Computer Science

Open, Small Lecture—Fall

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 they were hesitant 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 will begin with the central concept of the limit and proceed to explore the dual processes of differentiation and integration. Numerous applications of the theory will be examined. Weekly group conferences will be conducted in hands-on workshop mode. This small lecture 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

• Daniel King

Open, Lecture—Fall

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 will focus 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. Calculator and spreadsheet software will be used extensively in this course, but no prior experience with these technologies 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.

Faculty

• Daniel King

Intermediate, Seminar—Fall

What is truth? One idea is that if that something is true, if using a small collection of assumptions and a few basic rules, then we can prove our claim from those assumptions. In this course, we will focus on mathematical proof and how it represents a formal backbone on which both theoretical computer science and most of the rest of mathematics can be constructed. We will work from the ground up, starting with Boolean logic and deductive arguments and moving onto elementary number theory where we will focus on the use of induction (e.g., to establish a formula for triangular numbers) and contradiction (e.g., to prove the infinitude of primes). We will introduce a formal notion of algorithm and demonstrate how number theory can be used to explain the principles behind modern cryptography. We will study sets, both finite and infinite, and how they can be used to formalize relations and functions. We will introduce basic notions of combinatorics (a fancy word for counting) with emphasis on the import of exponential growth. (Example: If you walked into a pizza shop that offered ten different toppings, would you want to sample all of the combinations?) We will then use our improved methods of counting to develop a basic theory of probability. Near the end of the semester, we will apply most, if not all, of the earlier concepts to introduce the theory of graphs. Along the way, we will explore the interplay between discrete mathematics and computation including recursion and programming; big-oh notation and categorizing the efficiency of algorithms; and graph theory's role in circuit design. Time permitting, we will circle back to the original question and investigate the limits of proof by trying to show that some true things can never be proven! For conference, students will do a deep dive on a related mathematical or computational topic. Examples include, but are not limited to: studying the proof and applications of a famous theorem (e.g., Fermat's "little" theorem); explaining how computers can be used (without so-called "artificial intelligence (AI)") to verify the validity of a formal proof; learning to program using logic; measuring the performance of related algorithms; or designing and simulating nontrivial digital circuits.

Faculty

• Michael Siff

Intermediate, Seminar—Year

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 multivariable. This course will introduce 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. Specific topics to be covered will 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.

Faculty

• Melvin Irizarry-Gelpi

Open, Small Lecture—Spring

Calculus is the mathematical gift that keeps on giving—thank you, Newton and company! In this course, students will expand their knowledge of limits, derivatives, and integrals with concepts and techniques that will enable them to solve many important problems in mathematics and the sciences. Topics will include differentiation review, integration review, integration with non-polynomial 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, differential equations and modeling dynamical systems, and, time permitting, parametric equations of a curve and polar coordinates. Weekly group conferences will be conducted in hands-on workshop mode. This course 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

• Melvin Irizarry-Gelpi

Intermediate, Seminar—Fall

Explore the beautiful mathematics and physics of waves through both theory and experiment. This course will teach students valuable mathematical methods and basic computational skills that are necessary for more advanced physical-science courses. Laboratory class time will include using advanced lab equipment, analyzing data using Jupyter (IPython) notebooks, learning numerical techniques, and reporting the results using LaTeX. For conference work, students are encouraged to choose an experiment or an American Journal of Physics article to replicate, analyze, and present their findings at the semiannual Sarah Lawrence College Science & Mathematics Poster Session.

Faculty

• Sarah Racz

Open, Small Lecture—Spring

Do you enjoy designing and building things? Do you have lots of ideas for things that you wish 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 be broken down into four primary units: design and modeling; materials, tools, and construction; electronics and microcontrollers; and simple machines and mechanisms. 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. The course will have a weekly workshop for team-based projects in addition to the lecture. Let’s get tinkering!

Faculty

• Merideth Frey

Open, Small Lecture—Fall

What makes linguistic communication possible? Do other primates “talk”? How do we understand messages from one another despite uncertainty and noise? In this course, we will consider central questions about language: Are we the only ones who have it? When did we learn it? How does artificial intelligence mimic it? This course will start with an introduction to comparative research with other species (nonhuman primates, whales, and insects), allowing students to consider many possible forms of communication. Next, we will look at humans. What can studies with babies and children tell us about the nature of our communication system? Finally, we will explore how large language models, such as ChatGPT, produce text that might look and feel like human writing. What have these models learned, and how should we study them? Students should come prepared to engage with the topic of communication from multiple perspectives, including empirical/scientific and critical. Through weekly small-group conferences, students will develop projects that relate the course to their collective interests, such as learning and communicating in Toki Pona (a philosophical artistic-constructed language), researching the limits of artificial intelligence language models, observing and analyzing children’s communication, or designing a behavioral intervention study that implements and evaluates different communication practices.

