2012-2013 |
Algebra II |
3 |
Spring 2011-2012 |
Algebra II |
3 |
Spring 2010-2011 |
Algebra II |
3 |
Spring 2009-2010 |
Algebra II |
3 |
Spring 2008-2009 |
Algebra II |
3 |
Spring 2007-2008 |
Algebra II |
3 |
Spring 2005-2006 |
Algebra II |
3 |
Spring 2004-2005 |
Algebra II |
3 |
Spring 2003-2004 |
Algebra II |
3 |
Spring 2001-2002 |
Algebra II |
3 |
Fall 2001-2002 |
Algebra II |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 513 Group Theory |
3 Credits |
Basic constructions with groups: direct,
semidirect products, projective limits;
finitely generated abelian groups, free
groups, solvable and nilpotent groups,
divisible groups, permutation groups, linear
groups, group representations.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2008-2009 |
Group Theory |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 514 Finite Fields and Applications I |
3 Credits |
Characterization of finite fields, roots of irreducible
polynomials, traces, norms, and bases, representation of
elements of finite fields. Order of polynomials,
irreducible polynomials and their construction.
Factorization of polynomials. Linear recurring sequences.
Introduction to applications of finite fields; algebraic
coding theory and cryptology.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2023-2024 |
Finite Fields and Applications I |
3 |
Fall 2021-2022 |
Finite Fields and Applications I |
3 |
Fall 2016-2017 |
Finite Fields and Applications I |
3 |
Spring 2014-2015 |
Finite Fields and Applications I |
3 |
Spring 2012-2013 |
Finite Fields and Applications I |
3 |
Fall 2011-2012 |
Finite Fields and Applications I |
3 |
Fall 2010-2011 |
Finite Fields and Applications I |
3 |
Fall 2009-2010 |
Finite Fields and Applications I |
3 |
Spring 2005-2006 |
Finite Fields and Applications I |
3 |
Spring 2004-2005 |
Finite Fields and Applications I |
3 |
Fall 2002-2003 |
Finite Fields and Applications I |
3 |
Fall 2001-2002 |
Finite Fields and Applications I |
3 |
Spring 2000-2001 |
Finite Fields and Applications I |
3 |
Spring 1999-2000 |
Finite Fields and Applications I |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 515 Finite Fields and Applications II |
3 Credits |
Normal bases, arithmetic in normal bases representation, the
complexity of normal basis. Dual bases, self-dual
bases, existence of self-dual normal
bases, Characters and Gaussian sums, primitive
elements with prescribed trace. The discrete
logarithm problem. Elliptic curves over finite fields.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2001-2002 |
Finite Fields and Applications II |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 519 Algebraic Number Theory |
3 Credits |
Contents: The aim of the course is to give an introduction
to the basic concepts of algebraic number theory.
Following topics will be covered: algebraic number fields,
rings of integers in number fields, integral bases,
discriminants, unique factorization of ideals and
Dedekind domains, ideal class group and class number,
structure of the group of units (Dirichlet´s theorem),
ramification of prime ideals in extensions of number fields.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2022-2023 |
Algebraic Number Theory |
3 |
Fall 2021-2022 |
Algebraic Number Theory |
3 |
Fall 2018-2019 |
Algebraic Number Theory |
3 |
Fall 2016-2017 |
Algebraic Number Theory |
3 |
Spring 2012-2013 |
Algebraic Number Theory |
3 |
Fall 2009-2010 |
Algebraic Number Theory |
3 |
Fall 2003-2004 |
Algebraic Number Theory |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 522 Partial Differential Equations |
3 Credits |
Linear and quasilinear first order equations, main concepts.
The Cauchy Kowalevski theorem. Classification. Initial
and/or boundary value problems. The concept of a well posed
problem. Basic techniques and existence-uniqueness
theorems for hyperbolic, elliptic and parabolic equations.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2020-2021 |
Partial Differential Equations |
3 |
Spring 2012-2013 |
Partial Differential Equations |
3 |
Spring 2010-2011 |
Partial Differential Equations |
3 |
Spring 2008-2009 |
Partial Differential Equations |
3 |
Fall 2005-2006 |
Partial Differential Equations |
3 |
Fall 2000-2001 |
Partial Differential Equations |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 523 Riemann Surfaces |
3 Credits |
Riemann surfaces. Coverings, Homotopy, Fundamental group.
Universal coverings. Sheaves. Algebraic functions.
