Mathematics & Physical Sciences

This course explores the fundamentals of biochemistry. Emphasis will be placed on the flow and regulation of genetic information from DNA to RNA to protein, protein composition, structure and function, enzyme kinetics, metabolic pathways, and sensory systems. The integration of these key concepts will be explored through the lens of drugs: mechanism of action, metabolism in the body, and manipulation of protein and pathway function. This course should be especially useful to students with an interest in medicine, nutrition, physiology, toxicology, genetics, and pharmacology. This class meets for three hours of lecture per week; some sessions will include laboratory demonstrations and/or experiments. Evaluations are based on class preparation and participation, mid-term exam, and final paper.

This course will provide students with a toolbox of techniques in statistical analysis, with a focus on the biological sciences. Students will learn how to choose and apply a variety of widely used statistical tests, how to design experiments and studies with statistical analysis in mind, and how to use a range of specialized statistical approaches for data types frequently encountered in the biological sciences. The methods we will cover include parametric and nonparametric tests; approaches designed for categorical, ordinal, and continuous data; biodiversity statistics and ordination methods; Bayesian vs. frequentist inference; and robust experimental design. The class will highlight the assumptions involved in statistical inference and the conditions that must be met in order to use statistical tests appropriately. In the lab, students will use the statistical programming language R to explore, display, and analyze data using the methods covered in class. By the end of the term, students should be able to choose appropriate analytical methods for a wide range of data types, design statistically valid experiments, and write code for basic statistical tests in R. Students will be evaluated based on daily homework assignments, weekly lab work, several take-home exams, and a final group presentation based on an original analysis of an archived data set chosen by the students. Note: each student should have a laptop for lab (PC preferred; limited support will be provided for Mac users). Contact the instructor if you do not have your own laptop.

The goal of this sequence of courses is to develop the essential ideas of single-variable calculus: the limit, the derivative, and the integral. Understanding concepts is emphasized over intricate mathematical maneuverings. The mathematics learned are applied to topics from the physical, natural, and social sciences. There is a weekly lab/discussion section. Evaluations are based on homework, participation in class and lab, and tests.

This course is the continuation of Calculus I. It begins by considering further applications of the integral. We then move to approximations and series; we conclude the course with a brief treatment of differential equations. The mathematics learned are applied to topics from the physical, natural, and social sciences. There is a weekly lab/discussion section. Evaluations are based on homework, participation in class and lab, and tests.

Introductory chemistry and biology are explored in the context of food and drink: the biology of crops, culinary chemistry, and the biochemistry of brewing. Major chemistry topics include atomic structure, periodicity, bonding, acid base chemistry, kinetics, equilibrium, colloids, and solubility of gases in liquids. Major biology topics include photosynthesis, respiration, plant and yeast life histories, cellular reproduction, and metabolism. We will also explore agricultural chemistry from a systems perspective: examining strategies to for keeping pace with the demand for nitrogen and phosphorous in soils. This course is meant to offer important, fundamental chemistry and biology through the framework of food, a universal human experience. These fundamental topics in Chemistry and Biology will be explored from the ground up, so no prior experience is required. Meanwhile, the culinary and agricultural framework should offer enough new content for students with a background in natural sciences. Students will be evaluated based on participation in classroom and laboratory sessions, projects, and quizzes.

This is the first half of a two-term sequence designed to help students describe and understand properties of materials. The course first explores how atomic and molecular structure relates to the physical properties of materials and their reactivity. The course explores the reasons, rates, and outcomes of chemical reactions. Course material is applied to better understand living systems, the natural environment, and industrial products. Evaluations are based on problem sets, lab reports, and quizzes.

This is the second half of a two-term sequence designed to help students describe and understand properties of materials. Topics include kinetics, equilibria, thermodynamics, electrochemistry, chemistry of the nucleus, and an introduction to organic chemistry, with a focus on applications in each case.

The course meets for three hours of lecture/discussion and for three hours of lab each week. Students are strongly urged to take both terms of this course. Evaluations are based on problem sets, lab reports, and quizzes.

This class will explore general weather and climate patterns on global, regional, and local scales. We will discuss the major forcings driving global climate fluctuations – on both long (millions of years) and short (days) timescales, including natural and anthropogenic processes. We will also learn about basic meteorology and the processes producing some common spectacular optical weather phenomena (rainbows, coronas, cloud-types, etc). Students will complete a term project comprising a photo-documentary journal of the different weather phenomena they observe during the 10-week term. The field component of this course will be self-guided through the observation and documentation of weather phenomena. Who should take this course: No prior geology/science experience is needed – but expect to do a bit of basic math in this course! The course level is intermediate because it will not cover foundational principles of geology (or other sciences) but instead the course will be integrative and require students to practice both their quantitative and qualitative skills. Take this course if you are passionate or curious about climate change, but do not know much about the science of climate and weather!

