Mathematics

Whether they had any interest in mathematics in high school, students often discover a new appreciation for the field at Sarah Lawrence College. In our courses—which reveal the inherent elegance of mathematics as a reflection of the world and how it works—abstract concepts literally come to life. That vitality further emerges as faculty members adapt course content to fit student needs, emphasizing the historical context and philosophical underpinnings behind ideas and theories.

By practicing rigorous logic, creative problem solving, and abstract thought in small seminar discussions, students cultivate habits of mind that they can apply to every interest. With well-developed, rational thinking and problem-solving skills, many students continue their studies in mathematics, computer science, philosophy, medicine, law, or business; others go into a range of careers in fields such as insurance, technology, defense, and industry.

2018-2019 Courses

Mathematics

First-Year Studies: The New Elements: Mathematics and the Arts

Open , FYS—Year

The development of linear perspective in Renaissance painting presents one of the clearest examples of the intersection of mathematics and the arts. To paraphrase art historian Erwin Panofsky, perspective recasts perceptual space as a uniform, infinite, abstract space with its own logical and aesthetic properties. The mathematics needed in perspectival constructions was worked out by Euclid in antiquity. What novel aesthetic and logical forms are made possible by the mathematics beyond Euclid’s Elements? This seminar will explore the bearing of modern mathematical ideas on 20th-century Western creative and performing arts. While we will not aim for a comprehensive survey of the entire last century, we will investigate a sequence of case studies, including: De Stijl and the painting of Piet Mondrian; serialism and the music of Arnold Schoenberg; the Bauhaus in Germany and its legacy; OuLiPo, “a secret laboratory of literary structures” in postwar French literature; American postmodern dance; and structural film, among others. Mathematical topics will include sets, logic, non-Euclidean geometry, topology, and chance. A central goal of the seminar is to assess the meaning of structure as it pertains to artistic and mathematical practices. This course assumes no particular expertise with mathematics or cultural history. Seminar readings and a program of art viewings will establish a basis for investigating the relevance of fundamental mathematical concepts to modern literature and the arts. Outside the seminar, students will attend both individual and group conferences. Weekly individual conference meetings for the first six weeks of the fall semester will give students the opportunity to develop their first individualized conference projects, focusing on a particular mathematical structure. Individual conferences after the first six weeks will be held on a weekly or biweekly basis, depending on student progress. During the fall semester, a series of group conferences will afford students time for art viewings and collaborative writing and problem solving.

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An Introduction to Statistical Methods and Analysis

Open , Lecture—Fall

Mathematical prerequisite: basic high-school algebra and geometry.

Correlation, regression, 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? And why are they important? And what exactly fueled the failure of statistical polls and projections leading up to the 2016 US presidential election? 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; specific topics of exploration will be drawn from experimental design, sampling theory, data analysis, and statistical inference. Applications will be considered in current events, business, psychology, politics, medicine, and 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. Conference work will serve as a complete practicum of the theory learned in lecture: Students working closely in small teams will conceive, design, and fully execute a small-scale research study. This lecture is recommended for anybody wishing to be a better-informed consumer of data and strongly recommended for those planning to pursue graduate work and/or research in the natural sciences or social sciences.

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Game Theory: The Study of Conflict and Strategy

Open , Lecture—Spring

The minimum required preparation for successful study of game theory is one year each of high-school algebra and geometry. No other knowledge of mathematics or social science is presumed.

Warfare, elections, auctions, labor-management negotiations, inheritance disputes, even divorce—these and many other conflicts can be successfully understood and studied as games. A game, in the parlance of social scientists and mathematicians, is any situation involving two or more participants (players) capable of rationally choosing among a set of possible actions (strategies) that lead to some final result (outcome) of typically unequal value (payoff or utility) to the players. Game theory is the interdisciplinary study of conflict, whose primary goal is the answer to the single, simply-stated, but surprisingly complex question: What is the best way to “play”? Although the principles of game theory have been widely applied throughout the social and natural sciences, their greatest impact has been felt in the fields of economics, political science, and biology. This course represents a survey of the basic techniques and principles in the field. Of primary interest will be the applications of the theory to real-world conflicts of historical or current interest.