Differantial forms. Cohomogies. Theorems of Dolbeault and
de Rham. Riemann-Roch theorem.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2019-2020 |
Riemann Surfaces |
3 |
Spring 2014-2015 |
Riemann Surfaces |
3 |
Fall 2013-2014 |
Riemann Surfaces |
3 |
Fall 2011-2012 |
Riemann Surfaces |
3 |
Spring 2009-2010 |
Riemann Surfaces |
3 |
|
Prerequisite: MATH 505 - Masters - Min Grade D |
or MATH 505 - Doctorate - Min Grade D |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 524 Probability Theory |
3 Credits |
Semi-algebras and sigma-algebras of events,
Kolmogorov?s axioms of probability, consequences
thereof, probability spaces, measurability, random
variables as measurable mappings, random vectors,
probability measures induced on Borel sigma-algebras by
random vectors, distributions and distribution functions,
extension of probability measure starting by
semi-algebras, mathematical expectation, expected values
of non-negative simple, non-negative and general
random variables, properties, conditional distributions
and independence, Borel-Cantelli lemma, conditional
expectation given a sub sigma-algebra,
Radon-Nikodym theorem, different modes of convergence,
almost sure convergence, convergence in
probability, convergence in L^p, convergence in
distribution, different implications between them,
characteristic functions, inversion formulas, relation
to convergence concepts, the weak and the strong
law of large numbers, central limit theorem.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2018-2019 |
Probability Theory |
3 |
Fall 2017-2018 |
Probability Theory |
3 |
Fall 2010-2011 |
Probability Theory |
3 |
Fall 2009-2010 |
Probability Theory |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 525 Compact Riemann Surfaces |
3 Credits |
The following topics will be covered:
introductory notions, cohomology groups,
Dolbeault’s Lemma, Finiteness Theorem, exact cohomology
sequences, Riemann-Roch Theorem, Serre Duality
Theorem, functions and forms with prescribed
principal parts, Abel’s Theorem, Jacobi’s Inversion Problem.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2013-2014 |
Compact Riemann Surfaces |
3 |
|
Prerequisite: MATH 505 - Doctorate - Min Grade D |
or MATH 505 - Masters - Min Grade D |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 526 Projective Geometry |
3 Credits |
Homogeneous coordinates, projective spaces, the
principle of duality, projective planes and the
configurations of Desargues and Pappus, collineations
and correlations, perspectivities, the projective groups,
polarities, algebraic varieties, classical polar spaces,
Plücker coordinates, the Klein quadric,
Segre varieties, Veronese varieties.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2021-2022 |
Projective Geometry |
3 |
Fall 2020-2021 |
Projective Geometry |
3 |
Fall 2019-2020 |
Projective Geometry |
3 |
Fall 2017-2018 |
Projective Geometry |
3 |
Fall 2016-2017 |
Projective Geometry |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 527 Finite Geometry |
3 Credits |
Ovals and Ovoids, Arcs and Caps, Blocking sets, Linear
Sets, Translation Planes, Semifields, Generalized
Polygons. Applications in coding theory and
cryptography.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2019-2020 |
Finite Geometry |
3 |
|
Prerequisite: (MATH 511 - Doctorate - Min Grade D |
or MATH 511 - Masters - Min Grade D) |
and (MATH 526 - Doctorate - Min Grade D |
or MATH 526 - Masters - Min Grade D) |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 531 Introduction to Cryptography |
3 Credits |
Complexity of calculations. Public key cryptography,
RSA, discrete logarithm, Diffie-Hellman problem, stream
ciphers, knapsack. Primality and factoring. Elliptic curve
cryptosystems.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2013-2014 |
Introduction to Cryptography |
3 |
Spring 2000-2001 |
Introduction to Cryptography |
3 |
Spring 1999-2000 |
Introduction to Cryptography |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 532 Introduction to Coding Theory |
3 Credits |
Linear codes, some good codes, bounds on codes,
cyclic codes, Goppa codes, algebraic geometry codes.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2020-2021 |
Introduction to Coding Theory |
3 |
Spring 2017-2018 |
Introduction to Coding Theory |
3 |
Fall 2012-2013 |
Introduction to Coding Theory |
3 |
Spring 2005-2006 |
Introduction to Coding Theory |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 541 Introduction to Algebraic Geometry |
3 Credits |
Algebraic varieties, affine and projective varieties,
dimensions of varieties, singular points, divisors,
differentials, intersections. Schemes, cohomology,
curves and surfaces, varieties over the complex numbers.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2018-2019 |
Introduction to Algebraic Geometry |
3 |
Spring 2015-2016 |
Introduction to Algebraic Geometry |
3 |
Fall 2013-2014 |
Introduction to Algebraic Geometry |
3 |
Spring 2008-2009 |
Introduction to Algebraic Geometry |
3 |
Spring 2002-2003 |
Introduction to Algebraic Geometry |
3 |
Fall 2002-2003 |
Introduction to Algebraic Geometry |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 542 Algebraic Curves |
3 Credits |
Plane curves, affine and projective varieties, intersection
of curves, Bezout's theorem, analysis of singularities,
Riemann Roch theorem.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2021-2022 |
Algebraic Curves |
3 |
Fall 2019-2020 |
Algebraic Curves |
3 |
Fall 2017-2018 |
Algebraic Curves |
3 |
Fall 2007-2008 |
Algebraic Curves |
3 |
Spring 2002-2003 |
Algebraic Curves |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 543 Elliptic Curves |
3 Credits |
Weierstrass equations, group law, isogenies, Tate
module, Weil pairing, endomorphism ring.
