School of Mathematics
The School of Mathematics, a unit of Georgia Tech's College of Sciences, is among the nation's top public university Mathematics departments. The Master of Science in Applied Mathematics has been offered since 1952, and the doctoral program was begun in 1963. Georgia Tech enjoys a strong reputation in science and engineering and the graduates are in demand by industry and academia.
All materials in SMARTech are protected under U.S. Copyright Law and all rights are reserved. Such materials may be used, quoted or reproduced for educational purposes only with prior permission, provided proper attribution is given. Any redistribution, reproduction or use of the materials, in whole or in part, is prohibited without prior permission of the author.
Collections in this community

Graph Theory @ Georgia Tech [33]
Clough Undergraduate Learning Commons, May 711, 2012 
ProofReader [5]
The annual newsletter of the School of Mathematics. 
School of Mathematics Faculty Publications [119]
Preprints by faculty members in the School of Mathematics 
School of Mathematics OSP Research Reports [89]
OSP research reports by faculty and researchers in the School of Mathematics 
School of Mathematics Theses and Dissertations [350]
Original work by students in the School of Mathematics 
School of Mathematics Undergraduate Research Option Theses [1]
Research Thesis Option for Mathematics Majors 
Stelson Lecture Series [5]
Annual lectures in honor of Hugh Stelson
Recent Submissions

The Complexity of Random Functions of Many Variables
(Georgia Institute of Technology, 20160831)A function of many variables, when chosen at random, is typically very complex. It has an exponentially large number of local minima or maxima, or critical points. It defines a very complex landscape, the topology of its ... 
Statistical inference for large matrices
(Georgia Institute of Technology, 20160729)This thesis covers two topics on matrix analysis and estimation in machine learning and statistics. The first topic is about density matrix estimation with application in quantum state tomography. The density matrices are ... 
Transverse Surgery on Knots in Contact ThreeManifolds
(Georgia Institute of Technology, 20160519)We study the effect of surgery on transverse knots in contact $3$manifolds by examining its effect on open books, the Heegaard Floer contact invariant, and tightness in general. We first compare surgery on transverse ... 
A study of stochastic differential equations and FokkerPlanck equations with applications
(Georgia Institute of Technology, 20160415)FokkerPlanck equations, along with stochastic differential equations, play vital roles in physics, population modeling, game theory and optimization (finite or infinite dimensional). In this thesis, we study three topics, ... 
Open book decompositions in high dimensional contact manifolds
(Georgia Institute of Technology, 20160527)In this thesis, we study the open book decompositions in high dimensional contact manifolds. We focus on the results about open book decomposition of manifolds and their relationship with contact geometry. 
Numerical algorithms based on the back and forth error compensation and correction
(Georgia Institute of Technology, 20141218)In this thesis we carry out a further study of the back and forth error compensation and correction (BFECC) method. The first part discusses the time reversibility of numerical schemes. Motivated by the BFECC method, a ... 
Dynamics and variational problems
(Georgia Institute of Technology, 20100601) 
Combinatorial problems for graphs and partially ordered sets
(Georgia Institute of Technology, 20151113)This dissertation has three principal components. The first component is about the connections between the dimension of posets and the size of matchings in comparability and incomparability graphs. In 1951, Hiraguchi proved ... 
Thermostated Kac models
(Georgia Institute of Technology, 20151116)We consider a model of N particles interacting through a Kacstyle collision process, with m particles among them interacting, in addition, with a thermostat. When m = N, we show exponential approach to the equilibrium ... 
The Filippov moments solution on the intersection of two and three manifolds
(Georgia Institute of Technology, 20151118)In this thesis, we study the Filippov moments solution for differential equations with discontinuous righthand side. In particular, our aim is to define a suitable Filippov sliding vector field on a codimension $2$ ... 
Fields program on new trends in harmonic analysis  international U.S. participation
(Georgia Institute of Technology, 20080801) 
The geometry and topology of the Jones polynomial
(Georgia Institute of Technology, 20090501) 
Multivariable moments and factorizations and other problems in analysis
(Georgia Institute of Technology, 20080801) 
Mathematical modeling of heterogeneous media
(Georgia Institute of Technology, 20080501) 
A numerical study of vorticityenhanced heat transfer
(Georgia Institute of Technology, 20140626)In this work, we have numerically studied the effect of the vorticity on the enhancement of heat transfer in a channel flow. In the first part of the work, we focus on the investigation of a channel flow with a vortex ... 
Multifold sums and products over R, and combinatorial problems on sumsets
(Georgia Institute of Technology, 20150722)We prove a new bound on a version of the sumproduct problem studied by Chang. By introducing several combinatorial tools, this expands upon a method of Croot and Hart which used the TarryEscott problem to build distinct ... 
Symmetric ideals and numerical primary decomposition
(Georgia Institute of Technology, 20150727)The thesis considers two distinct strategies for algebraic computation with polynomials in high dimension. The first concerns ideals and varieties with symmetry, which often arise in applications from areas such as algebraic ... 
Minimization problems involving polyconvex integrands
(Georgia Institute of Technology, 20150602)This thesis is mainly concerned with problems in the areas of the Calculus of Variations and Partial Differential Equations (PDEs). The properties of the functional to minimize with respect to the given topology play an ... 
Complete nonnegatively curved spheres and planes
(Georgia Institute of Technology, 20150602)We study the space of complete Riemannian metrics of nonnegative curvature on the sphere equipped with C^{k+\alpha} topology. We show the space is homogenous for k>=2. If k is infinite, we show that the space is homeomorphic ... 
Smalltime asymptotics of call prices and implied volatilities for exponential Lévy models
(Georgia Institute of Technology, 20150108)We derive atthemoney callprice and implied volatility asymptotic expansions in time to maturity for a selection of exponential Lévy models, restricting our attention to assetprice models whose log returns structure is ...