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Dissertations / Theses on the topic 'MATHEMATICS / Discrete Mathematics'

Author: Grafiati

Published: 4 June 2021

Last updated: 27 July 2025

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1

Riley, Patrick Anthony Meahan. "Visualization in discrete mathematics." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/MQ38404.pdf.

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2

Du, Toit Jacques Pierre. "The discrete pulse transform and applications." Thesis, Link to the online version, 2007. http://hdl.handle.net/10019/1052.

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3

Olsson, Christoffer. "Discreet Discrete Mathematics : Secret Communication Using Latin Squares and Quasigroups." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-136860.

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This thesis describes methods of secret communication based on latin squares and their close relative, quasigroups. Different types of cryptosystems are described, including ciphers, public-key cryptosystems, and cryptographic hash functions. There is also a chapter devoted to different secret sharing schemes based on latin squares. The primary objective is to present previously described cryptosystems and secret sharing schemes in a more accessible manner, but this text also defines two new ciphers based on isotopic latin squares and reconstructs a lost proof related to row-latin squares.<br>

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4

Nezami, Ahmad Reza. "DiscMath, an intelligent tutoring system for discrete mathematics." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape17/PQDD_0012/MQ35514.pdf.

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5

Haven, Andrew J. "Automated proof checking in introductory discrete mathematics classes." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/85424.

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Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2013.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (page 61).<br>Mathematical rigor is an essential concept to learn in the study of computer science. In the process of learning to write math proofs, instructors are heavily involved in giving feedback about correct and incorrect proofs. Computerized feedback in this area can ease the burden on instructors and help students learn more efficiently. Several software packages exist that can verify pr

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6

Norton, Carolyn H. (Carolyn Haibt). "Problems in discrete optimization." Thesis, Massachusetts Institute of Technology, 1993. http://hdl.handle.net/1721.1/12490.

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7

Bai, Wei. "Percolation: Discrete and Continuum Models." Kent State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=kent1406757985.

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8

Chen, Lin. "Parallel complexity of discrete problems /." The Ohio State University, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487684245466027.

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9

Bruen, Trevor Cormac Vincent. "Discrete and statistical approaches to genetics." Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=102964.

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This thesis presents a number of major innovations in related but different areas of research. The contributions range along a continuum from mathematical phylogenetics, to development of statistical methodology for detecting recombination and finally to the application of statistical techniques to understand Feline Immunodeficiency Virus (FIV) an important pathogen. An underlying theme is the application of combinatorial and statistical ideas to problems in evolutionary biology and genetics.<br>Chapter 2 and Chapter 3 give a number of results relevant to mathematical phylogenetics, in particu

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10

Rivera-Marrero, Olgamary. "The place of discrete mathematics in the school curriculum: An analysis of preservice teachers' perceptions of the integration of discrete mathematics into secondary level courses." Diss., Virginia Tech, 2007. http://hdl.handle.net/10919/27280.

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The integration of discrete mathematics into the secondary school curriculum (grades 7-12) is an important consideration because the mathematical area is dynamic and interesting, providing students the development of mathematical thinking. Also, it provides for teachers the opportunity to develop innovative mathematics instruction. Since the publication of the document Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989), it has been difficult to determine how many schools have integrated discrete mathematics as a separate or as an integrated course in the school mathematics

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11

Wallace, Brian John Michael. "Some applications of discrete mathematics to the theory of communications." Thesis, Royal Holloway, University of London, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.272153.

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12

Havlíčková, Markéta. "Boundaries of K-types in discrete series." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/43796.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.<br>Includes bibliographical references (p. 75-76).<br>Abstract: A fundamental problem about irreducible representations of a reductive Lie group G is understanding their restriction to a maximal compact subgroup K. In certain important cases, known as the discrete series, we have a formula that gives the multiplicity of any given irreducible K-representation (or K-type) as an alternating sum. It is not immediately clear from this formula which K-types, indexed by their highest weights, have non-zero multiplicit

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13

Cheng, Yu-Wen 1961. "Endomorphisms of modules over discrete valuation domains." Diss., The University of Arizona, 1997. http://hdl.handle.net/10150/282294.