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Calculus I: The Study of Motion and Change

Open , Seminar—Fall

Prerequisites: the minimum required preparation for study of the calculus is successful completion of study in trigonometry and precalculus topics. Students concerned about meeting the course prerequisites are encouraged to contact the instructor as soon as possible. This course is also being offered in the spring semester of this academic year.

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 and study the motion and change happening around us. The Ancient Greeks began a detailed study of change but were scared to wrestle with the infinite; 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.

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Calculus II: Further Study of Motion and Change

Open , Seminar—Fall

Prerequisites: one year of high-school calculus or one semester of college-level calculus. Students concerned about meeting the course prerequisites are encouraged to contact the instructor as soon as possible. This course is also being offered in the spring semester of this academic year.

This course continues the thread of mathematical inquiry following an initial study of the dual topics of differentiation and integration (see Calculus I course description). Topics to be explored in this course include the calculus of exponential and logarithmic functions, applications of integration theory to geometry, alternative coordinate systems, infinite series, and power series representations of functions. 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. The theory of limits, differentiation, and integration will be briefly reviewed at the beginning of the term.

Faculty

Calculus I: The Study of Motion and Change

Open , Seminar—Spring

Prerequisites: the minimum required preparation for study of the calculus is successful completion of study in trigonometry and precalculus topics. Students concerned about meeting the course prerequisites are encouraged to contact the instructor as soon as possible. This course is also being offered in the fall semester of this academic year.

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 and study the motion and change happening around us. The Ancient Greeks began a detailed study of change but were scared to wrestle with the infinite; 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.

Faculty

Calculus II: Further Study of Motion and Change

Open , Seminar—Spring

Prerequisites: one year of high-school calculus or one semester of college-level calculus. Students concerned about meeting the course prerequisites are encouraged to contact the instructor as soon as possible. This course is also being offered in the fall semester of this academic year.

This course continues the thread of mathematical inquiry following an initial study of the dual topics of differentiation and integration (see Calculus I course description). Topics to be explored in this course include the calculus of exponential and logarithmic functions, applications of integration theory to geometry, alternative coordinate systems, infinite series, and power series representations of functions. 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. The theory of limits, differentiation, and integration will be briefly reviewed at the beginning of the term.

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Multivariable Mathematics: Linear Algebra, Vector Calculus, and Differential Equations

Intermediate , Seminar—Year

Prerequisite: Successful completion of Calculus II or a score of 4 or 5 on the AP Calculus BC exam.

This yearlong course will cover the central ideas of linear algebra, vector calculus, and differential equations from both a theoretical and a computational perspective. These three topics typically comprise the intermediate series of courses that students study after integral calculus but before more advanced topics in mathematics and the sciences. This course will be especially meaningful for students interested in pure or applied mathematics, the natural sciences, economics, and engineering but would also be a great choice for students who have completed the calculus sequence and are simply curious to see how deep the rabbit hole goes. While our focus will be primarily on the mathematics itself, the tools we will develop are useful for modeling the natural world—and we will look at some of those applications. Conference work will revolve around pursuing the theory or application of those topics on a deeper level, according to students' personal interests.

Faculty

Discrete Mathematics: A Bridge to Advanced Mathematics

Intermediate , Seminar—Fall

Your voice will produce a mostly continuous sound signal when you read this sentence out loud. As it appears on the page, however, the previous sentence is composed of 79 distinct characters—including letters and a punctuation mark. Measuring patterns—whether continuous or discrete—is the raison d'être of mathematics, and different branches of mathematics have developed to address the two sorts of patterns. Thus, a course in calculus treats motion and other continuously changing functions. In contrast, discrete mathematics addresses problems of counting, order, computation, and logic. We will explore these topics and their implications for mathematical philosophy and computer science. The form of this seminar will be that of a (mathematical) writing workshop. We will work collaboratively to identify and reproduce the key formal elements of mathematical exposition and proof as they appear in both mathematical literature and each other's writing. This seminar is designed for students interested in advanced mathematical study and highly recommended for students with an interest in computer science, law, logic, or philosophy. Some prior study of calculus is highly recommended.

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Introduction to Real Analysis

Advanced , Seminar—Spring

Prerequisite: Successful completion of a yearlong study of calculus. Completion of an intermediate-level course (e.g., Discrete Mathematics, Complex Variables, Modeling I, etc.) is strongly recommended.

