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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.
In this course, students will work on an extended piece (10+ minutes), as well as a suite of miniatures (< 30 seconds). By playing with scale and continuity, students will be challenged to find their own way to extend their ideas while enriching their own musical language. Students can propose a piece in any style or forces, and we will work together to recruit instrumentalists or resources towards an end-of-term performance or installation.
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.