Academic Coursework
A detailed overview of my undergraduate and graduate courses in Mathematics, Physics, Statistics, and Computer Science.
15
Mathematics & Related
8
Advanced coursework
3.7
Ohio State University
4
Math, Physics, Stats, CS
Math Courses
Main Topics Covered:
This course covers group theory, ring theory, and field theory. Topics include fundamental concepts such as homomorphisms, isomorphisms, and basic properties of algebraic structures.
Textbook:
Abstract Algebra by David S. Dummit and Richard M. Foote
Main Topics Covered:
This course covers measure theory, Lebesgue integration, and differentiation. Topics include sigma-algebras, measurable functions, and the Lebesgue integral.
Textbook:
Real Analysis: Measure Theory, Integration, and Hilbert Spaces by Elias M. Stein and Rami Shakarchi
Main Topics Covered:
This course covers prime numbers, Diophantine equations, and modular arithmetic. Topics include the distribution of primes, congruences, and quadratic reciprocity.
Textbook:
A Classical Introduction to Modern Number Theory by Ireland and Rosen
Main Topics Covered:
This course covers partial differential equations, including the heat equation, wave equation, and Laplace equation. Topics include separation of variables, Fourier series, and boundary value problems.
Textbook:
Partial Differential Equations for Scientists and Engineers by Stanley J. Farlow
Main Topics Covered:
This course covers logic, set theory, and proof techniques. Topics include propositional logic, predicate logic, and methods of mathematical proof.
Textbook:
How to Prove It: A Structured Approach by Daniel J. Velleman
Main Topics Covered:
This course covers vector spaces, matrices, determinants, and eigenvalues. Topics include linear transformations, inner product spaces, and spectral theory.
Textbook:
Linear Algebra Done Right by Sheldon Axler
Main Topics Covered:
This course covers partial derivatives, multiple integrals, and vector calculus. Topics include gradients, divergence, curl, and the theorems of Green, Stokes, and Gauss.
Textbook:
Calculus: Early Transcendentals by James Stewart
Physics Courses
Main Topics Covered:
This course covers special relativity, four-vectors, and relativistic dynamics. Topics include Lorentz transformations, relativistic kinematics, and relativistic energy and momentum.
Textbook:
Introduction to Special Relativity by Robert Resnick
Main Topics Covered:
This course covers Newtonian mechanics, Lagrangian and Hamiltonian mechanics. Topics include equations of motion, conservation laws, and variational principles.
Textbook:
Classical Mechanics by John R. Taylor
Statistics Courses
Main Topics Covered:
This course covers statistical inference, hypothesis testing, and regression analysis. Topics include point estimation, interval estimation, and linear regression models.
Textbook:
Mathematical Statistics with Applications by Dennis D. Wackerly, William Mendenhall, and Richard L. Scheaffer
Main Topics Covered:
This course covers probability theory, random variables, and distributions. Topics include probability spaces, discrete and continuous random variables, and probability distributions.
Textbook:
Introduction to Mathematical Statistics by Robert V. Hogg, Joseph W. McKean, and Allen T. Craig
Main Topics Covered:
This course covers data analysis, experimental design, and quality control. Topics include descriptive statistics, hypothesis testing, and control charts.
Textbook:
Applied Statistics and Probability for Engineers by Douglas C. Montgomery and George C. Runger
Computer Science Courses
Main Topics Covered:
This course covers combinatorics, graph theory, and Boolean algebra. Topics include counting principles, graph algorithms, and logical structures.
Textbook:
Discrete Mathematics and Its Applications by Kenneth H. Rosen
Main Topics Covered:
This course covers software design, coding, testing, and debugging. Topics include software development lifecycle, coding standards, and debugging techniques.
Textbook:
Clean Code: A Handbook of Agile Software Craftsmanship by Robert C. Martin
Main Topics Covered:
This course covers object-oriented design, design patterns, and software architecture. Topics include design principles, common design patterns, and architectural styles.
Textbook:
Design Patterns: Elements of Reusable Object-Oriented Software by Erich Gamma, Richard Helm, Ralph Johnson, and John Vlissides