This course explores the nature of current developments in artificial intelligence and how they present challenges and opportunities in ways they are transforming the world. We will adopt a broad definition of AI that includes everything from simple thermostats to the most advanced machine learning systems and we will look at ways these are altering life processes in the natural world and institutions throughout society.

Course goals are: 1.) to advance understandings of different programming principles, research and development strategies and underlying philosophical assumptions guiding development in such technologies; 2.) to develop abilities to use interdisciplinary[, problem centered approaches to understand the distinctions between complicated and wicked problems associated with rapid technological change in this area and key approaches to dealing with them; 2.) to cultivate skills in working collaboratively on problem-centered studies as well as programming projects that deal with AI in areas of student interest, 4.) to develop meta-cognitive abilities to learn these kinds of material in groups as well as on your own.

A major part of the course for each student will be a term project which can be pursued either individually or collaboratively. It may take a variety of forms including, for instance: 1.) a ?F?utures ?S?tudies investigation using methods of historical and/or social science research culminating in a report on some emerging, AI-related social or environmental concern; 2.) a computer programming project that solves a practical problem, is conducive to artistic expression, performs scientific analysis of quantitative data, or demonstrates an established or experimental feature of an ML or otherwise AI system; 3.) a philosophical and/or theoretical critical analysis of underlying concepts, values or assumptions that are at stake in the emerging AI technologies.

Readings will include some classic texts in AI theory, philosophy, and futures studies as well as selections from standard texts on AI programming. We will also use podcasts, films, and other media to pursue key topics and trends. There will be a series of short programming activities to study basic principles and try modeling aspects of more complicated and/or complex systems. These will be done, at least initially, in block coding which will be accessible to students without any previous programming experience and which allows people to see how this translates into other languages such as C or Python.[ We will examine the ways in which they can be coded in Python and students familiar with that or other languages will be able to pursue homework and final project work in whatever language they may prefer. We will also explore methods of prompt engineering for working with emerging systems that have dialogical interfaces.

The course will include two weekly class sessions as well as a lab. Class sessions will vary in format from extended discussion of texts and problems to supplementary lecture, visiting speaker, collaborative coding activities and extended project work. The class as a group will develop at least one major hackathon style project as a way of exploring key issues and developing key skills.

Evaluation will be based on the extent to which students demonstrate in homework, class participation and individual projects that they have advanced in each of the four main goals for the course.

This class will be especially well suited for students who want to continue computer assisted research, art work, coding or other projects they previously explored in other classes.

Differential equations are an application of calculus used to model a wide variety of physical and natural phenomena. The rate at which a cup of coffee cools, populations of predators and prey in ecosystems, the spread of disease, and the behavior of electric circuits, are all examples of systems that have been described with differential equations. This course is an introduction to ordinary differential equations, intended for students who have completed a single-variable calculus course. The course covers a variety of techniques for solving and understanding differential equations, including numerical and qualitative solution methods. Students will learn to solve and analyze differential equations using the python programming language. Students will also gain experience formulating mathematical models using differential equations. To do so, we will discuss general modeling principles and also consider several case studies. In addition to learning the mathematics of differential equations, a central goal of this course is to gain skills necessary for research in the mathematical, natural, and social sciences. This includes conceptualizing and framing a research question, conducing a literature review, giving a research presentation, and writing up results in a style appropriate for publication.

Evaluation will be based on class participation, bi-weekly problem sets, and a term-long project culminating in a presentation and short research paper. Some computer work will be required, but no computer experience is necessary.

