Alex Lyford
Assistant Professor of Mathematics
- Office
- Warner 210
- Tel
- (802) 443-5564
- alyford@middlebury.edu
- Office Hours
- Fall 2022: Monday 12:10--1:30, Tuesday 9--10, Wednesday 3-Infinity, and by appointment.
- Additional Programs
- Mathematics
Alex Lyford is an Assistant Professor of Statistics, and he has been at Middlebury College since 2017. He received a Ph.D. in Statistics from the University of Georgia, and his research areas of interest are machine learning, text analysis, statistics education, and math games. Alex’s hobbies include sports, hiking, and playing board games. Alex also hosts Board Game Night in the Math department once a month on Mondays.
Students interested in doing research with Alex should stop by his office any time or contact him via email.
Courses Taught
BIOL 1230
DataScience Across Disciplines
Course Description
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 meaningful visualizations, and communicating insights from the data in a meaningful manner. During morning sessions, students will attend a combined lecture where they will learn the tools and techniques required to explore new and exciting data sets. During afternoon sessions, students will break out into smaller groups to apply these tools to domain-specific research projects in Art History, Biology, Economics, or Japanese and Linguistics.
Students enrolled in Professor Abe’s (Japanese) afternoon section will use the tools of data science to create visualizations of social and emotive meanings that surface through Japanese language/culture materials. Participants will use these visualizations to engage in various theoretical and pedagogical topics pertaining to (educational) linguistics.
Students enrolled in Professor Allen’s (Biology) afternoon section will use the tools of data science to investigate the drivers of tick abundance and tick-borne disease risk. To do this students will draw from a nation-wide ecological database.
Students enrolled in Professor Anderson’s (History of Art and Architecture) afternoon section 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.
Students enrolled in Professor Myers’ (Economics) afternoon section will use the tools of data science to create an interactive visualization of the landscape of abortion policy and access in the United States. This visualization will allow users to explore how abortion access varies across the country and how this variation in turn correlated with demographic, health, and economic outcomes.
This course will utilize the R programming language. No prior experience in statistics, data science, programming, art history, biology, economics, or Japanese is necessary.
Terms Taught
Requirements
ECON 1230
DataScience Across Disciplines
Course Description
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 meaningful visualizations, and communicating insights from the data in a meaningful manner. During morning sessions, students will attend a combined lecture where they will learn the tools and techniques required to explore new and exciting data sets. During afternoon sessions, students will break out into smaller groups to apply these tools to domain-specific research projects in Art History, Biology, Economics, or Japanese and Linguistics.
Students enrolled in Professor Abe’s (Japanese) afternoon section will use the tools of data science to create visualizations of social and emotive meanings that surface through Japanese language/culture materials. Participants will use these visualizations to engage in various theoretical and pedagogical topics pertaining to (educational) linguistics.
Students enrolled in Professor Allen’s (Biology) afternoon section will use the tools of data science to investigate the drivers of tick abundance and tick-borne disease risk. To do this students will draw from a nation-wide ecological database.
Students enrolled in Professor Anderson’s (History of Art and Architecture) afternoon section 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.
Students enrolled in Professor Myers’ (Economics) afternoon section will use the tools of data science to create an interactive visualization of the landscape of abortion policy and access in the United States. This visualization will allow users to explore how abortion access varies across the country and how this variation in turn correlated with demographic, health, and economic outcomes.
This course will utilize the R programming language. No prior experience in statistics, data science, programming, art history, biology, economics, or Japanese is necessary
Terms Taught
Requirements
ENVS 1230
DataScience Across Disciplines
Course Description
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.
Terms Taught
Requirements
FMMC 1230
DataScience Across Disciplines
Course Description
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.
Terms Taught
Requirements
FYSE 1216
Mathematics of Board Games
Course Description
Mathematics of Board Games
People have been playing games since as early as 2000 B.C. Since then, avid players have devised strategies to maximize their chances of winning. In this course we will dissect a variety of modern board games and analyze various strategies for each game using mathematics, computers, and intuition. We will further discuss whether an optimal strategy exists for each game and propose modifications to existing rules and scoring schemes. The course will culminate with a project to construct a board game. All are welcome regardless of mathematical background. 3 hrs. sem
Terms Taught
Requirements
HARC 1230
DataScience Across Disciplines
Course Description
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.
Terms Taught
Requirements
JAPN 1230
DataScience Across Disciplines
Course Description
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 meaningful visualizations, and communicating insights from the data in a meaningful manner. During morning sessions, students will attend a combined lecture where they will learn the tools and techniques required to explore new and exciting data sets. During afternoon sessions, students will break out into smaller groups to apply these tools to domain-specific research projects in Art History, Biology, Economics, or Japanese and Linguistics.
Students enrolled in Professor Abe’s (Japanese) afternoon section will use the tools of data science to create visualizations of social and emotive meanings that surface through Japanese language/culture materials. Participants will use these visualizations to engage in various theoretical and pedagogical topics pertaining to (educational) linguistics.
Students enrolled in Professor Allen’s (Biology) afternoon section will use the tools of data science to investigate the drivers of tick abundance and tick-borne disease risk. To do this students will draw from a nation-wide ecological database.
