Physics

On the first night, we will look up and see the stars. By the last, we will know what makes them “shine,” how they came to be, and their ultimate fates. In between, we will survey the universe and humankind’s investigations of it—from ancient navigation to modern cosmology. In addition to the stars themselves, we will learn about solar-system objects such as planets, asteroids, moons, and comets; the comparative astronomy of different eras and cultures; the properties, lifetimes, and deaths of galaxies, quasars, and black holes; and theories and evidence concerning the origin, evolution, and fate of the universe. In addition to readings and examination of multimedia material, students will be members of teams conducting astronomical observation and experiments—at first with an astrolabe, then a simple telescope, and finally with the most powerful telescopes on and around the Earth. Emphasis will be placed on modes of scientific communication, so that each student will participate in debates, present posters, write papers, and participate in the peer-review process. In addition, students will experience famous astronomical debates through role-play. Since science is a collaborative process, group work—both small and large—will be a central feature of this course.

Do you enjoy designing and building things? Do you have lots of ideas of things that you wished existed but do not feel you have enough technical knowledge to create yourself? Do you wish you could fix some of your favorite appliances that just stopped working? Do you want to help find solutions to problems in our community? This course is meant to give an introduction to tinkering, with a focus on learning the practical physics behind basic mechanical and electronic components while providing the opportunity to build things yourself. The course will have one weekly meeting with the whole class and three smaller workshop sessions to work on team-based projects. (You are expected to choose one of the three workshop sessions to attend weekly.) The course will be broken down into four primary units: design and modeling; materials, tools, and construction; electronics and microcontrollers; and mechanics. There will be weekly readings and assignments, and each unit will include both individual and small-group projects that will be documented in an individual portfolio to demonstrate the new skills that you have acquired. For a semester-long, team-based conference project, your team will create a display of your work that will be exhibited on campus and provide a description reflecting on the design, desired functionality, and individual contributions that led to the finished product. Let’s get tinkering!

General physics is a standard course at most institutions; as such, this course will prepare you for more advanced work in physical science, engineering, or the health fields. Lectures will be accessible at all levels, and through group conference you will have the option of either taking an algebra-based or calculus-based course. This course will cover introductory classical mechanics, including kinematics, dynamics, momentum, energy, and gravity. Emphasis will be placed on scientific skills, including: problem solving, development of physical intuition, scientific communication, use of technology, and development and execution of experiments. The best way to develop scientific skills is to practice the scientific process. We will focus on learning physics through discovering, testing, analyzing, and applying fundamental physics concepts in an interactive classroom, through problem solving, as well as in weekly laboratory meetings. Students enrolling in the calculus-based section are encouraged to have completed at least one semester of calculus as a prerequisite. It is strongly recommended that students who still need to complete a second semester of calculus enroll in Calculus II, as well. Calculus II, or equivalent, is highly recommended to take the calculus-based section of General Physics II (Electromagnetism and Light) in the spring.

General physics is a standard course at most institutions; as such, this course will prepare you for more advanced work in physical science, engineering, or the health fields. Lectures will be accessible at all levels, and through group conference you will have the option of either taking an algebra-based or calculus-based course. This course will cover waves, geometric and wave optics, electrostatics, magnetostatics, and electrodynamics. We will use the exploration of the particle and wave properties of light to bookend our discussions and ultimately finish our exploration of classical physics with the hints of its incompleteness. Emphasis will be placed on scientific skills, including: problem solving, development of physical intuition, scientific communication, use of technology, and development and execution of experiments. The best way to develop scientific skills is to practice the scientific process. We will focus on learning physics through discovering, testing, analyzing, and applying fundamental physics concepts in an interactive classroom, through problem solving, as well as in weekly laboratory meetings. Students enrolling in the calculus-based section are encouraged to have completed Calculus II as a prerequisite. It is highly recommended to have taken the first semester of General Physics I in the fall prior to enrolling in this course.

What is the nature of space and time? Can my twin ever age faster than me? What happens if I jump inside of a black hole? Explore these questions and more through Einstein’s theories of special and general relativity. This course serves as an introduction to both of these theories. We will see how Einstein revolutionized physics in the 20th century through these two theories. We’ll begin the semester by discussing what we mean by relativity in physics and the mathematical language we will need to understand the physical predictions of the theories. After a brief discussion of pre-relativity physics, we will learn the postulates of special relativity and where the most famous equation in physics, E=mc², comes from. Next, we will study the best theory of gravity that we have, Einstein’s general relativity, where we will develop the tools needed to understand black holes. All relevant mathematical concepts will be introduced in the course.