Zeta function of an elliptic curve, Weil conjectures.
Uniformization theorem. Elliptic curves over local
fields. Mordell-Weil theorem. Siegel's theorem.
Modular curves and L-series.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2020-2021 |
Elliptic Curves |
3 |
Spring 2018-2019 |
Elliptic Curves |
3 |
Spring 2003-2004 |
Elliptic Curves |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 544 Class Field Theory |
3 Credits |
General class field theory, local class field theory,Hilbert
symbols, Kummer extensions, class field axiom, global class
fields, zeta functions and L-series.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2001-2002 |
Class Field Theory |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 545 Representation Theory |
3 Credits |
Basic notions on representation theory. Language of
abelian categories: Grothendieck groups, projective
modules. Theory of blocks. Lifting of characteristic p
representations to characteristic 0 virtual representations.
Fong-Swan Theorem. Applications to the Artin representations
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2004-2005 |
Representation Theory |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 546 Commutative Algebra -1 |
3 Credits |
It is an introductory course on commutative algebra,
based on the book of M. F. Atiyah and I. G.
Macdonald, titled “Introduction to commutative
algebra”. This course aims to cover the following
topics.
1. Rings and ideals
2. Rings and Modules of fractions
3. Primary decomposition
4. Integral Dependence and valuations
5. Noether Normalization
6. Chain conditions
7. Noetherian and Artinian rings
8. The Nullstellensatz and Spec of a ring
9. Zariski topology on Spec of a ring
10. Graded rings and modules
11. Dimension theory
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2022-2023 |
Commutative Algebra -1 |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 547 Commutative Algebra 2 |
3 Credits |
This course explores homological theory
of commutative rings and aims to cover
the following topics:
1. Commutative rings and modules
2. Localization and Spec of a ring
3. Completions and Artin Rees Lemma
4. Graded rings, Hilbert function and the Samuel function
5. System of parameters and multiplicity
6. Regular sequences and depth
7. Koszul Complexes
8. Cohen-Macaulay rings and modules
9. Gorenstien rings
10. Regular rings
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2022-2023 |
Commutative Algebra 2 |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 551 Graduate Seminar 1 |
0 Credit |
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2023-2024 |
Graduate Seminar 1 |
0 |
Fall 2023-2024 |
Graduate Seminar 1 |
0 |
Fall 2022-2023 |
Graduate Seminar 1 |
0 |
Spring 2021-2022 |
Graduate Seminar 1 |
0 |
Fall 2021-2022 |
Graduate Seminar 1 |
0 |
Spring 2020-2021 |
Graduate Seminar 1 |
0 |
Fall 2020-2021 |
Graduate Seminar 1 |
0 |
Spring 2019-2020 |
Graduate Seminar 1 |
0 |
Fall 2019-2020 |
Graduate Seminar 1 |
0 |
Spring 2018-2019 |
Graduate Seminar 1 |
0 |
Fall 2018-2019 |
Graduate Seminar 1 |
0 |
Fall 2017-2018 |
Graduate Seminar 1 |
0 |
Spring 2016-2017 |
Graduate Seminar 1 |
0 |
Fall 2016-2017 |
Graduate Seminar 1 |
0 |
Fall 2015-2016 |
Graduate Seminar 1 |
0 |
Fall 2014-2015 |
Graduate Seminar 1 |
0 |
Fall 2013-2014 |
Graduate Seminar 1 |
0 |
Fall 2012-2013 |
Graduate Seminar 1 |
0 |
Fall 2011-2012 |
Graduate Seminar 1 |
0 |
Fall 2010-2011 |
Graduate Seminar 1 |
0 |
Fall 2009-2010 |
Graduate Seminar 1 |
0 |
Fall 2008-2009 |
Graduate Seminar 1 |
0 |
Fall 2007-2008 |
Graduate Seminar 1 |
0 |
Fall 2006-2007 |
Graduate Seminar 1 |
0 |
Fall 2005-2006 |
Graduate Seminar 1 |
0 |
Fall 2004-2005 |
Graduate Seminar 1 |
0 |
Fall 2003-2004 |
Graduate Seminar 1 |
0 |
Fall 2001-2002 |
Graduate Seminar 1 |
0 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 1 ECTS (1 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 552 Graduate Seminar II |
0 Credit |
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2022-2023 |
Graduate Seminar II |
0 |
Spring 2021-2022 |
Graduate Seminar II |
0 |
Fall 2016-2017 |
Graduate Seminar II |
0 |
Spring 2014-2015 |
Graduate Seminar II |
0 |
Spring 2013-2014 |
Graduate Seminar II |
0 |
Spring 2012-2013 |
Graduate Seminar II |
0 |
Spring 2011-2012 |
Graduate Seminar II |
0 |
Spring 2010-2011 |
Graduate Seminar II |
0 |
Spring 2009-2010 |
Graduate Seminar II |
0 |
Spring 2008-2009 |
Graduate Seminar II |
0 |
Spring 2007-2008 |
Graduate Seminar II |
0 |
Spring 2005-2006 |
Graduate Seminar II |
0 |
Spring 2002-2003 |
Graduate Seminar II |
0 |
Spring 2001-2002 |
Graduate Seminar II |
0 |
Spring 2000-2001 |
Graduate Seminar II |
0 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 1 ECTS (1 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 555 Proofs from the Notebook |
3 Credits |
The aim of this course is to introduce a selection
of proofs of some important theorems.