The calculus of Newton and Leibniz is very different from the calculus of modern mathematics. It took more than a century to develop a logically defensible approach to the “fluxions” and “evanescent quantities” of calculus. In a sense, the formalization of calculus as the study of functions of a real variable—real analysis—that took place in the 19th century was so successful that it became a model of the foundational rigor that would come to define mathematics as a discipline. This maturation is recapitulated in the typical undergraduate student upon taking the step from the techniques-based calculus course to a proof-based real analysis course. Although our topics will sound familiar to calculus—real numbers, sequences and series, limits, continuity, the derivative, and the integral—their presentation will feature a new level of mathematical rigor. The emphasis on precise definitions and explicit proofs is not merely to develop students’ technical abilities, though that is a desired outcome of the course. Rather, these finer distinctions will be motivated by counterexamples such as nowhere-differentiable continuous functions and rearrangements of infinite series, which challenge our basic intuitions about numbers and the real number line. Conference work will be allocated to clarifying seminar ideas and exploring additional mathematical topics.

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First-Year Studies: Achilles, the Tortoise, and the Mystery of the Undecidable

Open , FYS—Year

In this course, we will take an extended journey through Douglas Hofstadter's Pulitzer Prize-winning book, Gödel, Escher, Bach, which has been called “an entire humanistic education between the covers of a single book.” The key question at the heart of the book is: How can minds possibly arise from mere matter? Few people would claim that individual neurons in a brain are “conscious” in anything like the normal sense in which we experience consciousness. Yet self-awareness emerges, somehow, out of a myriad of neuronal firings and molecular interactions. How can individually meaningless physical events in a brain, even vast numbers of them, give rise to meaningful awareness, to a sense of self? And could we duplicate such a process in a machine? Considering those questions will lead us to explore a wide range of ideas from the foundations of mathematics and computer science to molecular biology, art, and music—and to the research frontiers of modern-day cognitive science and neuroscience. Along the way, we will closely examine Gödel's incompleteness theorem, mathematical logic and formal systems, the limits of computation, and the future prospects for artificial intelligence.

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Introduction to Computer Programming

Open , Lecture—Fall

This lecture presents a rigorous introduction to computer science and the art of computer programming, using the elegant, eminently practical, yet easy-to-learn programming language Python. We will learn the principles of problem solving with a computer while gaining the programming skills necessary for further study in the discipline. We will emphasize the power of abstraction, the theory of algorithms, and the benefits of clearly written, well-structured programs. Fundamental topics include: how computers represent and manipulate numbers, text and other data (such as images and sound); variables and symbolic abstraction; Boolean logic; conditional, iterative, and recursive computation; functional abstraction (“black boxes”); and standard data structures such as arrays, lists, and dictionaries. We will learn introductory computer graphics and how to process simple user interactions via mouse and keyboard. We will also consider the role of randomness in otherwise deterministic computation, basic sorting and searching algorithms, how programs can communicate across networks, and some principles of game design. Toward the end of the semester, we will investigate somewhat larger programming projects and so will discuss file processing; modules and data abstraction; and object-oriented concepts such as classes, methods, and inheritance. As we proceed, we will debate the relative merits of writing programs from scratch versus leveraging existing libraries of code. Discussion topics will also include the distinction between decidable and tractable problems, the relationship between programming and artificial intelligence, the importance of algorithmic efficiency to computer security, and Moore’s Law and its impact on the evolution of programming languages and programming style. Weekly hands-on laboratory sessions will reinforce the programming concepts covered in class.

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Introduction to Web Programming