In this course students will learn to make place-based observations of landscapes to consider the processes shaping them. Various climatic and tectonic processes such as erosion and active mountain building are continuously shaping Earth’s diverse landscapes. Humans and other organisms are also shaping and reshaping the Earth’s near surface and have been for at least thousands of years. We can describe these geomorphic processes both qualitatively and quantitatively in order to understand the rates and timescales over which different landscapes develop and evolve. Our descriptions and interpretations of evolving landscapes enable thoughtful interaction and inhabitation. Students will learn about the processes forming and shaping landscapes through both the interpretation of their own local observations as well as an exploration of prior accounts. We are fortunate to have a rich record of people’s interactions and considerations of the landscape of coastal Maine spanning thousands of years. Students will engage with different accounts of the regional landscape through readings, maps, and conversations with community members. We will also compare aspects of this region’s iconic glacially carved coastal landscape with that of other similarly formed landscapes that are currently located in different geographic, climatic, tectonic, and built environments and therefore exposed to different active processes. Students will learn methods of determining the rates of landscape-shaping processes in order to consider the role of human activities in landscape change. By combining different types of temporal and spatial information, students will learn to identify regional hazards such as mass-wasting events (landslides, debris flows, rock falls, etc.), flooding and coastal erosion. Students will be evaluated based on their performance on weekly assignments and a final project in which students choose one specific coastal Maine location to study. As we will engage with various materials describing landscapes throughout the term (i.e. narrative accounts, maps, scientific reports), this project will be an opportunity for students to practice place-based communication. This course does not have any prerequisites, but a college-level introductory geoscience course is recommended; this course will make use of algebra, GIS-online software, and digital spreadsheets (using Excel or similar software).

Contemporary marine science research relies on a rapidly developing world of aquatic technologies, yet there has also been a recent revolution in low-cost, DIY electronics and components. For experimentalists, there is immense value in having a broad knowledge of the assorted tools in your methodological “toolkit”. Often, the instrument to collect the data you need doesn’t exist or is unaffordable, in which case the best option may be to build it yourself. Learning how to operate, fix, or even construct instruments to answer a research question builds a strong and interconnected foundation of scientific skills, both concrete (programming, simple electronics, instrumentation, machining, and engineering) and cognitive (critical thinking, creative problem solving, cost-benefit analysis, forethought, resilience, and the “methods” part of the scientific method).

In this course you will (1) practice the practical and cognitive skills that experimental marine scientists use to do research, and (2) learn how to design and construct custom aquatic instrumentation to answer a scientific question. The course will start with you constructing a simple aquatic sensor to build basic skills, move on to creating a lab setup designed to manipulate some aspect of the aquatic environment, and end with self-directed research projects devising and building an instrument to explore your own scientific question. Much of our class time will be spent in a collaborative learning setting similar to a research group. Throughout the course, we will explore the ways that creative custom instrumentation can push the boundaries of science and make high-quality research more accessible.

This is a project-based course that is intended for STEM-motivated students. It would serve particularly well to bridge students into pursuing more advanced scientific research endeavors.

This class is very much a group effort, and assessment will be based on active participation in class experiences as well as written assignments in the style of a technical report, short weekly reflections, and a presentation at an end-of-term symposium. In addition to class meetings, expect to spend a substantive amount of time outside of class working on your projects.

In this course we will explore how geology has played a major role in human history and culture over multiple temporal and spatial scales. We will discuss underlying geological processes forming and influencing our environment and how this relates to human migration and settlement patterns, political boundaries, geohazards, resources, the modern landscape, and agriculture. This course will appeal to students interested in exploring connections between geology and other subject areas, or who are curious about humanity’s place in geologic time. This course will implement readings from a range of sources: geologic textbooks, excerpts from short historical texts, and scientific journal articles. We will use class time in a variety of ways: lecture-based, seminar-style discussion, and laboratories spent visiting local field sites. Students will be evaluated based on their performance on weekly problem sets or writing assignments, a midterm quiz, as well as a term project with both oral and written presentation components.

This course is designed to introduce students to geological concepts, tools of the trade, and to the geological history of Mount Desert Island. Throughout the course, students will learn skillsets (topographic and geologic map reading, orienteering, field observation, note taking, field measurements) and geologic principles (rock types, stratigraphy, plate tectonics, earth systems, geologic time, surface processes) both in the classroom and in the field. We will conduct multiple short field excursions on MDI and one extended weekend field trip to explore the regional geology. Students will submit a term project complete with their own field data, maps, photos, and analysis of the local and regional geology. Students will be evaluated on the term project, short quizzes, additional written assignments and lab reports. Offered every fall.