These proofs require moderate background but
high ingenuity. Among the topics are:
Division algorithm, prime factorization theorem,
some primitive results on the distribution of primes.
Greatest common divisor. Euler's totient function.
Phytagorean triples. A short survey of metric
spaces; continuity, compactness, connectedness.
Stone- Weierstrass approximation theorem.
Geometry of the sphere. Brouwer fixed point
theorem. Borsuk's antipodal mapping theorem.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2020-2021 |
Proofs from the Notebook |
3 |
Fall 2014-2015 |
Proofs from the Notebook |
3 |
Fall 2013-2014 |
Proofs from the Notebook |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 561 Algebraic Combinatorics |
3 Credits |
Group representations, representations of the symmetric
group, combinatorial algorithms, symmetric
functions, ordinary partitions, Young tableaux,
plane partitions and applications in other enumerative
problems.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2021-2022 |
Algebraic Combinatorics |
3 |
Spring 2016-2017 |
Algebraic Combinatorics |
3 |
Fall 2012-2013 |
Algebraic Combinatorics |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 571 Introduction to Mathematical Analysis |
3 Credits |
The least upper bound property in R, equivalents and
consequences. Metric spaces. Completeness, compactness,
connectedness. Functions,continuity. Sequences and series of
functions. Contraction mapping theorem and applications to
calculus: Inverse and implicit function theorems.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2023-2024 |
Introduction to Mathematical Analysis |
3 |
Fall 2022-2023 |
Introduction to Mathematical Analysis |
3 |
Fall 2021-2022 |
Introduction to Mathematical Analysis |
3 |
Fall 2020-2021 |
Introduction to Mathematical Analysis |
3 |
Fall 2019-2020 |
Introduction to Mathematical Analysis |
3 |
Fall 2017-2018 |
Introduction to Mathematical Analysis |
3 |
Fall 2016-2017 |
Introduction to Mathematical Analysis |
3 |
Fall 2015-2016 |
Introduction to Mathematical Analysis |
3 |
Fall 2014-2015 |
Introduction to Mathematical Analysis |
3 |
Fall 2013-2014 |
Introduction to Mathematical Analysis |
3 |
Fall 2012-2013 |
Introduction to Mathematical Analysis |
3 |
Fall 2011-2012 |
Introduction to Mathematical Analysis |
3 |
Fall 2010-2011 |
Introduction to Mathematical Analysis |
3 |
Fall 2009-2010 |
Introduction to Mathematical Analysis |
3 |
Fall 2008-2009 |
Introduction to Mathematical Analysis |
3 |
Fall 2007-2008 |
Introduction to Mathematical Analysis |
3 |
Fall 2006-2007 |
Introduction to Mathematical Analysis |
3 |
Fall 2005-2006 |
Introduction to Mathematical Analysis |
3 |
Fall 2023-2024 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2022-2023 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2021-2022 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2020-2021 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2019-2020 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2018-2019 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2017-2018 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2016-2017 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2015-2016 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2014-2015 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2013-2014 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2012-2013 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2011-2012 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2010-2011 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2009-2010 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2008-2009 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2007-2008 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2006-2007 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2005-2006 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2004-2005 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2003-2004 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2002-2003 |
Introduction to Mathematical Analysis (MATH301) |
3 |
Fall 2001-2002 |
Introduction to Mathematical Analysis (MATH301) |
3 |
|
Prerequisite: __ |
Corequisite: MATH 571R |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 571R Introduction to Mathematical Analysis |
0 Credit |
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2023-2024 |
Introduction to Mathematical Analysis |
0 |
Fall 2022-2023 |
Introduction to Mathematical Analysis |
0 |
|
Prerequisite: __ |
Corequisite: MATH 571 |
ECTS Credit: NONE ECTS (NONE ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 572 Introduction to Algebra |
3 Credits |
Basic theory of groups, rings and fields is covered.