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The primary objective of this dissertation is to study isomorphism theorems (or isomorphism problems) for modules over either complete or non-complete discrete valuation domains. The first chapter of the dissertation lays the foundation for all the remaining chapters. We first review the definition and some important facts about modules over discrete valuation domains. p-adic topologies and the notion of complete modules are then introduced, and indecomposable modules are examined. Then, we list some facts on homomorphism algebras of modules over discrete valuation domains that are necessary f

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14

Rocha-Martinez, Jose Maria. "Discrete imperfect repair." Diss., The University of Arizona, 1992. http://hdl.handle.net/10150/185763.

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A discrete imperfect repair model is studied, it consists of units that try to perform jobs dynamically in time and that at failure may be repaired and are allowed to try to do again the jobs in which they failed until either eventual completions of the corresponding jobs or unsuccessful repairs of failed units. Of interest then is the numbers of completed jobs by the units before the occurrences of unsuccessful repairs, that is, the waiting times for an unsuccessful repair in the model. In many practical situations some information about the model is provided in the form of parameters. These

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15

Labra, Bahena Luis R. "Multilevel Solution of the Discrete Screened Poisson Equation for Graph Partitioning." Thesis, California State University, Long Beach, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10638940.

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<p> A new graph partitioning algorithm which makes use of a novel objective function and seeding strategy, Product Cut, frequently outperforms standard clustering methods. The solution strategy on solving this objective depends on developing a fast solution method for the systems of graph--based analogues of the screened Poisson equation, which is a well-studied problem in the special case of structured graphs arising from PDE discretization. </p><p> In this work, we attempt to improve the powerful Algebraic Multigrid (AMG) method and build upon the recently introduced Product Cut algorithm.

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16

Wei, Zhiyan. "Studies in discrete and continuum mechanics." Thesis, Harvard University, 2014. http://dissertations.umi.com/gsas.harvard:11582.

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We have used a combination of theory and computation to investigate collective aspects of discrete mechanical systems. The analysis involves considerations from geometry, elasticity and hydrodynamics. We have developed continuum theories to describe these systems, in the spirit of compressing information by mathematical abstraction from the discrete description.<br>Engineering and Applied Sciences

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17

Chen, Chung-Chuan. "Convolution operators and the discrete Laplacian." Thesis, Queen Mary, University of London, 2009. http://qmro.qmul.ac.uk/xmlui/handle/123456789/437.

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In this thesis, we obtain new results for convolution operators on homogeneous spaces and give applications to the Laplacian on a homogeneous graph. Some of these results have been published in joint papers [13, 14] with my supervisor. Let be a homogeneous space of a locally compact group G and let T : Lp( ) ! Lp( ) be a convolution operator induced by a measure on G, where 1 p < 1. When is symmetric and absolutely continuous, we describe the L2- spectrum of T in terms of the Fourier transform of . An operator T is said to be hypercyclic if there is a vector x 2 Lp( ) such that the orbit fx; T

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18

Uyanik, Meltem. "Analysis of Discrete Fractional Operators and Discrete Fractional Rheological Models." TopSCHOLAR®, 2015. http://digitalcommons.wku.edu/theses/1491.

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This thesis is comprised of two main parts: Monotonicity results on discrete fractional operators and discrete fractional rheological constitutive equations. In the first part of the thesis, we introduce and prove new monotonicity concepts in discrete fractional calculus. In the remainder, we carry previous results about fractional rheological models to the discrete fractional case. The discrete method is expected to provide a better understanding of the concept than the continuous case as this has been the case in the past. In the first chapter, we give brief information about the main result

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19

Aubin, Caroline. "On the geometric representation theory of discrete groups." Thesis, McGill University, 2000. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=33375.

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First, the set of G-representations of a finitely generated group is described. This set of functions endowed with the compact-open topology will be used to prove some results in combinatorial group theory. Then we will see that the set of SL2( C )-representations may be viewed as an algebraic set. This new structure will allow some more applications in group theory. Finally, we will describe the set of characters of a finitely generated group and we will show that the set of characters associated to SL2( C )-representations also inherits an algebraic set structure.

