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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. This process involves isolating the essential variables and
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),
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.
Written about 150 CE, Ptolemy's Almagest collected and systematized the knowledge of astronomers of the time to give a system which roughly predicted the
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,
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