Fundamental concepts of Galois Theory are also given.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2023-2024 |
Introduction to Algebra |
3 |
Spring 2020-2021 |
Introduction to Algebra |
3 |
Spring 2017-2018 |
Introduction to Algebra |
3 |
Spring 2016-2017 |
Introduction to Algebra |
3 |
Spring 2014-2015 |
Introduction to Algebra |
3 |
Spring 2012-2013 |
Introduction to Algebra |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 573 Complex Calculus |
3 Credits |
Analytic functions, Cauchy's theorem and the Cauchy integral
formula. Taylor series. Singularities of analytic functions,
Laurent series and the calculus of residues. Infinite
products. Conformal mappings.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2021-2022 |
Complex Calculus |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 574 Partial Differential Equations |
3 Credits |
Classification, the concept of a well-posed problem. Initial
and boundary value problems. Fourier series. The heat
equation, the wave equation and the Laplace equation.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2023-2024 |
Partial Differential Equations |
3 |
Spring 2021-2022 |
Partial Differential Equations |
3 |
Fall 2020-2021 |
Partial Differential Equations |
3 |
Fall 2018-2019 |
Partial Differential Equations |
3 |
Spring 2011-2012 |
Partial Differential Equations |
3 |
Spring 2009-2010 |
Partial Differential Equations |
3 |
Spring 2007-2008 |
Partial Differential Equations |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 575 Introduction to Functional Analysis |
3 Credits |
Uniform convergence. Stone Weierstrass approximation
theorem. Arzela -Ascoli theorem. Baire's theorem.
Vector spaces and linear operators. Normed spaces .
Completion .Duality and Hahn-Banach extension
theorem. Bounded linear operators. Banach-Steinhaus
theorem. Open mapping and closed graph
theorems.Hilbert spaces. Introduction to Banach algebras.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2011-2012 |
Introduction to Functional Analysis |
3 |
Fall 2009-2010 |
Introduction to Functional Analysis |
3 |
Fall 2007-2008 |
Introduction to Functional Analysis |
3 |
|
Prerequisite: MATH 301 - Undergraduate - Min Grade D |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 576 Integration |
3 Credits |
The Riemann integral. The Riemann-Stieltjes
integral, functions of bounded variation.
Lebesgue integral and convergence theorems.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2013-2014 |
Integration |
3 |
Spring 2008-2009 |
Integration |
3 |
Spring 2007-2008 |
Integration |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 577 Introduction to Stochastic Calculus |
3 Credits |
Basic concepts of stochastic processes, Brownian
motion, Gaussian white noise. Conditional
expectations and their properties, martingale processes.
Stochastic integrals, motivations for the Ito
stochastic integral. Ito stochastic integral for
simple processes and the general case. Ito Lemma and
its different versions. Introduction to stochastic
differential equations (s.d.e.) . Solving the Ito s.d.e.
by the Ito Lemma and the Stratonovich integration.
Homogeneous equations with multiplicative
noise. The general s.d.e. with additive noise.
A short excursion into finance. Option pricing
problem, the Black and Scholes formula.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2010-2011 |
Introduction to Stochastic Calculus |
3 |
Spring 2007-2008 |
Introduction to Stochastic Calculus |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 578 Dynamical Systems |
3 Credits |
Qualitative theory of ordinary differential
equations (ODEs). Existence and uniqueness, geometrical
representation of ODEs. Construction of phase portraits.
Nonlinear systems, local and global behavior, the
linearization theorem. Periodic orbits and limit
sets, Poincare-Bendixson theory. The stable manifold
theorem, homoclinic and heteroclinic
points. Bifurcation diagrams. State reconstruction
from data, embedding.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2022-2023 |
Dynamical Systems |
3 |
Fall 2013-2014 |
Dynamical Systems |
3 |
Spring 2010-2011 |
Dynamical Systems |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 58000 Special Topics in MATH: Commutative Algebra |
3 Credits |
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2020-2021 |
Special Topics in MATH: Commutative Algebra |
3 |
Fall 2019-2020 |
Special Topics in MATH: Commutative Algebra |
3 |
Fall 2017-2018 |
Special Topics in MATH: Commutative Algebra |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 58001 Special Topics in MATH: Partial Differential Equations |
3 Credits |
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2023-2024 |
Special Topics in MATH: Partial Differential Equations |
3 |
Fall 2017-2018 |
Special Topics in MATH: Partial Differential Equations |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 58002 Special Topics in MATH: An Introduction to Homological Algebra |
3 Credits |
1) Categories and functors
2) Modules 3) Tensor products of modules
4) Projective, Injective, Flat modules 5) Localization
6) Homology 7) Tor and Ext
8) Homology and rings
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2020-2021 |
Special Topics in MATH: An Introduction to Homological Algebra |
3 |
Spring 2018-2019 |
Special Topics in MATH: An Introduction to Homological Algebra |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 58003 Special Topics in MATH: Integer partitions and q-series. |
3 Credits |
Integer partitions; q-series, elementary identities