In this introductory geoscience course students will learn foundational principles and concepts such as plate tectonics, geologic time, climate and weather, rocks and minerals, and surface processes through an exploration of some of the National Parks of the United States. Through virtual field trips of various parks, students will visualize how regional climate and surface processes such as rivers, glaciers, and wind interact with the bedrock and surficial materials to produce some of the most iconic landscapes. While Acadia National Park offers a view of an ancient and eroded supervolcano, Yellowstone offers a glimpse of a dynamic landscape built on a modern supervolcano. While a few glaciers still cling to the high peaks of Glacier National Park, Yosemite hosts steep glacially carved valleys and polished domes reminiscent of a glaciated past. Class time will be used for lectures, discussions of readings, and laboratory exercises. During labs, students will get to know approximately 6 different parks in detail through interaction with geologic maps, rock samples, aerial imagery, and scientific reports. The students will be evaluated based on laboratory exercises and a final project through which students will explore one park of their choosing.

Glaciers are rapidly retreating around the planet and predicted to continue this trend in the coming centuries. The decline of the world’s ice sheets and mountain glaciers will impact sea level, infrastructure, and fresh-water resources for communities around the world. To put current changes into a long-term geologic context, students will learn the processes, landforms, and impact of glaciers on the Earth’s surface as the planet has cycled through ice ages. This course is designed to provide students with a solid understanding of the dynamic interactions between ice, climate, landscapes, and humans over varying spatial and temporal scales. In addition, we will cover the basics of glaciology and the physics that influence the structure, size, and movement of ice. Through class discussions and assigned problem sets, students will reinforce the content covered in lectures. In addition, this course will give students hands-on experience with tools and methods commonly used to study glaciers and ice sheets (such as: ground-penetrating radar, LiDAR, rock sampling for cosmogenic analysis). This course will have various field trips during class time on Mount Desert Island to explore how an ice sheet shaped the region’s landscape during the Last Glacial Maximum. Students will be evaluated on weekly problem sets and readings and a final project and presentation related to this history of glaciation in Maine.

This course presents an elementary introduction to chaos and fractals. The main focus will be on using discrete dynamical systems to illustrate many of the key phenomena of chaotic dynamics: stable and unstable fixed and periodic points, deterministic chaos, bifurcations, and universality. A central result of this study will be the realization that very simple non-linear equations can exhibit extremely complex behavior. In particular, a simple deterministic system (i.e., physical system governed by simple, exact mathematical rules) can behave in a way that is unpredictable and random, (i.e., chaotic). This result suggests that there are potentially far-reaching limits on the ability of science to predict certain phenomena. Students in this class will also learn about fractals—self-similar geometric objects—including the Mandelbrot set and Julia sets. We will also read about and discuss the development of the field of chaos. In so doing, we will examine the nature of scientific communities, with a particular eye toward how changes in scientific outlooks occur. Throughout the course, students will be encouraged to explore the relations between chaos, fractals, and other areas of study such as literature, art, and cultural studies. Students who successfully complete this class should gain a quantitative and qualitative understanding of the basic ideas of chaos and fractals, a greater understanding of the cultural practice of science, and improved mathematical skills. Evaluation will be based on class and lab participation, weekly problem sets several short writing assignments and a final project.

As our access to data and compute power have increased, more and more disciplines rely on computer science techniques to analyze, visualize, and process information. As such, coding skills and computational thinking are increasingly important for work in a wide variety of fields and disciplines. This course is an introduction to computer science, designed to teach students general computational skills and habits of mind that will be immediately useful and practical, and which will also prepare them for further study in computer science and related areas. Students who successfully complete this course will be able to: read a simple program and correctly describe the outcome, take a problem statement and convert it into code, and gain an understanding of how basic computer memory works and why this matters. Topics covered will include conditionals and loops, data types, functions, as well as higher-level concepts such as abstraction, version control, and debugging. The context for this class is data; students will learn how to import and generate data, manipulate and transform it, and visualize it.

This course is intended for students who have little to no computer experience and who are interested in learning the foundations of computer science through projects that require working with data. We will use examples in class and you will implement projects throughout the course where we both generate and use data coming from across the physical, natural, and social sciences. It will be helpful if you are interested in data, but no prior experience with any particular type of data is necessary.

The course is taught in Python. Students will be evaluated on weekly quizzes and weekly projects. This course, or the equivalent, is required for many further courses in computer science, machine learning, data science, robotics, and related areas.

Did you know, computers can be used to build and modify images and sound bytes? In this course, students with little to no prior computer experience will learn the foundations of computer science through projects focused on visual media and sound. This work will culminate in a final project consisting of an interactive display or exhibit. It will be helpful if you are interested in art and sound, but no prior experience is necessary. Students who successfully complete this course will have learned:

1)How to read a simple program and correctly describe the outcome,

2)How to take a problem statement and convert it into code, and

3)How basic computer memory works.