This lab-based course is designed to teach students critical advanced laboratory skills while exploring the fascinating phenomenon of resonance and its many applications. The course will be broken into three main units: mechanical resonators, electronic resonators, and quantum mechanical resonators. Resonators are physical systems that undergo periodic motion and react quite dramatically to being driven at particular frequencies (like the opera singer hitting just the right note to break a wine glass). These systems are very common in everyday life, as well as inside many important technological devices. Each unit will explore a particular application of resonance (e.g., building RLC tank circuits for electronic resonance and utilizing our benchtop NMR spectrometer to explore quantum mechanical resonance). Although some class time will be spent going over the relevant theory, the majority of the class time will be spent designing and doing experiments using advanced lab equipment, analyzing data using Jupyter (iPython) notebooks, and reporting the results using LaTeX. For conference work, students are encouraged to develop an experimental research question, design an experiment to answer that question, perform the experiment, analyze the data, present their findings at the Science Poster Session, and write up their results in the form of a short journal article.

Learn to appreciate the complex order that can be found in chaos! This course introduces the beautiful world of nonlinear and chaotic dynamics and also provides the mathematical and numerical tools to explore the astounding patterns that can arise from these inherently unpredictable systems. We shall see how chaos emerges from fairly simple nonlinear dynamical systems; utilize numerical methods to simulate the dynamics of chaotic systems; and explore characteristics of chaos using iterated maps, bifurcation diagrams, phase space, Poincaré sections, Lyapunov exponents, and fractal dimensions. Class time will oscillate between the presentation of new material and workshops for hands-on exploration. Students are encouraged to build and/or analyze their own chaotic system as potential conference projects. No previous programming experience is required, and all relevant mathematical concepts will be introduced.

This course will cover the fundamentals of the theory that governs the smallest scales of our universe: quantum mechanics. Throughout the semester, we’ll take a deep dive into the formalism behind, and physical predictions of, the theory. We’ll start by analyzing an experiment that can only be explained by a quantum theory and then dive into the mathematics that underlie quantum mechanics. We’ll then discuss matter waves along with the Schrödinger wave equation, as well as a variety of example problems, as we build intuition for the theory. We will conclude the course with a study of entanglement and quantum information. Familiarity with complex numbers, vector calculus, and matrices will be useful but not required.

The human brain contains roughly 80 billion neurons connected by trillions of synapses. This uniquely complex organ is responsible for our remarkable capabilities, including the sensation and perception of diverse internal and external stimuli; the performance of precise movements and behaviors; and the ability to learn and remember an extraordinary amount of information. In this lecture course, we will investigate the nervous system from molecular, cellular, and systems-level perspectives. We will delve into the structure and function of neurons, including the molecular mechanisms underlying the action potential and synaptic transmission. We will learn how sensory systems detect diverse external and internal stimuli and how they communicate this information to the brain. We will also explore how the brain drives motor output, from the motor cortex to the neuromuscular junction, and the areas of the brain that control distinct aspects of language. Students will regularly engage in active learning through in-class, small-group exercises that complement content covered in lectures. In group conference, we will learn about neurodivergence and neurological disorders through discussions centered on the book, The Disordered Mind: What Unusual Brains Tell Us about Ourselves, by Nobel Prize-winning neuroscientist Eric Kandel. Students should leave this course with a solid understanding of the principles of neuroscience, which will prepare them for further study in neuroscience, physiology, and medicine.

This course is a rigorous introduction to digital communication networks from a liberal-arts perspective. The main question that we will address is how information of all kinds can be transmitted efficiently, between two points at a distance, in such a way that very little assumption need be made about the physical mode of transport and how the route the information travels need not be known in advance. We emphasize the importance of abstraction and the use of redundancy to establish error-free transmission even in the face of significant noise. We study protocol stacks from the application layer (canonical example: web browser) down to the physical transmission medium. We analyze how high-level information (for instance, a message including an image attachment being sent via email) is translated to bits, broken into discrete packets, sent independently using the basic building blocks of the Internet—and then how those packets are reassembled, seemingly instantaneously, in the correct order. We will attempt to demystify the alphabet soup of networking terminology, including TCP/IP, HTTP, HTTPS, VPN, NFC, WiFi, Bluetooth, and 5G. We will consider major shifts in technology that have transformed communication networks from the telegraph to the telephone to radio, from copper wire to fiberoptics and satellite, and the ubiquity of cellular networks. We also will consider the close relationship between the open-source movement and the rise of the Internet and web.

