Connecting mathematical classes to their applications in an inclusive setting.
Scripps College Mathematics Senior Thesis
If you are interested in discussing a Senior Thesis with me, as either a First or Second Reader, please feel free to reach out. The Scripps Senior Thesis template is this Overleaf file which you can copy to use, note the Scripps Senior Thesis due date is the Friday before Spring Break.
Below are some of the thesis projects I am a part of, as you will see the range of topics is wide.
A Mathematical Model of Malaria with Temperature-Dependent Parameters, Kaia M. Smith - Scripps 2023S, First Reader with Second Reader Adam Landsberg
Knot theory: Exploring the relationship between the Alexander polynomial and Alexander tribracket knot invariants, Lily Wartman - Scripps 2023S, First Reader with Second Reader Sherilyn Tamagawa
Migration and Modelling - A Mathematical Approach to Game Theory and the 1947 Partition, Perbhaat Khowaja - Scripps 2023S, Dual Thesis, Second Reader with First Reader Tahir Andrabi, and Nayana Bose
Correlation Does Not Imply Correlation: A Thesis on Causal Influence and Simpson's Paradox, Emily Naitoh - Scripps 2022F, First Reader with Second Reader Winston Ou
An Examination of Legionnaires' Disease Through the Lens of ODE Modeling, Kimi Miramontes - Scripps 2022S, First Reader with Second Reader Winston Ou
Utilizing Deep Learning to Analyze Queer-Coded Villains, Stone Van Allen - Scripps 2022S, Dual Thesis, First Reader Along with Piya Chatterjee
Examining Bias Against Women in Professional Settings through Bifurcation Theory, Lauren Cashdan - Claremont McKenna 2021F, First Reader with Second Reader Sam Nelson
Bayesian Network Predictions for Title IX Policy Changes, Jordan Wellington - Scripps 2021S, Dual Thesis - First Reader Along with Sue Castagnetto
Investigating changes in the SEIRMD model applied to COVID-19, Anne Leisenring Cohen - Scripps 2021S, Second Reader with First Reader Jo Hardin
Mathematical Analysis of COVID-19, Karmishtha Seth- Scripps 2021S, Second Reader with First Reader Weiqing Gu
Random Matrix Theory: A Combinatorial Proof of Wigner's Semicircle Law, Vanessa Wolf - Scripps 2021S, Second Reader with First Reader Michael O'Neill
Convergence Time of the Recombination Markov Chain on Small Planar Graphs, Emma Kolesnik - Scripps 2020F, Second Reader with First Reader Sarah Cannon
Winning Moves: Mathematical strategies behind certain games and their philosophical implications, Ellye Groh - Scripps 2020S, Dual Thesis - First Reader Along with Dion Scott-Kakures
MATH 185 - Methods in Modern Modeling
Models are applied on a daily basis to provide insight into any number of current world problems. From diseases to government policy, modeling techniques are being used to predict outcomes and manage populations. With the advent of more computational power and data collection, novel model types and techniques for analysis are being derived. We will explore current models and techniques which are used across multiple disciplines. We will consider agent-based (or individual-based) modeling, and ordinary differential equation models with parameter estimation, along with additional topics. Students will have a chance to investigate using analytical and computational skills, that can be applied across a diversity of fields.
MATH 183 - Modeling and Simulation
This course is an introduction to mathematical models with deterministic and stochastic dynamics and with discrete and continuous time. Students will learn the mathematical analysis and numerical simulations for these models, and then present their results in both written and verbal forms. The models will be applied to various applications.
MATH 102- Differential Equations and Modeling
In this course, we will introduce some basic models including Lotka-Volterra (Predator-Prey) models, as well as some standard modeling techniques. The emphasis in the course will be placed on qualitative methods and the use of software to understand solutions. Eigenvalues and eigenvectors will be introduced to fully solve linear systems in the plane. Linear and non-linear systems of differential equations will be analyzed by classifying orbits near fixed-point solutions. Students may not receive credit for both MATH 102 and MATH 111.