(q-binomial theorem, Heine's transformation,
Jacobi's triple product identity, Ramanujan's
1-psi-1 transformation) and corollaries; q-series as
partition generating functions; Ramanujan's
congruences for the partition function, Rogers-
Ramanujan generalizations.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2022-2023 |
Special Topics in MATH: Integer partitions and q-series. |
3 |
Fall 2018-2019 |
Special Topics in MATH: Integer partitions and q-series. |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 58005 Special Topics in MATH: Wave Theory |
3 Credits |
Wave phenomena; governing equations for wave
models; classifications of the problems, linear and
nonlinear problems; ; hyperbolic waves and
qualitative properties; dispersive waves and
qualitative properties; water waves, linear and
nonlinear theory.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2019-2020 |
Special Topics in MATH: Wave Theory |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 58006 Special Topics in MATH: Introduction to Diophantine equations and function fields |
3 Credits |
The aim of this course is to provide an introduction
into several topics in Algebra, Geometry and Number
Theory, and to point out how they are related to each
other. This should enable students to choose the
direction of their future studies and/or to see their own
research in a wider context. We will not give full
proofs of all results but rather aim to clarify their
relevance.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2019-2020 |
Special Topics in MATH: Introduction to Diophantine equations and function fields |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 590 Master Thesis |
0 Credit |
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2023-2024 |
Master Thesis |
0 |
Fall 2023-2024 |
Master Thesis |
0 |
Spring 2022-2023 |
Master Thesis |
0 |
Fall 2022-2023 |
Master Thesis |
0 |
Spring 2021-2022 |
Master Thesis |
0 |
Fall 2021-2022 |
Master Thesis |
0 |
Spring 2020-2021 |
Master Thesis |
0 |
Fall 2020-2021 |
Master Thesis |
0 |
Spring 2019-2020 |
Master Thesis |
0 |
Fall 2019-2020 |
Master Thesis |
0 |
Spring 2018-2019 |
Master Thesis |
0 |
Fall 2018-2019 |
Master Thesis |
0 |
Spring 2017-2018 |
Master Thesis |
0 |
Fall 2017-2018 |
Master Thesis |
0 |
Spring 2016-2017 |
Master Thesis |
0 |
Fall 2016-2017 |
Master Thesis |
0 |
Spring 2015-2016 |
Master Thesis |
0 |
Fall 2015-2016 |
Master Thesis |
0 |
Spring 2014-2015 |
Master Thesis |
0 |
Fall 2014-2015 |
Master Thesis |
0 |
Spring 2013-2014 |
Master Thesis |
0 |
Fall 2013-2014 |
Master Thesis |
0 |
Spring 2012-2013 |
Master Thesis |
0 |
Fall 2012-2013 |
Master Thesis |
0 |
Spring 2011-2012 |
Master Thesis |
0 |
Fall 2011-2012 |
Master Thesis |
0 |
Spring 2010-2011 |
Master Thesis |
0 |
Fall 2010-2011 |
Master Thesis |
0 |
Spring 2009-2010 |
Master Thesis |
0 |
Fall 2009-2010 |
Master Thesis |
0 |
Spring 2008-2009 |
Master Thesis |
0 |
Fall 2008-2009 |
Master Thesis |
0 |
Spring 2007-2008 |
Master Thesis |
0 |
Fall 2007-2008 |
Master Thesis |
0 |
Spring 2006-2007 |
Master Thesis |
0 |
Fall 2006-2007 |
Master Thesis |
0 |
Spring 2005-2006 |
Master Thesis |
0 |
Fall 2005-2006 |
Master Thesis |
0 |
Spring 2004-2005 |
Master Thesis |
0 |
Fall 2004-2005 |
Master Thesis |
0 |
Spring 2003-2004 |
Master Thesis |
0 |
Fall 2003-2004 |
Master Thesis |
0 |
Spring 2002-2003 |
Master Thesis |
0 |
Fall 2002-2003 |
Master Thesis |
0 |
Spring 2001-2002 |
Master Thesis |
0 |
Fall 2001-2002 |
Master Thesis |
0 |
Spring 2000-2001 |
Master Thesis |
0 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 50 ECTS (50 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 603 Selected Topics in Operator Theory |
3 Credits |
Banach algebras and spectral theory; operators on
Hilbert spaces; the Hardy-Hilbert space; Toeplitz
and composition operators
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2020-2021 |
Selected Topics in Operator Theory |
3 |
Spring 2011-2012 |
Selected Topics in Operator Theory |
3 |
Fall 2007-2008 |
Selected Topics in Operator Theory |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 604 Unbounded Operators in Hilbert Spaces |
3 Credits |
The course is an introduction to the theory
of unbounded operators in Hilbert spaces and
consists of two parts: Part 1 develops the general
theory of unbounded operators. The main topics
here are domains, graphs, adjoint
operators, spectrum, resolvent, symmetric
operators and quadratic forms, symmetric
extensions, deficiency indices, self-adjoint
operators, Cayley transform, Spectral theorem, Stone
theorem. Part 2 is an introduction to the spectral
theory of differential operators (Sturm-Liouville
operators and Hill-Schrödinger operators). The main
topics include domains, spectra localization,
asymptotics of eigenvalues and eigenfunctions,
bases of root functions, convergence of
spectral decompositions.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2022-2023 |
Unbounded Operators in Hilbert Spaces |
3 |
Spring 2010-2011 |
Unbounded Operators in Hilbert Spaces |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 610 Fourier Analysis |
3 Credits |
The course is an introduction to the Fourier Analysis for
graduate students in Mathematics. The
syllabus includes
Fourier series (point wise and uniform convergence,
Riemann localization Principle, norm convergence,
summability, examples of divergent Fourier
series); Fourier Transform (basic properties, Riemann
-Lebesgue lemma, inversion, L2-theory in Rn);
Fourier Analysis in Lp-spaces (Riesz-Thorin
interpolation theorem, Hilbert transform).