Students enrolled in Professor Anderson’s (History of Art and Architecture) afternoon section 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.
Students enrolled in Professor Myers’ (Economics) afternoon section will use the tools of data science to create an interactive visualization of the landscape of abortion policy and access in the United States. This visualization will allow users to explore how abortion access varies across the country and how this variation in turn correlated with demographic, health, and economic outcomes.
This course will utilize the R programming language. No prior experience in statistics, data science, programming, art history, biology, economics, or Japanese is necessary
Terms Taught
Requirements
MATH 0106
Math and Board Games
Course Description
Math and Board Games
Have you ever spent minutes agonizing over which move to make in a board game? Out of all the possible options, how could you possibly determine which move is best? Was there even an objectively best decision? In this course, we will explore the mathematics and underlying gameplay structures of several modern board games. In addition to playing these games during class, we’ll use math and logic to assess and quantify the value of a range of possible in-game decisions. Using formal mathematical proofs, papers, and in-class discussions, we’ll analyze the fairness and equity of strategies across a wide variety of games. We’ll finish the course by designing our own board game based on what we’ve learned! (Students who have completed FYSE1216 are not eligible to enroll in MATH 0106.)
Terms Taught
Requirements
MATH 0116
Intro to Statistical Science
Course Description
Introduction to Statistical Science
A practical introduction to statistical methods and the examination of data sets. Computer software will play a central role in analyzing a variety of real data sets from the natural and social sciences. Topics include descriptive statistics, elementary distributions for data, hypothesis tests, confidence intervals, correlation, regression, contingency tables, and analysis of variance. The course has no formal mathematics prerequisite, and is especially suited to students in the physical, social, environmental, and life sciences who seek an applied orientation to data analysis. (Credit is not given for MATH 0116 if the student has taken ECON 0111 (formerly ECON 0210) or PSYC 0201 previously or concurrently.) 3 hrs. lect./1 hr. computer lab.
Terms Taught
Requirements
MATH 0118
Introduction to Data Science
Course Description
Introduction to Data Science
In this course students will gain exposure to the entire data science pipeline: forming a statistical question, collecting and cleaning data sets, performing exploratory data analyses, identifying appropriate statistical techniques, and communicating the results, all the while leaning heavily on open source computational tools, in particular the R statistical software language. We will focus on analyzing real, messy, and large data sets, requiring the use of advanced data manipulation/wrangling and data visualization packages. Students will be required to bring alaptop (owned or college-loaned) to class as many lectures will involve in-class computational activities. (formerly MATH216) 3 hrs lect./disc.
Terms Taught
Requirements
MATH 0216
Introduction to Data Science
Course Description
Introduction to Data Science
In this course students will gain exposure to the entire data science pipeline: forming a statistical question, collecting and cleaning data sets, performing exploratory data analyses, identifying appropriate statistical techniques, and communicating the results, all the while leaning heavily on open source computational tools, in particular the R statistical software language. We will focus on analyzing real, messy, and large data sets, requiring the use of advanced data manipulation/wrangling and data visualization packages. Students will be required to bring their own laptops as many lectures will involve in-class computational activities. 3 hrs lect./disc.
Terms Taught
Requirements
MATH 0218
Upcoming
Statistical Learning
Course Description
Statistical Learning
This course is an introduction to modern statistical, machine learning, and computational methods to analyze large and complex data sets that arise in a variety of fields, from biology to economics to astrophysics. The theoretical underpinnings of the most important modeling and predictive methods will be covered, including regression, classification, clustering, resampling, and tree-based methods. Student work will involve implementation of these concepts using open-source computational tools. (MATH 0118, or MATH 0216, or BIOL 1230, or ECON 1230, or ENVS 1230, or FMMC 1230, or HARC 1230, or JAPN 1230, or LNGT 1230, or NSCI 1230, or MATH 1230 or SOCI 1230) 3 hrs. lect./disc.
Terms Taught
Requirements
MATH 0311
Statistical Inference
Course Description
Statistical Inference
An introduction to the mathematical methods and applications of statistical inference using both classical methods and modern resampling techniques. Topics will include: permutation tests, parametric and nonparametric problems, estimation, efficiency and the Neyman-Pearsons lemma. Classical tests within the normal theory such as F-test, t-test, and chi-square test will also be considered. Methods of linear least squares are used for the study of analysis of variance and regression. There will be some emphasis on applications to other disciplines. This course is taught using R. (MATH 0310) 3 hrs. lect./disc.
Terms Taught
Requirements
MATH 0500
Current
Upcoming
Advanced Study
Course Description
Advanced Study
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.
Terms Taught
MATH 0711
Statistics Capstone Seminar
Course Description
Statistics Capstone Seminar
In this course we will work with community partners to solve real-world problems using modern statistical and data science techniques. Students will work in small groups to translate research questions into actionable analysis and visualizations. Students will select a project of interest from a subset of community partners, maintain contact and collaboration with the community partner, and present their findings in a final symposium. (MATH 0218, MATH 0311, or by approval) 3 hrs. sem.
Terms Taught
Requirements
NSCI 1230
DataScience Across Disciplines
Course Description
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.
Terms Taught
Requirements
SOCI 1230
DataScience Across Disciplines
Course Description
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.
Terms Taught
Requirements