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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: