Paul Dougall
Academics
Publications
Modeling optimal reopening strategies for COVID-19 and its variants by keeping infections low and fixing testing capacity
Extended an SIR model to test various reopenning strategies for universities considering varrying tranmission rates and "super spreader" events.
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Applicable Classes
Classes that I have taken and the materials that were covered. Classes marked with an asterisk are classes that I am currently enrolled in.
Mathematics
Mathematical Foundation of Data-Driven Science and Machine Learning - 4.0 - Spring 2022
- Learned about various machine learning techniques, applications, and common misconceptions
- Properties of sets, covers of sets, closure, sequences, and series.
- Sigma algebras, general measure spaces, lebesgue measure, measure integration, and LP spaces
- Studied common matrix factorizations used in applied mathematics including SVD, LU, Cholesky, QR, Jordan, and Schur as well as least squares
- Study of operators, Banach spaces, LP spaces, Hilbert spaces
- Studied topological spaces, openess, compactness, connectedness, boundaries, density, continuity, and f-sigma sets
- A mathematically theoretical approach to the study of the Complex Numbers. The Riemann sphere and path integrals were both studied in addition to the analysis the complex counterpart to common calculus theorems.
- An independent research project with once a week presentations to faculty and students focuing on the fundamentals of algebra from an extremely abstract point of view. Propositional logic was used and explored working from the ground up to define things from a perspective not often done in a typical mathematics graduate program. Boolean algebra, sigma algebras, varieties, lattices, filters, Ideals, ultrafilters, ultrproducts, Stone Duality, and the Stone-Cech compactification.
- A pure math approach to Linear Algebra focusing on vector spaces, various important subspaces such as the column space and null space, constructing a basis for a subspace, and eigenvalues and eigenvectors.
- An independent research project with once a week presentations to faculty and students focuing on the fundamentals of algebra from an extremely abstract point of view. Propositional logic was used and explored working from the ground up to define things from a perspective not often done in a typical mathematics graduate program. Boolean algebra, sigma algebras, varieties, lattices, filters, Ideals, ultrafilters, ultrproducts, Stone Duality, and the Stone-Cech compactification.
- An in depth mathematically theoretical approach to the study of Neural Networks. Tensors, gradients, Jacobian mattrices, gradient descent, backwards propegation, equations whose derivative can be written in terms of the original equation, image classification, hyperfeatures, activation functions and loss functions, and convolutional neural networks were all covered.
- Graduate study of algebraic structures, ring theory, and some field theory.
- Further study of algebraic structures.
- Graduate study of real analysis covering sigma algebras, Lebesgue outer measure, and Lebesgue measure
- Graduate study of topology
- Study of topological spaces and structures
- Analysis of the reals and extended reals
- Graduate study of algebraic structures and group theory
- Major Theorems: Euclidean Algorithm, Lagrange's Theorem, Isomorphism Theorems, Sylow Theorems
- Basic concepts of algebraic structures.
- Graduate study of real analysis covering properties of sets, covers of sets, closure, sequences, and series.
- Major Theorems: Bolzano-Weierstrass Theorem, Extreme Value Theorem, Heine-Borel Theorem, Monotone Convergence Theorem, Nested Interval Theorem, Squeeze Theorem.
- Mathematical analysis of sets at the graduate level
- Study of algebra of sets, Cardinality, and constructing the natural numbers.
- Major Theorems: Axiom of Choice, Zorn's Lemma
- Introduction to matrices and their properties
- Study of systems of linear equations, vectors, matrices, null spaces, eigenvectors, and vector spaces
- Major Theorems: Invertible Matrix Theorem
- Applied set theory and logic to calculus theorems and concepts
- Learned about the technical definitions of addition, multiplication, absolute value, and sequences
- Problem solving using mathematical reasoning
- Learned how to logically prove mathematical formulas
- Major Theorems: Division Algorithm, Principle of Mathematical Induction, Well-Ordering Principle,
- Student driven teaching method involving daily presentations of materials not yet covered in class
- Study of differential forms, divergence, Gauss's Law, Green's Theorem, matrix calculus, and partial derivatives
Computer Science
Advanced Algorithms - 4.0 - Spring 2022
Selected Languages - Satisfactory - Spring 2017
- Walked through complicated proofs that were groundbreaking in the field of theoretical computer science such as:
- Lovász Local Lemma and the Moser-Tardos Algorithm
- Maximum Cut of a Connected Graph is NP-Complete
- Karger's Algorithm for Minimum Cut of a Connected Graph
- For k>3, k-SAT is NP-Complete
- PAC learnability and having a sample compression scheme are equivalent
- Lovász Local Lemma and the Moser-Tardos Algorithm
- Additionally studied:
- Semidefinite Programming (SDP)
- Linear Programming
- Semidefinite Programming (SDP)
- Wrote a final paper and presented on Kurt Godel's First Incompleteness Theorem
Selected Languages - Satisfactory - Spring 2017
- Quickly learned the basics of C++ in a half semester 1-credit course
- Learned the basics of object-oriented programming
- Obtained a functional understanding of Java
Biology/Bioinformatics
Directed Study in Biology - 4.0 - Fall 2021
Bioinformatics - 3.3 - Spring 2021
Bioinformatics - 3.3 - Spring 2021
- Studied the evolution of sequencing technology through to Next Generation Sequencing (NGS)
- Utilized sequencing databases and tools such as NCBI and BLAST
- Learned about De Novo and reference based assembly and how they are performed
- Developed an understanding of the types of genetic mutations such as SNPs and indels
- Read about and discussed the five senses, how they work, and what regions of the brain they are involved with
- Learned about movement, consciousness, balance, attention, learning, language, sleep, and how each of them interact with the brain
- Studied the various diseases that target and affect the nervous system
- Learned about the various cells that comprise the human body, DNA, and diseases that target them
- Studied the 11 major systems of the human body
Data Analytics
Bayesian Data Analysis - 3.7 - Fall 2020
Info Visualization - 3.7 - Fall 2020
Applied Machine Learning - 4.0 - Spring 2020
Info Visualization - 3.7 - Fall 2020
Applied Machine Learning - 4.0 - Spring 2020
- Learned about various machine learning methods such as linear regression, SVM, clustering, and decision trees
- Applied methods utilizing python and various common machine learning problems/datasets such as classification of the Iris flower dataset, classification of the MNIST dataset, and creation of the logic gates using neural networks
- Taught and implemented various statistical methods and tests both parametric and nonparametric including t-test, One-way ANOVA, Two-way ANOVA, MANOVA, chi-square goodness of fit, chi-square test of independence, Wilcoxon-Mann-Whitney test, Fisher’s exact test, Kruskal Wallis test, and the Wilcoxon signed rank sum test.
General Business
Microeconomics - 3.7 - Spring 2020
Digital Marketing - 3.0 - Fall 2019
Finance - 3.0 - Fall 2018
Digital Marketing - 3.0 - Fall 2019
Finance - 3.0 - Fall 2018
- Study of accounting ratios, risk and return, net present value, and cost of capital.
- In depth financial assessment of a company (ZOOM Corporation)
- More in depth study of Equity, Liabilities, Cash Flows, Budgets, Bonds, Income Statements and Financial Statements
- Study of GDP, GNP, Unemployment, and the Business Cycle
- Created a theoretical marketing plan for a local business
- Overview of common marketing terms
- Created balance sheets, trial balances, journal entries, and general ledgers
- Understanding of management concepts and theories
- Knowledge of managerial competencies and personal assessment
- Advanced speaking skills by giving numerous presentations
Music Business
Essential Practices of Music Business - 4.0 - Fall 2018
- Studied various professional practices
- Researched resume and cover letter writing techniques, interview techniques, career planning strategies, and job/interview searching strategies.
- Created and pitched a business plan for a hypothetical business venture (A Contemporary Arts Festival).
- Networked with guest speakers
- In depth usage of a recording studio and pro tools
- Discussed contracts, copyright, the court system, publishing, record deals, and trademarks
- Learned of the various fields and job possibilities within the music industry
- Researched the process of marketing research in application to the music industry
- Experimented with various programs commonly used in the music business industry
- Experience with Audacity, Garage Band, Logic, Noteflight, MuseScore, and Weebly
- Use of a professional studio including both digital and physical aspects
- Extensive use of Pro Tools and the various features of the program
- Researched dramatic scoring for a paper and presentation
- Networked and communicated with guest speakers