Introduction to Numerical Analysis We will study the development, analysis, and implementation of numerical methods for approximating solutions to mathematical problems. We will begin with applications of Taylor polynomials, computer representation of numbers, and types of errors.  Other topics will include polynomial and spline interpolation, numerical integration and differentiation, rootfinding, and numerical solutions of differential equations.  Accuracy will be quantified by the concept of numerical error.  Additionally, we will study the stability, efficiency, and implementation of algorithms.  We will utilize the software MATLAB throughout to demonstrate concepts, as well as to complete assignments and projects.

Advanced Mathematical Modeling Seminar A tutorial on advanced mathematical model building and analysis for students who have completed work in Differential Equations and Probability. We will study deterministic and stochastic models of interacting populations with a focus on mathematical ecology and epidemiology. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. Fulfills the capstone senior work requirement for the mathematics major. (Approval Only) 3 hrs. Sem.

Linear Algebra Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule.

Partial Differential Equations An introduction to partial differential equations (PDEs) with an emphasis on first and second-order  linear equations. Using analytical, qualitative, and numerical techniques, we will study the Laplace,  heat, and wave equations, as well as their applications. MATLAB will be used where applicable.  (MATH  0223 and either of MATH 0225 or MATH 0226) 3 hr lect.

Differential Equations This course provides an introduction into ordinary differential equations (ODEs) with an emphasis on linear and nonlinear systems using analytical, qualitative, and numerical techniques.  Topics will include separation of variables, integrating factors, eigenvalue method, linearization, bifurcation theory, and numerous applications.  In this course, we will introduce MATLAB programming skills and develop them through the semester.

Calculus II A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. MATH 0121 or equivalent, or by placement)

Mathematical modeling An introduction into the process of developing and interpreting mathematical models within the framework of numerous applications. In this course, we will utilize discrete, continuous, and probabilistic approaches to explore applications such as population dynamics, epidemiology, and neuron activity.  Time permitting, we may also introduce the derivation of spatiotemporal models.  MATLAB will be used to implement and analyze several of these models.

Data Science Across Disciplines In this course, we will gain exposure to the entire data science pipeline—obtaining and cleaning large and messy data sets, exploring these data and creating engaging visualizations, and communicating insights from the data in a meaningful manner. During morning sessions, we will learn the tools and techniques required to explore new and exciting data sets. During afternoon sessions, students will work in small groups with one of several faculty members on domain-specific research projects in Geography, Political Science, Restorative Justice, or Healthcare. This course will use the R programming language. No prior experience with R is necessary.  MATH/STAT 1230: Students will explore pediatric healthcare data to better understand the risks correlated with various childhood illnesses through an emphasis on the intuition behind statistical and machine learning techniques. We will practice making informed decisions from noisy data and the steps to go from messy data to a final report. Students will become proficient in R and gain an understanding of various statistical techniques.  GEOG 1230: In this section, students will use data science tools to explore the ways migration systems in the United States changed during the COVID-19 pandemic. We will draw on data collected from mobile phones recording each phone’s monthly place of residence at the census tract level. The dataset includes monthly observations from January 2019 through December 2021 allowing the analysis to compare migration systems pre-pandemic with those during the pandemic.  INTD 1230A: Data is a powerful tool for improving health outcomes by making programmatic choices to support justice. In this afternoon section of Data Across the Disciplines, students will be working with Addison County Restorative Justice (ACRJ) on understanding patterns in the occurrence of driving under the influence. ACRJ has over 1,000 cases and would like to better understand their data and come up with ways to access information. We will explore how identity, geography, and support impact outcomes from DUI cases. Using statistical analysis and data visualizations, along with learning about ethical data practices, we will report our findings.   INTD 1230B: Let’s dive into the minutes and reports of local towns to develop an accessible news and history resource. Could this be a tool for small newspapers to track local news more easily? Can we map this fresh data for a new look across geographies? Do you want to help volunteer town officials make decisions and better wrangle with their town’s history and data?  In this course we will develop a focused database of documents produced by several municipal boards and commissions. We will engage in conversation with local officials, researchers, and journalists. This course aims to introduce students to making data from real world documents and the people that make them to generate useful information that is often open but frequently difficult to sift through.  PSCI 1230: How do candidates for U.S. national office raise money? From whom do they raise it? In this section we will explore these questions using Federal Election Commission data on individual campaign contributions to federal candidates. Our analysis using R will help us identify geographic patterns in the data, as well as variations in funds raised across types of candidates. We will discuss what implications these patterns may have for the health and functioning of democracy in the U.S.