Faculty

• Sammy Floyd

Advanced, Seminar—Fall

In this research internship course, students will gain research experience through active engagement in a psychology research lab with a member of the psychology faculty. This will involve an internship within a research lab on campus, including a weekly lab meeting, a weekly collaborative meeting across labs, ongoing contributions towards research and practice within their lab and/or community settings, additional individual and group meetings as needed, and additional synchronous and asynchronous research work. Weekly lab meetings will involve reading and discussing research articles and research-methods papers specific to the topics of research being undertaken by each student and faculty member. Students will be expected to learn the current research approaches being employed by their supervising faculty member and to contribute toward ongoing research in the form of a research practicum. They may also have the opportunity to develop and implement their own independent research projects within the labs in which they are working, depending on lab priorities. Students will be expected to make progress on research projects between meetings, as determined in collaboration with their primary supervising faculty.

The weekly collaborative cross-labs meeting will include readings on, and discussions of, research methods and ethics—both broad and specific to the research in which students are involved—as well as the discussion of contemporary research articles that are relevant to student and faculty research projects. All faculty and students involved in the research experience will take turns leading the discussion of current research, with faculty taking the lead at the beginning of the semester and students taking the lead as their expertise develops. 

Students participating in the course will be expected to attend and actively participate in weekly collaborative cross-labs meetings and weekly lab meetings; keep an ongoing journal and/or scientific lab notebook; select and facilitate group and lab discussions of relevant contemporary research articles (at least once for each meeting type); work within a lab and/or community setting, as appropriate for their projects; contribute toward ongoing research and practice within their lab or community settings; report on their ongoing lab research in the form of a short paper prepared for possible publication and a poster at the Science and Math Poster Symposium; and provide their colleagues with ongoing verbal and written feedback on their projects. Students will be responsible for working collaboratively with their colleagues to further develop their understanding of each of the topics covered in class.

Faculty

• Kim Ferguson
• Linwood J. Lewis
• Maia Pujara
• Sammy Floyd

Intermediate, Seminar—Spring

We have never known as much about the minds of children as we do now. Using the same tools, our understanding of adult cognition has also led us to surprising conclusions: Babies are often better than adults at distinguishing faces of other races, and toddlers perform spontaneous scientific experiments with their toys. This research has also raised questions: Why do adept adult readers seem to skip over entire words? Can we simultaneously entertain multiple possible interpretations of the sentences that we see and hear? And, as the movie Frozen forces us to consider: How do we finish each other’s sandwiches? In this course, students will learn about classical and cutting-edge methods for studying learning and reasoning. This course will be a deep dive into multiple measures of behavior, starting with measurements of looking behaviors (e.g., real-time eye tracking, habituation paradigms, headturn methods), reading time, reaction time measures, and naturalistic tasks and interviews with toddlers and children. We will also review the promise of neural methods (fNIRS, fMRI, EEG), as well as their constraints. For each of these methods, we will explore how they shape ongoing debates about how best to design experiments, analyze data, and build inclusive theories that reflect human variation. In conference projects, using one of the studied behavioral methods, students will design an experiment to test their own research question, revise the proposal after peer review, and analyze and present their findings in an APA-style scientific paper. During lab sessions and conference meetings, students will learn to use their chosen behavioral method, implement the experiment, and collect preliminary data. By the end of the course, students will have a strong understanding of several central research methods in psychology, their own perspective of the strengths and limitations of different approaches, and the tools to critically evaluate and communicate about published findings.

Faculty

• Sammy Floyd

Advanced, Seminar—Spring

In this research internship course, students will gain research experience through active engagement in a psychology research lab with a member of the psychology faculty. This will involve an internship within a research lab on campus, including a weekly lab meeting, a weekly collaborative meeting across labs, ongoing contributions towards research and practice within their lab and/or community settings, additional individual and group meetings as needed, and additional synchronous and asynchronous research work. Weekly lab meetings will involve reading and discussing research articles and research-methods papers specific to the topics of research being undertaken by each student and faculty member. Students will be expected to learn the current research approaches being employed by their supervising faculty member and to contribute toward ongoing research in the form of a research practicum. They may also have the opportunity to develop and implement their own independent research projects within the labs in which they are working, depending on lab priorities. 

The weekly collaborative cross-labs meeting will include readings on, and discussions of, various concepts in research related to open science practices, finding funding/grant writing, collecting and analyzing data, as well as the discussion of contemporary research articles that are relevant to student and faculty research projects. All faculty and students involved in the research experience will take turns leading the discussion of current research, with faculty taking the lead at the beginning of the semester and students taking the lead as their expertise develops. 

Students participating in the course will be expected to attend and actively participate in weekly collaborative cross-labs meetings and weekly lab meetings; keep an ongoing journal and/or scientific lab notebook; select and facilitate group and lab discussions of relevant contemporary research articles (at least once for each meeting type); work within a lab and/or community setting, as appropriate for their projects; contribute toward ongoing research and practice within their lab or community settings; report on their ongoing lab research in the form of a short paper prepared for possible publication and a poster at the SciMath Poster Symposium; and provide their colleagues with ongoing verbal and written feedback on their projects. Students will be responsible for working collaboratively with their colleagues to further develop their understanding of each of the topics covered in class.

Faculty

• Kim Ferguson
• Sammy Floyd