Open , Lecture—Spring

This lecture introduces the fundamental principles of computer science via the creation of interactive Web pages. We will focus on the core triumvirate of Web technologies: HTML for content, CSS for layout, and—most important for us—JavaScript for interactivity. Examples of the kinds of Web applications that we will build include a virtual art gallery; a password generator and validator; and an old-school, arcade-style game. We will learn programming from the ground up and demonstrate how it can be used as a general-purpose, problem-solving tool. Throughout the course, we will emphasize the power of abstraction and the benefits of clearly written, well-structured code. We will cover variables, conditionals, loops, functions, recursion, arrays, objects, JSON notation, and event handling. We will also discuss how JavaScript communicates with HyperText Markup Language (HTML) via the Document Object Model (DOM) and the relationship of HTML, JavaScript, and Cascading Style Sheets (CSS). Along the way, we will discuss the history of the Web, the challenge of establishing standards, and the evolution of tools and techniques that drive the Web’s success. We will learn about client-server architectures and the differences between client-side and server-side Web programming. We will consider when it makes sense to design from the ground up and when it might be more prudent to make use of existing libraries and frameworks rather than reinvent the wheel. We will also discuss the aesthetics of Web design: Why are some pages elegant (even art) when others are loud, awkward to use, or—worse yet—boring. Weekly hands-on laboratory sessions will reinforce the programming concepts covered in lecture. No prior experience with programming or Web design is necessary (nor expected nor even desirable).

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Privacy, Technology, and the Law

Open , Seminar—Fall

What do digital currency, self-driving vehicles, and Edward Snowden have in common? The answer lies in this course, which focuses on how a few very specific computer technologies are dramatically altering daily life. In lecture, we will develop a series of core principles that explain the rapid change and help us chart a reasoned path to the future. We begin with a brief history of privacy, private property, and privacy law. Two examples of early 20th-century technologies that required legal thinking to evolve are: 1) whether a pilot (and passengers) of a plane are trespassing when the plane flies over someone's backyard; and, 2) whether the police can listen to a phone call from a phone booth (remember those?) without a warrant. Quickly, we will arrive at the age of information and can update those conundrums to, for example: a drone flies by with an infrared camera, a copyrighted video is viewed on YouTube via public WiFi, a hateful comment is posted on reddit, a playful tweet is taken out of context and goes viral for all to see, an illicit transaction involving Bitcoin is made between seemingly anonymous parties via Venmo. To get a better handle on the problem, we will consider the central irony of the Internet. It was developed at the height of the Cold War as a way to maintain a robust communication system in the event of a nuclear attack. Now, its open nature puts us at risk of 21st-century security threats such as electronic surveillance, aggregation and mining of personal information, and cyberterrorism. We will contrast doomsday myths popularized by movies such as War Games with more mundane scenarios such as total disruption of electronic commerce. Along the way, we will address questions such as: Does modern technology allow people to communicate secretly and anonymously? Can a few individuals disable the entire Internet? Can hackers launch missiles or uncover blueprints for nuclear power plants from remote computers on the other side of the world? We will also investigate other computer-security issues, including spam, computer viruses, and identity theft. Meanwhile, with our reliance on smart phones, text messages, and electronic mail, have we unwittingly signed ourselves up to live in an Orwellian society? Or can other technologies keep 1984 at bay? Our goal is to investigate if and how society can strike a balance so as to achieve computer security without substantially curtailing rights to free speech and privacy. Along the way, we will introduce the science of networks and describe the underlying theories that makes the Internet and its related technologies at once tremendously successful and so challenging to regulate. A substantial portion of the course will be devoted to introductory cryptology—the science (and art) of encoding and decoding information to enable private communication. We will conclude with a discussion of how cutting-edge technologies, such as blockchains, are impacting commerce today and how quantum cryptography and quantum computing may impact the privacy of communications tomorrow.

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Principles of Programming Languages

Intermediate , Seminar—Fall

No prior knowledge of Scheme is needed, but at least one semester of prior programming experience is expected.

This course explores the principles of programming-language design through the study and implementation of computer programs called interpreters, which are programs that process other programs as input. A famous computer scientist once remarked that if you don't understand interpreters, you can still write programs—and you can even be a competent programmer—but you can’t be a master. We will begin by studying functional programming, using the strangely beautiful and recursive programming language Scheme. After getting comfortable with Scheme and recursion, we will develop an interpreter for a Scheme-like language of our own design, gradually expanding its power in a step-by-step fashion. Along the way, we will become acquainted with the lambda calculus (the basis of modern programming language theory), scoping mechanisms, continuations, lazy evaluation, nondeterministic programming, and other topics if time permits. We will use Scheme as our "meta-language" for exploring those issues in a precise, analytical way—similar to the way in which mathematics is used to describe phenomena in the natural sciences. Our great advantage over mathematics, however, is that we can test our ideas about languages, expressed in the form of interpreters, by directly executing them on the computer.