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20

Mandich, Marc-Adrien. "One dimensional discrete Schrödinger operators." Thesis, McGill University, 2014. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=123158.

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We consider the one dimensional discrete Schrödinger operator h = h_0 + V on the full line and half line, where h_0 is the discrete Laplacian and V is a real-valued potential. We explain the Spectral theorem for the operator and give explicit formulas of the Green's function and spectral measures in case of the Laplacian. We explore the rank one potentials and compute their scattering operator. We also explore periodic potentials on the full line. We introduce random Schrödinger operators, and reproduce the proof of the celebrated theorem of Pastur that the spectrum is almost surely the same s

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21

Robbins, Christopher. "Discrete element simulation and applications." Thesis, University of Strathclyde, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365170.

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22

Kusdiantara, Rudy. "Homoclinic snaking in discrete systems." Thesis, University of Essex, 2018. http://repository.essex.ac.uk/23314/.

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In this thesis, we investigate analytically and numerically bifurcations of localized solutions in discrete systems, i.e., the discrete Swift-Hohenberg, an optical cavity equation, and the discrete Allen-Cahn equation, which have infinitely multiplicity called homoclinic snaking. First, we study the discrete Swift-Hohenberg equation with cubic and quintic nonlinearity, obtained from discretizing the spatial derivatives of the Swift-Hohenberg equation using central finite differences. We investigate the discretization effect on the bifurcation behavior, where we identify three regions of the co

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23

Charoenphon, Sutthirut. "Green's Functions of Discrete Fractional Calculus Boundary Value Problems and an Application of Discrete Fractional Calculus to a Pharmacokinetic Model." TopSCHOLAR®, 2014. http://digitalcommons.wku.edu/theses/1327.

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Fractional calculus has been used as a research tool in the fields of pharmacology, biology, chemistry, and other areas [3]. The main purpose of this thesis is to calculate Green's functions of fractional difference equations, and to model problems in pharmacokinetics. We claim that the discrete fractional calculus yields the best prediction performance compared to the continuous fractional calculus in the application of a one-compartmental model of drug concentration. In Chapter 1, the Gamma function and its properties are discussed to establish a theoretical basis. Additionally, the basics o

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24

Chua, Doi-eng, and 蔡岱榮. "Some variations on Discrete-Cosine-Transform-based lossy image compression." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31222523.

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25

Yates, Christian. "Comparing stochastic discrete and deterministic continuum models of cell migration." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:6f9cb70e-937c-441f-83c3-50e37e1cb420.

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Multiscale mathematical modelling is one of the major driving forces behind the systems biology revolution. The inherently interdisciplinary nature of its study and the multiple spatial and temporal scales which characterise its dynamics make cell migration an ideal candidate for a systems biology approach. Due to its ease of analysis and its compatibility with the type of data available, phenomenological continuum modelling has long been the default framework adopted by the cell migration modelling community. However, in recent years, with increased computational power, complex, discrete, cel

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26

Zhoroev, Tilekbek. "Controllability and Observability of Linear Nabla Discrete Fractional Systems." TopSCHOLAR®, 2019. https://digitalcommons.wku.edu/theses/3156.

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The main purpose of this thesis to examine the controllability and observability of the linear discrete fractional systems. First we introduce the problem and continue with the review of some basic definitions and concepts of fractional calculus which are widely used to develop the theory of this subject. In Chapter 3, we give the unique solution of the fractional difference equation involving the Riemann-Liouville operator of real order between zero and one. Additionally we study the sequential fractional difference equations and describe the way to obtain the state-space repre- sentation of

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27

Daghighi, Abtin. "The Dirichlet problem for certain discrete structures." Thesis, Uppsala University, Department of Mathematics, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-121384.

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28

Poufinas, Thomas. "Discrete-Time and Continuous-Time Option Pricing with Fees /." The Ohio State University, 1996. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487934589977028.

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29

Pestana, da Costa Fernando M. "Studies in discrete coagulation-fragmentation equations." Thesis, Heriot-Watt University, 1993. http://hdl.handle.net/10399/1469.

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30

Eberz-Wagner, Dorothea M. "Discrete growth models /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/5797.