In addition, students will gain new ways for conceptualizing and working with image and sound that they will be able to draw on in their creative and scholarly practice. While this is an introductory course, it is important to note that learning to program is like learning a new language. There is a time commitment to learning new syntax and understanding the language of computing. This course is taught in Python, and students will be evaluated on weekly check-ins and projects. This course, or the equivalent, is required for many further courses in computer science and related areas.

Mathematical models are an essential tool in epidemiology. Models are used in a number of ways, including: to predict the course of an epidemic; to estimate key epidemiological parameters; to determine an optimal vaccination strategy; or to gain a general, qualitative understanding of the salient features of the dynamics of a disease. This course will focus on differential equations, a class of mathematical models used across the sciences to model quantities that change continuously in time. The course will begin with a short introduction to differential equations. We will then step through the full “pipeline” of mathematical modeling using epidemiology as a case study. We will begin with a first-principles derivation of several models and will consider how the natural history of an infectious disease influences modeling choices. We will then see how to solve and analyze differential equations computationally. We will then cover how to calibrate a model to epidemiological data and estimate key model parameters in a principled way. Finally, we will see how to create model projections for different intervention scenarios and will explore the strengths and limitations of a mathematical model in relation to given research and policy questions. Through this process, students will gain skills and experiences that will apply to mathematical modeling in a range of settings across the natural and social sciences.

In addition to learning the mathematics of differential equations applied to epidemiology, a central goal of this course is to gain skills necessary for research in the mathematical, natural, and social sciences. This includes conceptualizing and framing a research question, formulating a model to explore that question, engaging with peer-reviewed research publications, and giving a research presentation and preparing a short technical report.

Evaluation will be based on class participation, problem sets and programming exercises, and a term-long project culminating in a research presentation and short technical report.

Planet Earth is misnamed. Seawater covers approximately 70% of the planet’s surface, in one giant all-connected ocean. This ocean has a profound effect on the planet’s climate, chemistry, ecosystem, and energy resources. Billions of years ago life began there, in what now we regard as the last unexplored frontier of this planet. In this course we examine the various disciplines within oceanography, including aspects of geology and sedimentology, chemical, dynamic and biological oceanography. The course concludes with an introduction to marine ecosystems examined at various trophic levels, including phyto/zooplankton, fish and other macrofauna. Fieldwork (weather dependent) includes trips on RV Indigo, trips to intertidal and estuarine ecosystems, and possible visits to the college’s islands, Mount Desert Rock and Great Duck Island. Evaluation will be by lab, quizzes and a final paper.

This course introduces the basics of statistical analysis that can be used in either a scientific or a social science frame of reference. While this course teaches you to perform both nonparametric and simple parametric analysis both by hand and computer, an emphasis will be placed on understanding the principles and assumptions of each test, rather than mathematical ability per se. We will also learn how to report statistical results in journal format, and there will be plenty of lab time to sharpen skills. Evaluation is based on lab participation, three quizzes, and a team project.

Computational text analysis (CTA) is an emerging field that uses computation to analyze texts. CTA draws on the fields of computer science, machine learning, computational linguistics, and literary theory. Using machine learning and statistics, computers can be used to explore how language is used in particular contexts, including how frequently different words are used, the sentiment of a word/text, as well as nuances in the ways words are associated with one another.

We will use CTA to engage in “Distant Reading”, a term coined by literary theorist Franco Moretti. Distant Reading stands in contrast to the more familiar “Close Reading”: a deep engagement with a particular text or a passage from a text. Distant Reading engages not with a particular text, but with a large corpus of texts: e.g., all novels published in English in the 20th century, all articles written in The New York Times and The Washington Post in the last decade, or the lyrics of all top-100 pop songs from the 1980s. Computational techniques applied to large collections of texts allow one to ask broad questions about structural and linguistic change over time and to look for patterns of language use that would not be evident from analysis of one or even several individual texts. Distant Reading, and computational text analysis more generally, is not intended to replace close reading, but to complement it.

We will use CTA to explore how power structures and systems—such as race, gender, and colonialism—manifest themselves in bodies of text. For example, CTA has been used to investigate Islamophobia, analyze race in US novels, explore settler colonialism in the Americas, and to investigate shifts in anti-Asian sentiments in the US brought on by the COVID crisis.

