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.

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  • Shortest closed curve to inspect a sphere 

    Wenk, James F. (Georgia Institute of Technology, 2022-07-30)
    We show that in Euclidean 3-space any closed curve γ which lies outside the unit sphere and contains the sphere within its convex hull has length ≥ 4π. Equality holds only when γ is composed of 4 semicircles of length π, ...
  • Algebraic and semi-algebraic invariants on quadrics 

    Jung, Jaewoo (Georgia Institute of Technology, 2022-07-30)
    This dissertation consists of two topics concerning algebraic and semi-algebraic invariants on quadrics. The ranks of the minimal graded free resolution of square-free quadratic monomial ideals can be investigated ...
  • Matching problems in hypergraphs 

    Yuan, Xiaofan (Georgia Institute of Technology, 2022-07-30)
    Kühn, Osthus, and Treglown and, independently, Khan proved that if H is a 3-uniform hypergraph on n vertices, where n is a multiple of 3 and large, and the minimum vertex degree of H is greater than {(n-1) choose 2} - {2n/3 ...
  • Application of The Circle Method in Five Number Theory Problems 

    Mousavi, Seyyed Hamed (Georgia Institute of Technology, 2022-08-01)
    This thesis consists of three applications of the circle method in number theory problems. In the first chapter, we study a question of Graham. Are there infinitely many integers $n$ for which the central binomial coefficient ...

    Qian, Yingjie (Georgia Institute of Technology, 2022-08-01)
    When developing a theory for 3-connected graphs, Tutte showed that for any 3-connected graph G and any three vertices a, b, c of G, G-c has an a-b path P such that G-P is connected. We call paths non-separating if their ...
  • Trellis Decoding And Applications For Quantum Error Correction 

    Sabo, Eric (Georgia Institute of Technology, 2022-08-08)
    Compact, graphical representations of error-correcting codes called trellises are a crucial tool in classical coding theory, establishing both theoretical properties and performance metrics for practical use. The idea was ...
  • Contact geometric theory of Anosov flows in dimension three and related topics 

    Hozoori, Surena (Georgia Institute of Technology, 2022-07-20)
    This thesis consists of the author's work on the contact and symplectic geometric theory of Anosov flows in low dimensions, as well as the related topics from Riemannian geometry. This includes the study of the interplay ...
  • Factorization theorems and canonical representations for generating functions of special sums 

    Schmidt, Maxie Dion (Georgia Institute of Technology, 2022-07-19)
    This manuscript explores many convolution (restricted summation) type sequences via certain types of matrix based factorizations that can be used to express their generating functions. The last primary (non-appendix) section ...
  • On embeddings of 3-manifolds in symplectic 4-manifolds 

    Mukherjee, Anubhav (Georgia Institute of Technology, 2022-07-13)
    We proposed a conjecture that every 3-manifolds smoothly embedded in some closed symplectic 4-manifolds. This work shows that any closed oriented 3-manifold can be topologically embedded in some simply-connected closed ...
  • Learning Dynamics from Data Using Optimal Transport Techniques and Applications 

    Ma, Shaojun (Georgia Institute of Technology, 2022-07-08)
    Optimal Transport has been studied widely in recent years, the concept of Wasserstein distance brings a lot of applications in computational mathematics, machine learning, engineering, even finance areas. Meanwhile, people ...
  • Erdos-Posa theorems for undirected group-labelled graphs 

    Yoo, Youngho (Georgia Institute of Technology, 2022-06-14)
    Erdős and Pósa proved in 1965 that cycles satisfy an approximate packing-covering duality. Finding analogous approximate dualities for other families of graphs has since become a highly active area of research due in part ...
  • A Novel Delay Differential Equation Model of the Germinal Center Reaction and an Algorithm for Minimum Length Surveillance Paths 

    Ide, Benjamin (Georgia Institute of Technology, 2022-05-19)
    The humoral adaptive immune system in vertebrates includes a process called the germinal center reaction in which B-cells rapidly increase their binding affinity to an antigen that is part of a pathogen. A fraction of ...
  • New Numerical And Computational Methods Leveraging Dynamical Systems Theory For Multi-Body Astrodynamics 

    Kumar, Bhanu (Georgia Institute of Technology, 2022-06-01)
    Many proposed interplanetary space missions, including Europa Lander and Dragonfly, involve trajectory design in environments where multiple large bodies exert gravitational influence on the spacecraft, such as the Jovian ...
  • Invariance principle of random matrix 

    Duan, Jun Tao (Georgia Institute of Technology, 2022-05-16)
    Random matrix has been found useful in many real-world applications. The celebrated Johnson-Lindenstrauss lemma states that certain geometric structure of deterministic vectors is preserved when projecting high dimensional ...

    Liu, Xiao (Georgia Institute of Technology, 2022-05-03)
    This work is concerned with the two dimensional capillary gravity water waves of finite depth $x_2 \in (-h, 0)$ linearized at a uniformly monotonic shear flow $U(x_2)$. We focus on the eigenvalue distribution and linear ...
  • Branched Covers and Braided Embeddings 

    Kolay, Sudipta (Georgia Institute of Technology, 2021-06-25)
    We study braided embeddings, which is a natural generalization of closed braids in three dimensions. Braided embeddings give us an explicit way to construct lots of higher dimensional embeddings; and may turn out to be as ...
  • On the Rank of Random, Symmetric Matrices over Z_2 via Random Graphs 

    Raghavan, Aaditya (Georgia Institute of Technology, 2022-05)
    It is well-known that the game of \textit{Lights Out} on a graph $G$ with $|V(G)| = n$ is universally solvable if and only if the sum of the adjacency matrix of $G$ and the identity matrix $I_{n}$ is invertible over $\Z_2$. ...
  • On difference graph covers and the local dimension of the Boolean lattice 

    Hall, Ariana (Georgia Institute of Technology, 2022-05-03)
  • Dual representations of polynomial modules with applications to partial differential equations 

    Harkonen, Marc N. (Georgia Institute of Technology, 2022-05-02)
    In 1939, Wolfgang Gröbner proposed using differential operators to represent ideals in a polynomial ring. Using Macaulay inverse systems, he showed a one-to-one correspondence between primary ideals whose variety is a ...
  • Duality Between Deep Learning And Algorithm Design 

    Chen, Xinshi (Georgia Institute of Technology, 2022-05-02)
    This thesis introduces 'Duality Between Deep Learning And Algorithm Design'. Deep learning is a data-driven method, whereas conventional algorithm design is a knowledge-driven method. Based on their connections and ...

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