MATH 060 - Linear Algebra
This course emphasizes vector spaces and linear transformations. Topics include linear independence, bases, nullity and rank of a linear transformation, The Dimension Theorem, the representation of linear transformations as matrices, eigenvalues and eigenvectors, and determinants. Additional topics may include inner product spaces and Gram-Schmidt orthogonalization.
MATH 052 - Introduction to Statistics
MATH 032 - Calculus III
This is the third course of a standard three-course sequence in calculus. The course covers calculus of multivariable and vector-valued functions. Topics include partial derivatives, the gradient, Lagrange multipliers, multiple integrals, change of variables, parameterized curves and surfaces, vector fields, line integrals, flux integrals, Green’s Theorem, the Divergence Theorem, and Stokes’ Theorem.
MATH 030 - Calculus I
MATH 030 is the first course of a standard three course sequence in calculus. The topics covered include differentiation, integration, mean value theorem, transcendental functions, and trigonometric functions.
CORE III - Histories of the Present - Living in a World of Numbers
In an age when we are bombarded with numbers, it is important to explore what stories are being told and how the numbers we observe are being formulated. We will investigate the interdisciplinary nature of dealing with numbers, considering a variety of disciplines and applications to life. Topics we will explore include social justice, journalism, disease outbreaks, politics, and more. Students will be encouraged to choose a field which interests them, then explore the field's use of numbers to communicate findings. Together we will examine various uses of numbers, looking for similarities and differences. Students will learn some basic analysis tools used across many disciplines, allowing students to understand presented results. Additionally, students will learn about different basic methods to create their own numbers, models, and analyses. With these skills students will then formulate their own findings, creating their own interdisciplinary work.
MATH 411 - Mathematical Modeling
Construction and analysis of mathematical models used in science and industry. Projects emphasized. Writing-emphasis course.
MATH 151- Mathematics for the Life Sciences I
For students majoring in the life sciences. Does not serve as a prerequisite for 231 or 241. Topics include descriptive statistics, linear regression, discrete probability, matrix algebra, difference equations, calculus, and differential equations. Emphasis on applications in the life sciences. Includes computer projects.
MATH 241 - Calculus III
Calculus of functions in two or more dimensions. Includes solid analytic geometry, partial differentiation, multiple integration, and selected topics in vector calculus.
MATH 208 - Calculus III
Vectors and surfaces, parametric equations and motion, functions of several variables, partial differentiation, maximum-minimum, Lagrange multipliers, multiple integration, vector fields, path integrals, Green's Theorem, and applications.
MATH 203- Contemporary Mathematics
Applications of quantitative reasoning and methods to problems and decision making in the areas of management, statistics, and social choice. Includes networks, critical paths, linear programming, sampling, central tendency, inference, voting methods, power index, game theory, and fair division problems.
MATH 103 - College Algebra and Trigonometry
First and second degree equations and inequalities, absolute value, functions, polynomial and rational functions, exponential and logarithmic functions, trigonometric functions and identities, laws of sines and cosines, applications, polar coordinates, systems of equations, graphing, conic sections.
MATH 101 - College Algebra
Real numbers, exponents, factoring, linear and quadratic equations, absolute value, inequalities, functions, graphing, polynomial and rational functions, exponential and logarithmic functions, system of equations.
MATH 107 - Calculus II - Teaching Assistant
Integration theory; techniques of integration; applications of definite integrals; series, Taylor series, vectors, cross and dot products, lines and planes, space curves.
This course promotes a deep understanding of geometry, measurement and algebraic thinking and its role in the K-3 mathematics curriculum. Emphasis is placed on mathematical argument related to geometric relationships, measurement, spatial reasoning, patterns, relations and functions. This is typically the second course in the Primarily Math sequence.
MATH 800P: Number and Operation for K-3 Math Specialist
This course strengthens teachers’ conceptual knowledge of number and operation in the K-3 mathematics curriculum and connects the intuitive mathematical understandings that children bring to school with an understanding of place value in the K-3 curriculum. The significance of base 10 in our place value system, along with its role in arithmetic operations and their properties, is a major emphasis of the course. This is typically the first course in the Primarily Math sequence.
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