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Databases

Intermediate , Seminar—Spring

Permission of the instructor is required. Students should have at least one semester of programming experience.

A modern database system is a collection of interrelated facts recorded on digital media and a set of computer programs that efficiently access those facts. In the 21st century, databases have become ubiquitous via the Web and {cloud computing” to the point that users may not even realize where their data is stored, how it is accessed, and who has access to it. This course attempts to shed light on why and how our society has become so dependent on information processing by examining software (and, to a lesser extent, hardware) techniques that lead to the efficient storage and retrieval of information. We will illustrate core principles by designing databases using open-source platforms (such as PostgreSQL, SQLite and MySQL) and designing websites to manipulate those databases using client-side technologies (such as HTML, CSS, JavaScript and a bit of AJAX) and server-side programming languages (such as PHP, Python and Node.js). Major topics include relational database design, query languages (e.g., SQL, its relatives, and lower-level embedded query languages), the object-relational model, ACID properties, and the client-server paradigm. We will also consider how the era of big data has challenged the supremacy of the ACID/SQL model and given rise to NoSQL database systems such as MongoDB, Cassandra, and Neo4J. Each student will be responsible for designing and implementing a Web-accessible database application of their own choosing, using open-source database software and a Web-application programming language such as Node, PHP, Python, or Ruby. Students will work on their projects throughout the course and will demonstrate them to rest of the class at the close of the semester. In addition to regular reading assignments, there will be several problem sets and short programming assignments. There will also be a more substantial programming assignment used to illustrate issues pertaining to the practical implementation of database systems. Example conference topics include data mining, database privacy and access control, geographic information systems (GIS), logic databases, and the implementation of a miniature database system.

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Econometric Analysis: Structural Explorations in the Social Sciences

Open , Lecture—Year

This lecture requires some basic knowledge (high-school level) of mathematics and statistics. A review of core concepts in these subjects will be carried out at the beginning of the fall semester.

The course is designed for all students interested in the social sciences who wish to understand the methodology and techniques involved in the estimation of structural relationships between variables. The course is intended for students who wish to be able to carry out empirical work in their particular field, both at Sarah Lawrence College and beyond, and critically engage empirical work done by academic or professional social scientists. The practical hands-on approach taken in this course will be useful to those students who wish to do future conference projects in the social (or natural) sciences with significant empirical content. It will also be invaluable for students who are seeking internships, planning to enter the job market, or desiring to pursue graduate education in the social sciences and public policy. After taking this course, students will be able to analyze questions such as the following: What is the relationship between slavery and the development of capitalist industrialization in the United States? What effects do race, gender, and educational attainment have in the determination of wages? How does the female literacy rate affect the child mortality rate? How can one model the effect of economic growth on carbon-dioxide emissions? What is the relationship among sociopolitical instability, inequality, and economic growth? How do geographic location and state spending affect average public-school teacher salaries? How do socioeconomic factors determine the crime rate in the United States? During the course of the year, we will study all of these questions. In the first semester, we will cover the theoretical and applied statistical principles that underlie Ordinary Least Squares (OLS) regression techniques. We will begin with the assumptions needed to obtain the Best Linear Unbiased Estimates of a regression equation, also known as the “BLUE” conditions. Particular emphasis will be placed on the assumptions regarding the distribution of a model’s error term and other BLUE conditions. We will also cover hypothesis testing, sample selection, and the critical role of the t- and F-statistic in determining the statistical significance of a social metric model and its associated slope or “β” parameters. Further, we will address the three main problems associated with the violation of a particular BLUE assumption: multicollinearity, serial correlation, and heteroscedasticity. We will learn how to identify, address, and remedy each of those problems. In addition, we will take a similar approach to understanding and correcting model specification errors. Finally, we will focus on the analysis of historical time-series models and the study of long-run trend relationships between variables. At the end of the fall semester, students will have to carry out an econometric analysis of a World Bank study on labor markets. The spring semester class will build on the fall class by introducing students to advanced topics in econometrics. We will study autoregressive dependent lag (ARDL) models, co-integration, and error correction models involving nonstationary time series. We will investigate simultaneous equations systems, vector error correction (VEC), and vector autoregressive (VAR) models. The final part of the seminar will involve the study of panel data, as well as logit/probit models. As with the fall class, the spring class will also be very “hands-on,” in that students will get ample exposure to concrete issues while also being encouraged to consider basic methodological questions (e.g., the debates between John Maynard Keynes and Jan Tinbergen) regarding the power and limitations of econometric analysis. At the end of the spring semester, students will have to do in-class presentations of self-designed econometric projects (either singly or in groups) on topics of their choice. The spring semester is particularly relevant to students who wish to pursue graduate studies in a social-science discipline, although it will be equally relevant for those seeking other types of graduate degrees that involve knowledge of intermediate-level quantitative analysis.

