Education
University of Minnesota – Twin Cities (Sept. 2021 – May 2022)
Post Secondary Enrollment – Full Time
GPA: 3.90
Deans List Award Fall & Spring Semester
Coursework
| Course Title | Course Number | Institution | Textbook(s) Used | Course Description | Grade Received |
|---|---|---|---|---|---|
| Multivariable Calculus | Math 2263 | University of Minnesota Twin Cities | Calculus: Early Transcendentals by James Stewart, Volume 2, 8th Edition | Derivative as linear map. Differential/integral calculus of functions of several variables, including change of coordinates using Jacobians. Line/surface integrals. Gauss, Green, Stokes Theorems. | A |
| CSE Linear Algebra and Differential Equations | Math 2373 | University of Minnesota Twin Cities | Differential Equations & Linear Algebra, Fourth Edition, Edwards, Penney, and Calvis | Linear algebra: basis, dimension, eigenvalues/eigenvectors. Differential equations: linear equations/systems, phase space, forcing/resonance, qualitative/numerical analysis of nonlinear systems, Laplace transforms. Use of computer technology. | A |
| Mathematical Reasoning | Math 109 | University of California San Diego | Mathematical Reasoning: Writing and Proof by Sundstrom, Version 2.1 An Introduction to Mathematical Reasoning by Conroy and Taggart | This course uses a variety of topics in mathematics to introduce the students to rigorous mathematical proof, emphasizing quantifiers, induction, negation, proof by contradiction, naive set theory, equivalence relations and epsilon-delta proofs. | A- |
| Applied Linear Algebra | Math 102 | University of California San Diego | S. Leon and L. de Pillis, Linear Algebra with Applications, 10th edition, Pearson, 2021. | Second course in linear algebra from a computational yet geometric point of view. Elementary Hermitian matrices, Schur’s theorem, normal matrices, and quadratic forms. Moore-Penrose generalized inverse and least square problems. Vector and matrix norms. Characteristic and singular values. Canonical forms. Determinants and multilinear algebra. | A |
| Elements of Complex Analysis | Math 120A | University of California San Diego | Complex Variables and Applications, Ninth edition, by Brown and Churchill, Published by McGraw-Hill, 2014. | Complex numbers and functions. Analytic functions, harmonic functions, elementary conformal mappings. Complex integration. Power series. Cauchy’s theorem. Cauchy’s formula. Residue theorem. | A- |
| Introduction to Analysis I | Math 142A | University of California San Diego | Elementary Analysis: The Theory of Calculus (Second Edition) by Kenneth A. Ross | First course in an introductory two-quarter sequence on analysis. Topics include the real number system, numerical sequences and series, infinite limits, limits of functions, continuity, differentiation. | B |
| Applied Complex Analysis | Math 120B | University of California San Diego | Complex Variables and Applications, Ninth edition, by Brown and Churchill, Published by McGraw-Hill, 2014. | Applications of the residue theorem. Conformal mapping and applications to potential theory, flows, and temperature distributions. Fourier transformations. Laplace transformations, and applications to integral and differential equations. Selected topics such as Poisson’s formula, Dirichlet’s problem, Neumann’s problem, or special functions. | A |
| Introduction to Analysis II | Math 142B | University of California San Diego | Elementary Analysis: The Theory of Calculus (Second Edition) by Kenneth A. Ross | Second course in an introductory two-quarter sequence on analysis. Topics include the Riemann integral, sequences and series of functions, uniform convergence, Taylor series, introduction to analysis in several variables. | B+ |
| Abstract Algebra I | Math 100A | University of California San Diego | Abstract Algebra, by I. N. Herstein | First course in a rigorous three-quarter introduction to the methods and basic structures of higher algebra. Topics include groups, subgroups and factor groups, homomorphisms, rings, fields. | In Progress |
| Foundations of Topology I | Math 190A | University of California San Diego | Topology, by James Munkres | An introduction to point set topology: topological spaces, subspace topologies, product topologies, quotient topologies, continuous maps and homeomorphisms, metric spaces, connectedness, compactness, basic separation, and countability axioms. Examples. Instructor may choose further topics such as Urysohn’s lemma, Urysohn’s metrization theorem. | In Progress |
| Enumerative Combinatorics | Math 184 | University of California San Diego | Miklós Bóna, A Walk Through Combinatorics, 4th edition | Introduction to the theory and applications of combinatorics. Enumeration of combinatorial structures (permutations, integer partitions, set partitions). Bijections, inclusion-exclusion, ordinary and exponential generating functions. | In Progress |
| Introduction to Numerical Analysis: Linear Algebra | Math 170A | University of California San Diego | Unknown | This course covers analysis of numerical methods for linear algebraic systems and least squares problems. Topics include orthogonalization methods. Ill conditioned problems. Eigenvalue and singular value computations. Knowledge of programming recommended. | Planned |
| Introduction to Probability | Math 180A | University of California San Diego | Unknown | Probability spaces, random variables, independence, conditional probability, distribution, expectation, variance, joint distributions, central limit theorem. | Planned |
| Introduction to Numerical Analysis: Approximation and Nonlinear Equations | Math 170B | University of California San Diego | Unknown | Rounding and discretization errors. Calculation of roots of polynomials and nonlinear equations. Interpolation. Approximation of functions. Knowledge of programming recommended. | Planned |
| Abstract Algebra II | Math 100B | University of California San Diego | Abstract Algebra, by I. N. Herstein | Second course in a rigorous three-quarter introduction to the methods and basic structures of higher algebra. Topics include rings (especially polynomial rings) and ideals, unique factorization, fields; linear algebra from perspective of linear transformations on vector spaces, including inner product spaces, determinants, diagonalization. | Planned |
| Abstract Algebra III | Math 100C | University of California San Diego | Unknown | Third course in a rigorous three-quarter introduction to the methods and basic structures of higher algebra. Topics include linear transformations, including Jordan canonical form and rational canonical form; Galois theory, including the insolvability of the quintic. | Planned |
| Introduction to Cryptography | Math 187A | University of California San Diego | Unknown | An introduction to the basic concepts and techniques of modern cryptography. Classical cryptanalysis. Probabilistic models of plaintext. Monalphabetic and polyalphabetic substitution. The one-time system. Caesar-Vigenere-Playfair-Hill substitutions. The Enigma. Modern-day developments. The Data Encryption Standard. Public key systems. Security aspects of computer networks. Data protection. Electronic mail. | Planned |