Progressive Junior College of New York
Pattern: An Interdisciplinary Course in Textile Design and Elementary Group Theory
This course will focus on the interplay between the art of designing repeat patterns and the mathematics of analyzing those patterns in terms of their symmetries. Through studying and creating works of art--ranging from mandalas to Islamic mosaics to Escher to wallpaper groups--students are introduced to elementary group theory. Developed and co-taught by a mathematician and an artist.
Geometry in Art and Architecture
Explores the multiplicity of connections between mathematics and art, from proportion to perspectives to knots to the influence of numerology on art. Developed and co-taught by a mathematician/artist and an art historian.
Mathematics and Culture: Renaissance Thought, Imagination and the New Universe
Focuses on the problem of planetary motion and the search for a satisfactory predictive model in the sixteenth and early seventeenth centuries, exploring the interactions between mathematical, scientific, political, philosophical, artistic and magical fields of discourse in the early modern period. Developed and co-taught by a mathematician and an English professor.
Renaissance Math in Fiction and Drama
Explores how scientific developments in Renaissance astronomy were portrayed in literature and drama past and present. Students use Renaissance technology to track the transit of Mars across the sky. Developed and co-taught by a mathematician and a drama professor.
Chaos: Attractive Disorder
Chaotic dynamical systems are everywhere: weather patterns, swinging pendula, population dynamics, even human heart rhythms. With a balance of theory and applications, this course will introduce: flows, fixed points, bifurcations, Lorenz equations, Lyapunov exponent, one-dimensional maps, period-doubling, Julia sets, fractal dimension, Hamiltonian systems, symbolic dynamics. Numerical explorations will form an integral part of the course. You will be introduced to a recent, exciting, and rapidly-growing area. Developed and taught by a mathematician.
A Matter of Time
Everybody knows about time. Our everyday language bears witness to the centrality of time with scores of words and expressions that refer to it as a measure, a frame of reference, or an ordering factor for our lives, feelings, dreams, and histories. For the Aztecs time was a series of 52-year cycles. At the end of each cycle, the sun would set and for three days and nights the universe was up for grabs before the beginning of a new cycle. The Bible, on the other hand, inscribed another concept of time, linear and chronological in the seven days of creation and the detailed chronicles of endless genealogies. Playing with time has been a favorite game in works of high culture--from the Greek sophists to cubism--and in popular culture--from H.G. Wells to Monty Python. And time is at the center of one of the most revolutionary scientific theories of all time: Einstein's Theory of Relativity. In this course we will use mathematics, literature, and the arts to travel through history, to explore and understand Time as a key concept and reality in the development of Western culture and in our own twentieth century view of ourselves and of the world.
Mathematics and Science Fiction: The Fire in the Equations
We shall challenge the widely-held assumption that readers and writers of science fiction feel more at home with physical than with mathematical sciences. In fact, a substantial body of novels and stories depends on mathematical ideas. Is the portrayal of mathematics in science fiction accurate or confused, speculation or mere technobabble? Is mathematics simply a way of mystifying, even intimidating readers or can understanding the underlying mathematics truly contribute to the total experience of reading a story? This course will present both the mathematics and the literary concepts necessary for an informed reading of the chosen texts. Although these texts will mostly be works of fiction, we shall also discuss some critical theory, with reference to current debates about post-modern consciousness, cultural politics, narrative structure, and the nature of artistic representation. Among the mathematical authors we sharll read are Edwin Abbott, Martin Gardner, Douglas Hofstadter, Stanislaw Lem, Ernst Mach, Blaise Pascal and Rudy Rucker; among the authors of novels or short stories, Greg Bear, Greg Egan, Robert Heinlein, Ursula Le Guin, Larry Niven, Rudy Rucker, and Kim Stanley Robinson; among writers on the theory and practice of science fiction, Samuel Delany, Ursula Le Guin, Joanna Russ, and Darko Suvin. Course requirements will include regular problem sets, a critical essay, and one or more drafts of a story.
Mathematics and Music
Sound and music are integral parts of all cultures and are critical to human and animal communications. The production, transmission, and perception of sound is woven through with mathematics. With the goal of expanding both scientific and artistic horizons (and teaching you some ear-opening practical skills) we explore vibration, resonance, waves, musical instruments, the human ear, speech, architectural acoustics, harmony and dissonance, tuning systems, and composition.
Topics of Applied Mathematics
The numerical nature of twenty-first century society means that applied mathematics is everywhere: animation studios, search engines, hedge funds and derivatives markets, and drug design. Students will gain an in-depth introduction to an advanced topic in applied mathematics. Possible subjects include digital signal and image processing, quantum chaos, computational biology, cryptography, coding theory, waves in nature, inverse problems, information theory, stochastic processes, machine learning, and mathematical finance.
Mathematics and Finance
Financial derivatives can be thought of as insurance against uncertain future financial events. This course will take a mathematically rigorous approach to understanding the Black-Scholes-Merton model and its applications to pricing financial derivatives and risk management. Topics may include: arbitrage-free pricing, binomial tree models, Ito calculus, the Black-Scholes analysis, Monte Carlo simulation, pricing of equities options, and hedging.
Applications of Calculus to Medicine and Biology
Did you ever wonder why medical schools require calculus? Or why biology has recently been describes as “the most mathematical science”? This course will show you how real researchers in medicine and ecology use mathematical models to predict change and design strategies for controlling epidemics, dosing medicine, and managing ecosystems. Using basic calculus and a friendly online application, you can study a multitude of real situations.