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31

Hao, Shuai. "An Introduction to Discrete Minimal Surfaces via the Enneper Surface." Thesis, Southern Illinois University at Edwardsville, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=1543912.

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<p> In this paper, we are exploring how to construct a discrete minimal surface. We map the conformal curvature lines of a parameterized continuous minimal surface to a unit sphere by the Gauss map. Then, based on a circle patterns we create, the Koebe polyhedron can be obtained. By dualizing the Koebe polyhedron, we are able to get the discrete minimal surface. Moreover, instead of only developing the method theoretically, we also show concrete procedures visually by Mathematica for Enneper with arbitrary domain. This is an expository project mainly based on the paper "Minimal surface from ci

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32

Srinivasan, Padmavathi. "Invariants linked to models of curves over discrete valuation rings." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104580.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 103-104).<br>This thesis consists of two parts. In part one of this thesis, we study the relationship between the Artin conductor and the minimal discriminant of a hyperelliptic curve defined over the fraction field K of a discrete valuation ring. The Artin conductor and the minimal discriminant are two measures of degeneracy of the singular fiber in a family of hyperelliptic curves. In the case of elliptic curves, the Og

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33

Dale, Wilbur Nolan. "Stabilization and robust stability of discrete-time, time- varying systems /." The Ohio State University, 1991. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487694389393404.

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34

Shipman, Stephen Paul 1968. "A continuum limit of a finite discrete nonlinear Schroedinger system." Diss., The University of Arizona, 1997. http://hdl.handle.net/10150/288763.

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A continuum limit of a discrete nonlinear Schrodinger system of ordinary differential equations is analyzed. The central question is the relation between the solution of the formally derived limiting system of partial differential equations and the limiting behavior of the solutions to the discrete systems. By setting appropriate boundary conditions on the initial data, a finite subchain decouples, and this system is known to be integrable and solvable by an inverse spectral method. In this thesis, it is found that subunitary data give rise to eigenvalues which are unitary and weighting consta

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35

Sze, Chuen-kan, and 施泉根. "On framelets and their applications: a discrete approach." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B29803937.

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36

Chumni, Wichai Dossey John A. "Discrete mathematics courses for the first two years of study in Thai universities." Normal, Ill. Illinois State University, 1991. http://wwwlib.umi.com/cr/ilstu/fullcit?p9219081.

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Thesis (D.A.)--Illinois State University, 1991.<br>Title from title page screen, viewed December 22, 2005. Dissertation Committee: John A. Dossey (chair), Albert D. Otto, Michael J. Plantholt, Lawrence E. Spence, Bill E. Swafford. Includes bibliographical references (leaves 121-123) and abstract. Also available in print.

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37

Martucci, Stephen A. "Symmetric convolution and the discrete sine and cosine transforms : principles and applications." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/15038.

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38

Yu, Sungwook. "VLSI implementation of multidimensional discrete Fourier transform and discrete cosine transform /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.

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39

Silva, Isabel Maria Marques da. "Contributions to the analysis of discrete-valued time series." Tese, Universidade do Porto. Reitoria, 2005. http://hdl.handle.net/10216/9742.

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Dissertação de Doutoramento em Matemática Aplicada apresentada à Faculdade de Ciências da Universidade do Porto<br>Séries temporais de contagem, categóricas ou binárias são exemplos de séries temporaisde valor discreto que aparecem frequentemente na prática. No entanto, uma vezque estas séries apresentam valores que pertencem a conjuntos finitos ou infinitosnumeráveis, os métodos tradicionais utilizados na análise de séries temporais não sãoadequados.Vários modelos para processos estacionários com distribuição marginal discreta têmsido propostos. Um desses modelos, particularmente usado para s

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40

Leader, Imre Bennett. "Discrete isoperimetric inequalities and other combinatorial results." Thesis, University of Cambridge, 1989. https://www.repository.cam.ac.uk/handle/1810/250940.

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41

Barwell, Andrew David. "Omega-Limit Sets of Discrete Dynamical Systems." Thesis, University of Birmingham, 2011. http://etheses.bham.ac.uk//id/eprint/1476/.

