M.S. Theses: Recent submissions

  • Reciprocity law of quadratic extensions 
    Tümel, Filiz. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2006., 2006.)
    In the first chapter, basic definitions and results which will be used in the following chapters of this thesis are presented. In the following chapter, ideal classes and classes of quadratic forms are reviewed. Then the ...
  • Generalized complex geometry and nilmanifolds 
    Güner, Murat. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2013., 2013.)
    The generalized complex geometry is a relatively new and highly popular subject which also has applications in theoretical physics. It studies the geometric structures on TM T M. That is to say, this new geometry develops ...
  • Construction of metrics on Sasaki-Einstein manifolds 
    Şenel, Güneş. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2013., 2013.)
    Sasaki-Einstein manifolds are Einstein manifolds occurring in odd dimensions, which have positive curvature and Calabi-Yau metric cones. We start with an introduction of Sasakian manifolds, following the historical development ...
  • On a volume estimate for some subsets of a Grassmannian 
    Demirkaya, Emre. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2013., 2013.)
    Measure theory gives us a technique for proving existence theorems. In simple terms this technique can be described as follows: start with a set and put a measure on it. Then nd the exact measure of a speci ed set A. By ...
  • Definable sets over finite fields 
    Güner, Kadir Güray. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2013., 2013.)
    Counting the number of points of an algebraic set over a finite field has been studied by Hasse [1], Lang and Weil [2], and is an important theme in algebra. In this thesis, we present the results found by Chatzidakis, van ...
  • Analysis of convergent integral equation methods for high-frequency scattering 
    Keserci, Samet. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2012., 2012.)
    The main aim of this thesis is to devise numerical methods for the solution of high-frequency scattering problems in 2 dimensional settings by utilizing geometrical optics ansatz and asymptotic properties of solutions for ...
  • Integration of the deterministic functions with respect to fractional Brownian motion 
    Yıldırım, Gökhan. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2006., 2006.)
    In this thesis, definition and the characteristic properties of fractional Brownian motion are presented and the general idea for the integration of deterministic functions is discussed with a specific class of integrands. ...
  • Space filling curve heuristic and the traveling salesman problem 
    Charyyev, Polat. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2012., 2012.)
    Let LSFC n denote the length of the path connecting n random points uniformly distributed over the unit square obtained by the space lling curve heuristic. For a Hilbert type of space lling curve such as; Peano, Moore, ...
  • Cascading behavior in infinite networks 
    Özdemir, Alperen Yaşar. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2012., 2012.)
    The aim of this master thesis is to analyze the underlying mathematical structure of the infinite network models of cascading behavior. Graph theoretical tools are essential to understand the structure of the network and ...
  • Quotients of Hom-functors 
    Bilgin, Zehra. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2012., 2012.)
    Quotients of Hom-functors are functors of the form HomR(P;{u100000})=HomR(P;{u100000})J where P is a projective R-module and J is a certain ideal of the endomorphism ring of P. These functors were used by R. Dipper in the ...
  • A mathematical model of drug delivery by modifying the tumor microenvironment: MMP activation 
    Kaba, Duygu. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2013., 2013.)
    Cancer modeling has become one of the challenging frontiers of applied mathematics mostly for two decades. Drug delivery to solid tumors also attracts both theorists and experimentalists due to its signi cance in cancer ...
  • O-minimal structures 
    Pehlivan, Cihan. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2011., 2011.)
    IfMis a o-minimal expansion of ordered eld of reals which contains a de nable function which can not dominated by polynomials, then exponential function appears as a de nable function. In this study rstly we introduce ...
  • Convexity in graphs 
    Erey, Aysel. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2011., 2011.)
    The idea of finding analogies and generalizations to some concepts from continuous mathematics has led to the study of several new topics in discrete structures. Convexity is such a concept that has been widely studied in ...
  • Positive definite functions on spheres 
    Yılmaz, Fatma. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2011., 2011.)
    Positive de nite functions play a central role in approximation theory as in many other areas of mathematical research. The methods for data interpolation on spheres can be e ectively used for analysis of large data sets ...
  • Propp-Wilson algorithm and beyond 
    Işlak, Ümit. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2010., 2010.)
    Propp-Wilson algorithm is a Markov chain Monte Carlo method that produces samples that are drawn exactly from the stationary distribution of a given Markov chain. The aim of this master thesis is to unify the underlying ...
  • Denseness of morse-smale systems on surfaces 
    Özsarfati, Metin. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2011., 2011.)
    Let M be a compact, connected 2-manifold without boundary. Morse-Smale fields are known to be dense in the space of all Cr vector elds on M when M is oriented or is one of RP2, Klein bottle or torus with a cross cap. In ...
  • Pseudo-Anosov diffeomorphisms and the monodromy of an open book 
    Eden, Sinan. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2011., 2011.)
    In this thesis, we study the proof of the fact that any mapping class on a compact oriented surface with non-empty boundary can be made pseudo-Anosov after a sequence of positive stabilizations. In the language of contact ...
  • Hopf galois extensions 
    Erey, Nursel. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2011., 2011.)
    Let H be a Hopf algebra which coacts to the right on A and let B be the subalgebra of coinvariants. The extension B A is said to be Hopf Galois if the canonical map ..... is a bijection. This work investigates this kind ...
  • Path algebras 
    Adanalı, Pınar. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2011., 2011.)
    In this thesis, we investigate path algebras and Leavitt path algebras. Some properties of path and Leavitt path algebras are given. Our aim is to see what conditions on the graph E makes Leavitt path algebras simple. We ...
  • On the role of diagonalization in Gödel's incompleteness and Tarski's theorems 
    Budak, Mehmet. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2010., 2010.)
    Three major theorems of arithmetics from early 1930s delineate the enterprise of formalization in mathematics: Gödel's First Incompleteness Theorem, Diagonalization Lemma and Tarski's Theorem. We begin the thesis with a ...

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