Climate change will be the defining issue of the coming decades. It threatens the ecosystems and infrastructure that human society relies upon and will impact most aspects of the global economy, policymaking, and day-to-day life. This First-Year Studies course will provide the basic foundation in earth systems and climate science needed for students who are interested in careers in environmental science, policy, law, or advocacy. It will also be valuable for students who are concerned about how climate change will impact their communities and their careers in other fields. In the early fall, students will participate in Climate Week New York City events, where they will learn about local climate-change issues along with international government and private-sector efforts to address climate change. During the rest of the fall semester, we will draw on fundamental concepts of physics, chemistry, biology, and earth science to learn about human-caused global warming and its context in the more than four billion-year history of our planet. For their first conference project, students will learn about climate-change indicators and will present their research on an indicator of their choice at the college poster symposium. In the spring, we’ll build upon this foundation to investigate the linkages among global climate, natural ecosystems, and human society. We will explore topics such as biodiversity, food and agriculture, adapting to climate-change impacts, and the energy-systems transition needed to prevent catastrophic global warming. We will also visit the Center for the Urban River at Beczak (CURB) to learn about climate change and the Hudson River Estuary. For their spring conference project, students will learn to conduct a scientific literature review and will write a research paper on the climate-change process or on an issue in which they’re most interested. Readings for the course will primarily be from an earth-science textbook but will also include scientific research studies, technical reports, and essays on climate change and society. There will also be four written assignments each semester and in-class quizzes to reinforce the concepts that we learn in class. This seminar will alternate biweekly one-on-one conferences with biweekly small-group workshops on climate data analysis, technical writing, the use of science to inform policy and advocacy, and communicating science.

Natural hazards are earth-system processes that can harm humans and the ecosystems on which we rely; these hazards include a wide variety of phenomena, including volcanoes, earthquakes, wildfires, floods, heat waves, and hurricanes. The terms “natural hazard” and “disaster” are often used interchangeably, and many examples of natural hazards have resulted in disastrous loss of life, socioeconomic disruption, and radical transformation of natural ecosystems. Through improved understanding of these phenomena, however, we can develop strategies to better prepare for and respond to natural hazards and mitigate harm. In this course, we will use case studies of natural-hazard events to explore their underlying earth-system processes—covering topics such as plate tectonics, mass wasting, weather, and climate—along with the social and infrastructure factors that determined their impact on people. We will also discuss related topics—such as probability, risk, and environmental justice—and the direct and indirect ways that different types of natural hazards will be exacerbated by global climate change. Students will attend one weekly lecture and one weekly group conference, where we will discuss scientific papers and explore data on natural hazards processes and case studies. This lecture will also participate in the collaborative interludes and other programs of the Sarah Lawrence Interdisciplinary Collaborative on the Environment (SLICE) Mellon course cluster.

As we want to engage in individual and collective efforts toward sustainable and climate-change mitigating solutions, this workshop offers an opportunity for students to explore the multiple ways in which “sustainability” can be fostered and developed at an institution like Sarah Lawrence College. Students will work in small groups on a variety of projects and produce research and educational material that can lead to concrete and actionable proposals for the College and our community to consider. Students will determine their own areas of interest and research, from energy and water-usage monitoring to composting solutions, recycling/reusing and consumer sobriety, landscaping choices, pollinators and natural diversity, food growing, natural and human history of the land, and community collaborations, to name a few. As part of their project effort, students will engage with College administrators who are actively working toward sustainable solutions, as well as student, staff, and faculty groups such as the Warren Green vegetable garden, the Sarah Lawrence Interdisciplinary Collective on the Environment (SLICE), and the Sustainability Committee. We will also explore the possibility of writing grants in coordination with other actors at the College. This workshop will meet once a week for one hour. It is offered as pass/fail based on attendance and a group project that will mostly be developed during our meeting time. It is open to all students, including first-year students. All skills and areas of expertise are welcome, from environmental science to writing and visual and studio arts—but any interest in issues of sustainability and a strong sense of dedication will suffice!