Data Science Across Disciplines In this course, we will gain exposure to the entire data science pipeline—obtaining and cleaning large and messy data sets, exploring these data and creating engaging visualizations, and communicating insights from the data in a meaningful manner. During morning sessions, we will learn the tools and techniques required to explore new and exciting data sets. During afternoon sessions, students will work in small groups with one of several faculty members on domain-specific research projects in Sociology, Neuroscience, Animation, Art History, or Environmental Science. This course will utilize the R programming language. No prior experience with R is necessary. ENVS: Students will engage in research within environmental health science—the study of reciprocal relationships between human health and the environment. High-quality data and the skills to make sense of these data are key to studying environmental health across diverse spatial scales, from individual cells through human populations. In this course, we will explore common types of data and analytical tools used to answer environmental health questions and inform policy. FMMC: Students will explore how to make a series of consequential decisions about how to present data and how to make it clear, impactful, emotional or compelling. In this hands-on course we will use a wide range of new and old art making materials to craft artistic visual representations of data that educate, entertain, and persuade an audience with the fundamentals of data science as our starting point. NSCI/MATH: Students will use the tools of data science to explore quantitative approaches to understanding and visualizing neural data. The types of neural data that we will study consists of electrical activity (voltage and/or spike trains) measured from individual neurons and can be used to understand how neurons respond to and process different stimuli (e.g., visual or auditory cues). Specifically, we will use this neural data from several regions of the brain to make predictions about neuron connectivity and information flow within and across brain regions. SOCI: Students will use the tools of data science to examine how experiences in college are associated with social and economic mobility after college.  Participants will combine sources of "big data" with survey research to produce visualizations and exploratory analyses that consider the importance of higher education for shaping life chances.  HARC: Students will use the tools of data science to create interactive visualizations of the Dutch textile trade in the early eighteenth century. These visualizations will enable users to make connections between global trade patterns and representations of textiles in paintings, prints, and drawings.

Topics in Linear Algebra and Differential Equations Topics may include diagonalization of matrices, quadratic forms, inner product spaces, canonical forms, the spectral theorem, positive matrices, the Cayley-Hamilton theorem, ordinary differential equations of arbitrary order, systems of first-order differential equations, power series, and eigenvalue methods of solution, applications.

Jennifer Crodelle

Reviews and ratings for Jennifer Crodelle at Middlebury College.Jennifer Crodelle teaches Intro to Numerical Analysis, Advanced Math Modeling Seminar, Linear Algebra and more.  Explore top rated instructors and find the best for you.Is Jennifer Crodelle good ? Find out on MiddCourses.

I really enjoyed taking this course. Prof. Crodelle is an excellent teacher, and going to office hours is extremely useful. Studying for the exams requires practicing problems from the textbook, not just reviewing past homework problems.

If you have never taken a class with Jen you definitely should! Her energy is just amazing. This class was also really well structured. I learned a lot. The exams were take home and then there was an oral component that essentially consisted of talking through two of the questions more in depth.

Jen is passionate about the content and extremely patient. Grading should not be a problem. The only thing I didn't like about this course is that linear algebra can be somewhat boring at times. I learned a lot, but I didn't get intellectually challenged as much as I expected.