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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.
鈥淣ot long ago, a near prerequisite for vanguard architecture was an engagement with theory; lately it has become an acquaintance with art鈥 or so observed Hal Foster in his 2011 book 鈥楾he Art Architecture Complex.鈥 While ideas about what constitutes cutting edge architecture may have transformed in the decade since, entanglements between art and architecture and the reciprocal effects that they have on each other remain central to architectural discourse.
鈥淣ot long ago, a near prerequisite for vanguard architecture was an engagement with theory; lately it has become an acquaintance with art鈥 or so observed Hal Foster in his 2011 book 鈥楾he Art Architecture Complex.鈥 While ideas about what constitutes cutting edge architecture may have transformed in the decade since, entanglements between art and architecture and the reciprocal effects that they have on each other remain central to architectural discourse.
Can architecture be understood in the same terms as a photograph? A piece of writing? A painting? A film? Or does it require its own vocabulary, rules, precedents, and sensibilities?