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This foundational class covers modes of reasoning used in quantitative sciences and mathematics. While learning the art of mathematical modeling, i.e. translating the physical systems/real-life situations into mathematics, we will apply problem solving and practice effective communication of mathematics.
Differential equations are a powerful and pervasive mathematical tool in the sciences and are fundamental in pure mathematics as well. Almost every system whose components interact continuously over time can be modeled by a differential equation, and differential equation models and analyses of these systems are common in the literature in many fields including physics, ecology, biology, astronomy, and economics.
I would (and will) argue that Newton's Principia is the most important book yet written. It is certainly the most important book that a vanishingly small number of people have actually read.
Together with calculus, linear algebra is one of the foundations of higher-level mathematics and its applications. This is NOT just the algebra you know from high school. There are several perspectives one can take on linear algebra: it is a method for handling large systems of linear equations, it is a theory of linear geometry (including in dimensions larger than three), it is matrix algebra, and it is a theoretical structure that appears throughout mathematics, physics, computer science, and statistics.
In the eighteenth and nineteenth centuries, mathematics underwent a vast expansion, into new, exciting, and increasingly counter-intuitive realms. The subject risked mystification and mutual incomprehensibility between experts in different sub-fields. In the first part of the twentieth century, a group of French mathematicians, under the pseudonym Bourbaki, undertook an ultimately successful program to use the foundation of set theory to put all of mathematics onto a common conceptual and logical foundation.
Students with little or no Spanish will learn the language through an immersion in Latin American painting. While there will be some discussion of standard tactics such as stylistic nuances and artists’ biographies, it is expected that we will rapidly develop sufficient linguistic ability to focus on movements, ranging from the republican art of nation-building in the 19th century to modernism, magical realism, and the postmodern, thus treating the works as ideologemes, representations of political and social import.
In lieu of more conventional advanced Spanish classes, paralleling a series of often disparate tutorials, with tutees working in relative isolation, the proposal is to allow students free reign over an idea for a final, term-long project, while concurrently offering them an educated, exoteric audience to assist in fleshing out their work. Faculty will provide key secondary and tertiary reading, common to all, some with immediate relevance to the projects in question, some deemed necessary for any culminating work, but the primary content of these sessions will be student-driven.
Low-intermediate level. More details to be announced soon.
High-intermediate level. More details to come soon.