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2012-2013 |
Fourier Analysis |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 636 Algebraic Function Fields |
3 Credits |
Places,valuation rings and discrete valuations of a function
field; the rational function field; divisors, Weil different
adeles, genus; Riemann-Roch Theorem and its
consequences; extensions of function fields, ramification,
Hurwitz genus formula; constant field extensions, Galois
extensions, Kummer and Artin-Schreier extensions.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2022-2023 |
Algebraic Function Fields |
3 |
Fall 2015-2016 |
Algebraic Function Fields |
3 |
Fall 2013-2014 |
Algebraic Function Fields |
3 |
Fall 2010-2011 |
Algebraic Function Fields |
3 |
Spring 2006-2007 |
Algebraic Function Fields |
3 |
Spring 2002-2003 |
Algebraic Function Fields |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 639 Algebraic Function Fields II |
3 Credits |
Ramification theory for function field
extensions, function fields over finite fields, rational
places, Hasse-Weil theorem (Riemann hypothesis), towers
of function fields, introduction to
Algebraic Geometry codes.
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2020-2021 |
Algebraic Function Fields II |
3 |
Spring 2015-2016 |
Algebraic Function Fields II |
3 |
Spring 2010-2011 |
Algebraic Function Fields II |
3 |
|
Prerequisite: (MATH 511 - Masters - Min Grade D |
or MATH 511 - Doctorate - Min Grade D) |
and (MATH 512 - Masters - Min Grade D |
or MATH 512 - Doctorate - Min Grade D) |
and (MATH 636 - Masters - Min Grade D |
or MATH 636 - Doctorate - Min Grade D) |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 664 Spectral Theory of one-dimensional periodic Schrödinger and Dirac operators |
3 Credits |
The course is an introduction to Spectral Theory
of Differential Operators. The syllabus includes: boundary
value problems, Floquet theory, structure
of the spectra, spectra localization, asymptotic
estimates for the resolvent, asymptotic formulas
for the eigenvalues and eigenfunctions, relations
between the spectral gaps decay and the potential
smoothness, existence of Riesz
bases consisting of root functions.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2012-2013 |
Spectral Theory of one-dimensional periodic Schrödinger and Dirac operators |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 68001 Special Topics in MATH: Differentaial Equations I |
3 Credits |
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2016-2017 |
Special Topics in MATH: Differentaial Equations I |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 68002 Special Topics in MATH: Complex Analysis |
3 Credits |
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2021-2022 |
Special Topics in MATH: Complex Analysis |
3 |
Fall 2018-2019 |
Special Topics in MATH: Complex Analysis |
3 |
Fall 2016-2017 |
Special Topics in MATH: Complex Analysis |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 68003 Special Topics in MATH Several Complex Variables |
3 Credits |
Complex diferentiation, subharmonic and pluri-subharmonik
(psh) functions, singularities of psh functions, maximal
psh functions, positive closed currents, complex Monge
-Ampere measure. Applications.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2019-2020 |
Special Topics in MATH Several Complex Variables |
3 |
Spring 2017-2018 |
Special Topics in MATH Several Complex Variables |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 68004 Special Topics in MATH: Special Topic in Algebra: Graded Syzygies |
3 Credits |
Graded rings and modules
Graded Free Resolutions.
How to compute Syzygy modules
Numerical data arising from graded
resolutions
Betti numbers and Hilbert function
Monomial resolutions
Resolutions of monomial ideals and Eliahou-
Kavaire formula Shifting theory
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2019-2020 |
Special Topics in MATH: Special Topic in Algebra: Graded Syzygies |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 68005 Special Topics in MATH: Analytic Number Theory |
3 Credits |
1 - Ability to utilize the properties of arithmetic
functions, compute their average orders.
2 - Ability to apply elementary theorems on
distribution of primes,
knowledge of the prime number theorem.
3 - Thorough understanding of Dirichlet's theorem on
primes in arithmetic progressions.
4 - Basic ability to manipulate Dirichlet series, Euler
products, zeta-and L-functions.
5 - Basic understanding of the components of the
proof of the prime number theorem.
* Arithmetic functions.
* Big-oh notation and average orders of arithmetic
functions.
* Elementary theorems on the distribution of prime
numbers, introduction to the prime number theorem.
* Characters of finite abelian groups.
* Dirichlet's theorem on primes in arithmetic progressions.
* Dirichlet series and Euler products.