Calculus is the mathematical gift that keeps giving. (Thanks Newton and company!) In this class, you will expand your knowledge of limits, derivatives, and integrals with concepts and techniques that will enable you to solve many important problems in mathematics and the sciences. You will be able to judge whether answers provided by WolframAlpha or ChatGPT are correct. Topics will include: differentiation review, integration review, integration with nonpolynomial functions, applications of integration (finding area, volume, length, center of mass, moment of inertia, probability), advanced techniques for integration (substitution, integration-by-parts, partial fractions), infinite sequences, infinite series, convergent and divergent sums, power series, and, time permitting, parametric equations of a curve and polar coordinates. Students will work on a conference project related to the mathematical topics covered in class and are free to choose technical, historical, crafty, computational, or creative projects. It is recommended that students have at least one semester of calculus at either college or high-school level or be very comfortable with quickly learning any missing material.

Rarely is a quantity of interest—tomorrow’s temperature, unemployment rates across Europe, the cost of a spring-break flight to Fort Lauderdale—a simple function of just one primary variable. Reality, for better or worse, is mathematically multivariable. This course introduces an array of topics and tools used in the mathematical analysis of multivariable functions. The intertwined theories of vectors, matrices, and differential equations and their applications will be the central themes of exploration in this yearlong course. Specific topics to be covered include the algebra and geometry of vectors in two, three, and higher dimensions; dot and cross products and their applications; equations of lines and planes in higher dimensions; solutions to systems of linear equations, using Gaussian elimination; theory and applications of determinants, inverses, and eigenvectors; volumes of three-dimensional solids via integration; spherical and cylindrical coordinate systems; and methods of visualizing and constructing solutions to differential equations of various types. Conference work will involve an investigation of some mathematically-themed subject of the student’s choosing.

Our existence lies in a perpetual state of change. An apple falls from a tree; clouds move across expansive farmland, blocking out the sun for days; meanwhile, satellites zip around the Earth transmitting and receiving signals to our cell phones. The calculus was invented to develop a language to accurately describe the motion and change happening all around us. The ancient Greeks began a detailed study of change but were scared to wrestle with the infinite, and so it was not until the 17th century that Isaac Newton and Gottfried Leibniz, among others, tamed the infinite and gave birth to this extremely successful branch of mathematics. Though just a few hundred years old, the calculus has become an indispensable research tool in both the natural and social sciences. Our study begins with the central concept of the limit and proceeds to explore the dual processes of differentiation and integration. Numerous applications of the theory will be examined. For conference work, students may choose to undertake a deeper investigation of a single topic or application of the calculus or conduct a study of some other mathematically-related topic. This seminar is intended for students interested in advanced study in mathematics or sciences, students preparing for careers in the health sciences or engineering, and any student wishing to broaden and enrich the life of the mind.

Variance, correlation coefficient, regression analysis, statistical significance, and margin of error—you’ve heard these terms and other statistical phrases bantered about before, and you’ve seen them interspersed in news reports and research articles. But what do they mean? How are they used? And why are they so important? Serving as an introduction to the concepts, techniques, and reasoning central to the understanding of data, this lecture course focuses on the fundamental methods of statistical analysis used to gain insight into diverse areas of human interest. The use, misuse, and abuse of statistics will be the central focus of the course; and specific topics of exploration will be drawn from experimental design theory, sampling theory, data analysis, and statistical inference. Applications will be considered in current events, business, psychology, politics, medicine, and many other areas of the natural and social sciences. Statistical (spreadsheet) software will be introduced and used extensively in this course, but no prior experience with the technology is assumed. Group conferences, conducted in workshop mode, will serve to reinforce student understanding of the course material. This lecture is recommended for anybody wishing to be a better-informed consumer of data and strongly recommended for those planning to pursue advanced undergraduate or graduate research in the natural sciences or social sciences. Enrolled students are expected to have an understanding of basic high-school algebra and plane coordinate geometry.

Calculus is the mathematical gift that keeps giving. (Thanks Newton and company!) In this class, you will expand your knowledge of limits, derivatives, and integrals with concepts and techniques that will enable you to solve many important problems in mathematics and the sciences. You will be able to judge whether answers provided by WolframAlpha or ChatGPT are correct. Topics will include: differentiation review, integration review, integration with nonpolynomial functions, applications of integration (finding area, volume, length, center of mass, moment of inertia, probability), advanced techniques for integration (substitution, integration-by-parts, partial fractions), infinite sequences, infinite series, convergent and divergent sums, power series, and, time permitting, parametric equations of a curve and polar coordinates. Students will work on a conference project related to the mathematical topics covered in class and are free to choose technical, historical, crafty, computational, or creative projects. It is recommended that students have at least one semester of calculus at either college or high-school level or be very comfortable with quickly learning any missing material.