Students will who successfully complete this course will: 1) gain a conceptual understanding of various CTA techniques, including word frequency analysis, topic modeling, and sentiment analysis; 2) learn how to apply these techniques using pre-existing software and doing their own coding; 3) gain experience asking questions about power structures/systems—race, gender, colonialism—and how those structures manifest themselves in corpora of text; 4) learn how these questions of power can be explored using algorithmic methods; and 5) gain experience critiquing algorithmic methods through the lenses of race, gender, and colonialism.

Classes will be a mixture of lecture, group exercises, discussion, and live coding. Readings will include case studies and selections from literary theorists. Evaluation will be based on participation in discussion and in-class activities, several short coding/analysis exercises, several short reflection assignments, and a group project on a topic of the students’ choosing.

Linear algebra is a foundational area of mathematics, finding widespread application in statistics, machine learning, economics, physics, and across the sciences. The starting point for this course is to consider basic properties of matrices and techniques for solving systems of linear equations. Abstracting and formalizing the process of solving linear equations leads us to the notion of a vector space and related ideas, such as linear independence, dimension, and basis. The course then turns to further properties of matrices and vector spaces, including determinants, eigenvalues and eigenvectors, and linear transformations. As time permits, we will study various applications of linear algebra, such as image compression, dynamical systems (with a focus on ecological applications), Markov chains, and Google’s PageRank algorithm. Students who successfully complete this course will gain a solid introduction to the calculational techniques and key constructions and ideas of linear algebra that will prepare them for further work in the sciences and mathematics. Additionally, students will gain experience working at a level of generality and abstraction above that encountered in a typical introductory calculus sequence. Evaluation will be based on weekly problem sets. Students who enroll in this course should have successfully completed a high-school-level algebra class and be motivated to explore a powerful and broadly-used branch of mathematics that for most has a very different feel than the functions-precalculus-calculus sequence. Calculus is not a prerequisite for this class.

Object-oriented programming is a design paradigm that encapsulates variables and functions into structures called objects. Understanding what objects are, how to use them, and how to write your own objects, is a foundational programming skill. An application area in which objects naturally occur is game design. The computer gaming industry is a multi billion dollar industry that combines art, sound, and computing into one package. In part, it is thanks to the computer game market that we have seen rapid advances in computer graphics and compute speed. Computer games are event-driven programs; meaning the sequence of operations is not predetermined but is controlled by the user’s mouse clicks or text responses to prompts. In this class students will develop a computer game as a means to learn object-oriented and event-driven programming. Students who successfully complete this course will gain: 1)a grounding in object-oriented design, 2) an introduction to finite state machines and event driven programming, and 3) experience transforming an idea into a working computer game prototype.

Students will gain Python coding experience and general skills that leave them better equipped to pursue a wide range of programming tasks. This course is intended for students who have some computer experience and are interested in independently learning new skills. While this course is designed to build on Introduction to Computer Science, adventurous beginners are encouraged to take this class. Students will be evaluated on weekly check-ins and assignments. The main project throughout the class will be to design, develop, and test a computer game prototype which culminates in a final demonstration. This course, or the equivalent, is required for many further courses in CS and related areas.

This course explores the physical, chemical, and environmental properties of carbon-containing materials such as plastics, solvents, dyes, as well as all living things, and once-living materials. The emphasis is on learning fundamental principles that allow one to understand and to predict the behavior of various types of organic substances. Evaluations are based on problem sets, lab reports, and quizzes. The equivalent of this course is a perquisite for biochemistry.

This course explores the physical, chemical, and environmental properties of carbon-containing materials such as plastics, solvents, dyes, and living things. The emphasis of this course is to apply foundational principles of Chemistry and Organic Chemistry I to gain perspective on how these processes fit into everyday life: materials and processing, research and medicine, connection to biochemistry, and food production. Evaluation will be based on: problem sets, quizzes, labs, a mid-term exam, and a final exam.

In this course students will learn content and skills so that they can participate effectively in sustainable energy projects, make personal and community decisions that reduce carbon emissions, and work in ventures in sustainable energy. Additionally, this course will be useful for those interested in energy and climate policy, either internationally or domestically. We will begin with a quick overview of current CO2 emissions levels and look at how this is related to energy use. We will then turn our attention to basic ideas from physics, including the definition of energy and the difference between energy and power. The bulk of the course will consist of a survey of different forms of energy consumption and generation. Throughout, we will quantitatively analyze technology from both a local and global point of view. For example, we will calculate how much electricity one can generate on a rooftop, and we will also examine the role that solar PV could play toward the goal of eliminating fossil fuel use worldwide. In a unit on financial mathematics, students will learn about the time value of money and several ways of quantifying investments, including ROI (return on investment) and IRR (internal rate of return). Students will apply these financial tools in several short case studies. If time permits, we may also cover negative emissions technologies and the electrical grid, including grid stability issues and the potential of smart-grid technology. This will be a demanding, introductory, class. Evaluation will be based on weekly problem sets.