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Omega-limit sets are interesting and important objects in the study of discrete dynamical systems. Using a variety of methods, we present and extend existing results in this area of research. Of particular interest is the property of internal chain transitivity, and we present several characterizations of omega-limit sets in terms of this property. In so doing, we will often focus our attention on the property of pseudo-orbit tracing (shadowing), which plays a central role in many of the characterizations, and about which we prove several new results. We also make extensive use of symbolic dyn

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42

Selamoglu, Birsen Irem. "The Plant Propagation Algorithm for discrete optimisation." Thesis, University of Essex, 2017. http://repository.essex.ac.uk/20198/.

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The thesis is concerned with novel Nature-Inspired heuristics for the so called NP-hard problems of optimisation. A particular algorithm which has been recently introduced and shown to be effective in continuous optimisation is the Plant Propagation Algorithm or PPA. Here, we intend to extend it to cope with combinatorial optimisation. In order to show that our extension is viable and effective, we consider three types of problems which are good representatives of the whole topic. These are the Travelling Salesman Problem or TSP, the Knapsack Problem or KP and the scheduling problem of Berth A

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43

Campbell, Sarah Janet. "A study of exactness for discrete groups." Thesis, University of Southampton, 2005. https://eprints.soton.ac.uk/361466/.

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We recall the concepts of exactness for both C*-algebras and groups. We explore some new properties linked or equivalent to exactness, including Property A, a second property we term Property O, and Hilbert space compression [GK2, O, Yu]. We use geometric methods to show that a variety of groups satisfy these properties. We then deduce that those groups are exact. In particular we show that Properties O and A are equivalent. We show that the integers, groups of subexponential growth, amenable groups and free groups satisfy Property O by constructing a family of Ozawa kernels for each case. To

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44

Gethner, Ellen. "Rational period functions for the modular group and related discrete groups /." The Ohio State University, 1992. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487779914826234.

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45

Kim, Seog Young. "Vector bundles on an elliptic curve over a discrete valuation ring." Diss., The University of Arizona, 2001. http://hdl.handle.net/10150/280386.

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We classify rank 2 vector bundles on a smooth curve X of genus 1 over a discrete valuation ring R. Atiyah [5] classified rank 2 vector bundles on elliptic curves over algebraically closed fields. The fact that a genus 1 curve over a discrete valuation ring has a codimension 2 subscheme prevents us from applying Atiyah's work directly. We find that genus 1 curve over an arbitrary field can have three types of rank 2 vector bundles. We classify rank 2 vector bundles on a curve of genus 1 over a discrete valuation ring using the classification on a curve of genus 1 over a field and quadruples (L

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46

Dykes, Laura R. "New Methods for Solution of Discrete Ill-posed Problems." Kent State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=kent1469796109.

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47

Wang, Yuqiong. "Optimal Stopping with Discrete Costly Observations." Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-358042.

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48

Zaczek, Kinga. "Development and evaluation of computer-aided assessment in discrete and decision mathematics." Thesis, Brunel University, 2015. http://bura.brunel.ac.uk/handle/2438/10973.

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This thesis describes the development of Computer-Aided Assessment questions for elementary discrete and decision mathematics at the school/university interface, stressing the pedagogy behind the questions’ design and the development of methodology for assessing their efficacy in improving students’ engagement and perceptions, as well as on their exams results. The questions give instant and detailed feedback and hence are valuable as diagnostic, formative or summative tools. A total of 275 questions were designed and coded for five topics, numbers, sets, logic, linear programming and graph th

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49

Cottrell, David Daniel. "Analysis of three stochastic models for discrete populations." Thesis, McGill University, 2010. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=86528.

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Stochastic models of discrete populations appear in a broad range of contexts. In this thesis, three of these modelling settings are considered: epidemics which spread through both blood transfusion and surgery, stochastic gene expression, and the accumulation of error in velocity statistics in Molecular Dynamics simulations. We examine specific models in each case, illustrating methods for extracting quantitative statistical information from the systems, and discuss how each approach fits into the more general mathematical framework for discrete populations evolving under stochastic dynamic

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50

Webster, Helen Nicola. "On the continuous and discrete third Painleve equations." Thesis, University of Kent, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.267390.

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