* Zeta- and L-functions.
* Analytic proof of the prime number theorem.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2023-2024 |
Special Topics in MATH: Analytic Number Theory |
3 |
Spring 2020-2021 |
Special Topics in MATH: Analytic Number Theory |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 68006 Special Topics in MATH: Pluripotential Theory |
3 Credits |
The aim of this Special Topics course is
to introduce the students the
pluripotential theory. This is a special
branch of several complex variables
and hence, it has many applications to
the theory of holomorphic functions.
The students acquire the language and
knowledge of this theory and make
connections of this theory with related
fields such as complex analysis,
operator theory and complex
geometry.
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2020-2021 |
Special Topics in MATH: Pluripotential Theory |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 68007 Special Topics in MATH: Mathematical Techniques in Cryptography |
3 Credits |
Perfect nonlinear functions, association schemes,
strongly regular graphs, spreads, difference sets,
APN functions, related mathematical structures
|
Last Offered Terms |
Course Name |
SU Credit |
Fall 2023-2024 |
Special Topics in MATH: Mathematical Techniques in Cryptography |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 68008 Special Topics in MATH: Algebraic and Combinatorial Coding Theory |
3 Credits |
Quantum error correcting codes, covering radius
of codes, decoding algorithms of codes, codes
and designs, locally recoverable codes
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2023-2024 |
Special Topics in MATH: Algebraic and Combinatorial Coding Theory |
3 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|
MATH 790 Ph.D. Dissertation |
0 Credit |
|
Last Offered Terms |
Course Name |
SU Credit |
Spring 2023-2024 |
Ph.D. Dissertation |
0 |
Fall 2023-2024 |
Ph.D. Dissertation |
0 |
Spring 2022-2023 |
Ph.D. Dissertation |
0 |
Fall 2022-2023 |
Ph.D. Dissertation |
0 |
Spring 2021-2022 |
Ph.D. Dissertation |
0 |
Fall 2021-2022 |
Ph.D. Dissertation |
0 |
Spring 2020-2021 |
Ph.D. Dissertation |
0 |
Fall 2020-2021 |
Ph.D. Dissertation |
0 |
Spring 2019-2020 |
Ph.D. Dissertation |
0 |
Fall 2019-2020 |
Ph.D. Dissertation |
0 |
Spring 2018-2019 |
Ph.D. Dissertation |
0 |
Fall 2018-2019 |
Ph.D. Dissertation |
0 |
Spring 2017-2018 |
Ph.D. Dissertation |
0 |
Fall 2017-2018 |
Ph.D. Dissertation |
0 |
Spring 2016-2017 |
Ph.D. Dissertation |
0 |
Fall 2016-2017 |
Ph.D. Dissertation |
0 |
Spring 2015-2016 |
Ph.D. Dissertation |
0 |
Fall 2015-2016 |
Ph.D. Dissertation |
0 |
Spring 2014-2015 |
Ph.D. Dissertation |
0 |
Fall 2014-2015 |
Ph.D. Dissertation |
0 |
Spring 2013-2014 |
Ph.D. Dissertation |
0 |
Fall 2013-2014 |
Ph.D. Dissertation |
0 |
Spring 2012-2013 |
Ph.D. Dissertation |
0 |
Fall 2012-2013 |
Ph.D. Dissertation |
0 |
Spring 2011-2012 |
Ph.D. Dissertation |
0 |
Fall 2011-2012 |
Ph.D. Dissertation |
0 |
Spring 2010-2011 |
Ph.D. Dissertation |
0 |
Fall 2010-2011 |
Ph.D. Dissertation |
0 |
Spring 2009-2010 |
Ph.D. Dissertation |
0 |
Fall 2009-2010 |
Ph.D. Dissertation |
0 |
Spring 2008-2009 |
Ph.D. Dissertation |
0 |
Fall 2008-2009 |
Ph.D. Dissertation |
0 |
Spring 2007-2008 |
Ph.D. Dissertation |
0 |
Fall 2007-2008 |
Ph.D. Dissertation |
0 |
Spring 2006-2007 |
Ph.D. Dissertation |
0 |
Fall 2006-2007 |
Ph.D. Dissertation |
0 |
Summer 2005-2006 |
Ph.D. Dissertation |
0 |
Spring 2005-2006 |
Ph.D. Dissertation |
0 |
Fall 2005-2006 |
Ph.D. Dissertation |
0 |
Spring 2004-2005 |
Ph.D. Dissertation |
0 |
Fall 2004-2005 |
Ph.D. Dissertation |
0 |
Spring 2003-2004 |
Ph.D. Dissertation |
0 |
Fall 2003-2004 |
Ph.D. Dissertation |
0 |
Fall 2002-2003 |
Ph.D. Dissertation |
0 |
|
Prerequisite: __ |
Corequisite: __ |
ECTS Credit: 180 ECTS (180 ECTS for students admitted before 2013-14 Academic Year) |
General Requirements: |
|
|