This course covers a range of standard introductory physics topics. The goals of the course are: to introduce students to important physical ideas both conceptually and mathematically; and to help students improve their quantitative skills. The first part of the course consists of a broad look at the three conservation laws: the conservation of momentum, energy, and angular momentum. Along the way, we’ll learn about vectors, work, potential energy, thermal energy, and the energy stored in chemical bonds. We’ll conclude with a treatment of Newton’s laws of motion. Evaluations will be based on participation in class and lab, weekly homework, and one or more open-notes exams. This course makes extensive use of algebra and trigonometry. Potentially difficult math topics will be reviewed as necessary. Prerequisites: High-school-level algebra.

This course is the first of a two course sequence covering a range of standard introductory physics topics. The goals of the course are: to introduce students to important physical ideas both conceptually and mathematically; and to help students improve their quantitative skills. The first part of the course consists of a broad look at the three conservation laws: the conservation of momentum, energy, and angular momentum. Along the way, we’ll learn about vectors, work, potential energy, thermal energy, and the energy stored in chemical bonds. We’ll conclude with a treatment of Newton’s laws of motion. If time permits, we may briefly cover some topics from chaotic dynamics. Evaluations will be based on participation in class and lab, weekly homework, and two untimed, open-notes exams. This course makes extensive use of algebra and trigonometry. Potentially difficult math topics will be reviewed as necessary. Prerequisites: Understanding Functions, a strong high school algebra background, or consent of the instructor.

What are relativity and quantum mechanics, and why were they viewed as revolutionary when they were formulated in the early 1900s? How and why does relativity and quantum mechanics compel us to discard commonsense ideas about the nature of the physical world that are part of classical mechanics? Why is there not agreement on how to interpret quantum mechanics, and why does quantum mechanics even need interpretation? This version of Physics II covers Einstein’s theory of special relativity and selected topics in quantum mechanics, and is designed to introduce students to some of the formalism and central results of relativity and quantum mechanics, so that they can formulate scientifically grounded answers to the above questions. Throughout the course we will start with first principles and carefully build toward key results, allowing students to see how relativity and quantum mechanics—two of the pillars of modern physics—were constructed and how they cohere as mathematically consistent and experimentally verified theories. The first half of the course will cover relativity topics including the principle of relativity, spacetime intervals and proper time, coordinate transformations, time dilation and Lorentz contraction, and relativistic energy and momentum. The second half of the course will turn toward the foundations of quantum mechanics, including: spin-1/2 particles, wave-particle duality, and Bell’s inequalities and the Einstein-Podolsky-Rosen paradox. If time permits, we may cover additional topics such as blackbody radiation, the photoelectric effect, Bohr’s model of the hydrogen atom, and quantum cryptography. To gain a sense of the scientific, social, and material context in which the theories of relativity and quantum mechanics were developed, we will read a number of papers and book chapters by historians and philosophers of science. This course is designed to appeal to a wide range of students—both those whose interests lie outside of science as well as those who are drawn toward the sciences or mathematics. Students who take this course should be comfortable working with mathematical abstraction. Evaluation is based on weekly problem sets, participation in weekly discussion sections, and several short reflection assignments.

Thermodynamics is the area of physics concerned with the behavior of very large collections of particles. Examples include the water molecules in glass of water, the electrons in a wire, or the photons given off by a light bulb. Thermodynamics studies properties of collections of particles that are largely independent of the particles’ detail, for example, the tendency for heat to flow from a hot object to a cold one.