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Classical Mechanics (Calculus-Based General Physics)

Open , Seminar—Fall

Permission of the instructor is required. Students must have completed one semester of calculus as a prerequisite. It is strongly recommended that students who have not completed the second semester of calculus enroll in Calculus II, as well. Classical Mechanics or equivalent, along with Calculus II or equivalent, is highly recommended in order to take Electromagnetism and Light (Calculus-Based General Physics) in the spring.

Calculus-based 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. (Alternatively, the algebra-based Introduction to Mechanics will also suffice for premedical students). The 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 and in weekly laboratory work.

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Introduction to Mechanics (General Physics Without Calculus)

Open , Seminar—Fall

This course or equivalent is required to take Introduction to Electromagnetism, Light, and Modern Physics (General Physics Without Calculus) in the spring.

This course covers introductory classical mechanics, including dynamics, kinematics, momentum, energy, and gravity. Students considering careers in architecture or the health sciences, as well as those interested in physics for physics’ sake, should take either this course or Classical Mechanics. 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. Seminars will incorporate discussion, exploratory activities, and problem-solving activities. In addition, the class will meet weekly to conduct laboratory work. A background in calculus is not required.

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Time to Tinker

Open , Seminar—Spring

Do you enjoy designing and building things? Do you have lots of ideas about things that you wished existed but do not feel you have enough technical knowledge to create it yourself? This course is meant to give an introduction to tinkering, with a focus on learning the practical physics behind basic mechanical and electronic components and providing the opportunity to build things yourself. We will have weekly, three-hour workshops in the physics lab, along with individual biweekly conference meetings. The course will be broken down into multiple units, including tools of the trade, mechanics, 3D printing, simple electronics, introduction to Arduino, and the engineering design process. Each unit will include a small group project to demonstrate the new skills that you have acquired. In addition, there will be weekly homework assignments, where you will need to create or bring in something related to the topic at hand. For your individual conference project, you will be developing your own engineered piece, with a report on its design and desired function, as well as any necessary material required for others to replicate the results (within desired copyright restrictions).

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Introduction to Electromagnetism, Light, and Modern Physics (General Physics Without Calculus)

Sophomore and above , Seminar—Spring

Calculus is not a requirement for this course. Students should have had at least one semester of physics (mechanics).

This course covers electromagnetism and optics, as well as selected topics in modern physics. Students considering careers in the health sciences, as well as those interested in physics for physics’ sake, should take either this course or Classical Mechanics. 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. Seminars will incorporate discussion and exploratory and problem-solving activities. In addition, the class will meet weekly to conduct laboratory work. A background in calculus is not required.

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Electromagnetism and Light (Calculus-Based General Physics)

Intermediate , Seminar—Spring

Prerequisites: Completion of Classical Mechanics or equivalent, along with Calculus II or equivalent.

This is the follow-on course to Classical Mechanics, where we will be covering 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. Seminars will incorporate discussion, exploratory, and problem-solving activities. In addition, the class will meet weekly to conduct laboratory work.

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Quantum Mechanics

Intermediate , Seminar—Spring

Prerequisites: Students must have completed one year of calculus, as well as one year of general physics.

Quantum mechanics, which describes physics at small scales, requires an entirely different set of principles, concepts, and mathematical techniques than the classical physics covered in introductory courses. In this course, we will introduce the basic principles of quantum theory and discuss their applications in atomic and subatomic physics—including, among others, the meaning and computation of particle wave functions, the energy levels of atoms, and the properties of quantum angular momentum (spin). This is an intermediate course recommended for students interested in pursuing physics, physical chemistry, or engineering.

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