This course will begin with a treatment of the first law of thermodynamics and basic thermal physics. Topics to be covered include the conservation of energy, heat and work, the ideal gas, the equipartition of energy, heat capacities, and latent heat. We will then move to the second law of thermodynamics, beginning with a statistical definition of entropy. This will require learning some combinatorics (a mathematical technique for counting) and approximation methods for working with very large numbers. This statistical approach will enable us to understand the origin of the second law of thermodynamics, and will lead naturally to statistical definitions of temperature, pressure, and chemical potential. We will then turn our attention to two broad areas of application. The first of these is heat engines and refrigerators, including heat pumps. The second set of applications involve free energy and chemical equilibrium. Depending on student interest, we will cover batteries and fuel cells, phase transitions, adiabatic lapse rates in meteorology, and nitrogen fixation. Thermodynamics is a broadly applicable field of physics, and so this course should be of relevance to students whose interests are in almost any area of science or engineering, as well as those who wish to gain a general introduction to a field that is one of the pillars of modern physical science. Evaluation will be based on weekly problem sets and a final research paper, presentation, or lab project.

Group theory is an area of mathematics that is concerned with symmetry. In this context, an object or system is said to be symmetric if it is unchanged after an action is performed on it. Examples of such actions include rotations, reflections, and permutations. Objects’ symmetries can be classified by the types of actions that leave them unchanged. A set of actions, together with rules for how those actions behave when combined, are (loosely speaking) what mathematicians refer to as a group. Group theory has applications in physics, chemistry, and pure and applied mathematics.

A group is an example of an algebraic structure, which (again loosely speaking) is a set together with a collection of rules for combining pairs of elements of that set. Algebraic structures are classified by the properties of the rules for combining pairs of elements. In addition to groups, other common algebraic structures include rings and fields. The broad study of the properties of different algebraic structures is known as “abstract algebra”.

This course is an introduction to group theory and will also serve as a springboard to the further study of abstract algebra. Topics to be covered will include: learning to identify groups using group axioms; Cayley diagrams; examples of different classes of groups, including abelian, cyclic, dihedral, and permutation groups; subgroups and Lagrange’s theorem; products and quotients; group homomorphisms; the fundamental theorem for abelian groups; and Sylow theory. Other topics and examples will depend on student interest.

This course will be taught in a seminar style; students will frequently be asked to prepare examples and proofs for discussion in class and to work collaboratively on problems, both in and out of class meetings. Evaluation will be based on problem sets and active and collaborative class participation.

This course is an introduction to mathematical structures, proof techniques, and the language and style of formal mathematics. Topics to be covered include: intuitive and direct proofs, sets and functions, induction, logic, the contrapositive, and proof by contradiction. Additionally, this course aims to introduce students to some of the key elements of higher mathematics, and so, as time permits, we will cover introductory topics from areas such as number theory, topology, real analysis, and group theory. Throughout the course we will emphasize clear mathematical exposition and methods of proof. In addition to gaining an understanding of the topics listed above, students who complete this course will be able to: read and understand mathematical exposition; think critically as mathematicians and present convincing arguments; and read and write formal proofs. This class will help prepare students for further advanced study in mathematics and related fields. It will also be of value to those who wish to explore the logical structure of mathematics, gain increased facility with abstract mathematical thought, or sharpen analytic and critical reasoning skills. This course will be taught in a seminar style; students will frequently be asked to prepare proofs and examples for discussion in class and to work collaboratively on problems. Evaluation will be based on problem sets and active and collaborative class participation.

Network science is an active and growing cross-disciplinary area that focuses on the description, representation, analysis, and modeling of complex social, biological, and technological systems as networks or graphs. At its simplest, a network is a collection of nodes, some of which are connected by edges.

For example, nodes might be scientists, and there would be an edge connecting two scientists if they co-authored a scientific paper. Or nodes might be facebook users, and there would be an edge between two users if they were facebook friends. Structures and systems modeled as networks are ubiquitous in the world around us: communication networks, networks of friends and acquaintances (online and in-person), gene regulatory networks, supply chains, and food webs, to name just a few.

In general, networks are used as models in situations in which the architecture of connectivity matters, but where that connectivity is neither random (as in an ideal gas or non-interacting agents) nor regular (as in a crystal lattice or a situation where agents interact spatially). Capturing, modeling, and understanding networks requires understanding both the mathematics of networks and the computational tools for identifying and explaining the patterns they contain.

This course will consist of a survey of techniques for modeling and analyzing the structure and dynamics of networks. We will begin with basic definitions and simple descriptive statistics. We will then look at random graphs, which are useful for generating intuition and serving as simple null models. We will then consider network prediction models that can be used to predict node attributes and missing edges, and approaches for detecting community structure. As time permits, we will examine dynamical models on networks, such as disease and rumor spreading. Throughout, we will take a computational approach, learning how to work with network data and how to implement algorithms for network models and data analysis.

Evaluation will be based on participation in class sessions, coding exercises, and a final project.