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Everything is geometry! This class is about two things: first, about how mathematicians have extended the concept of "geometry" beyond triangles and circles, into higher-dimensional spaces, curved spaces, spaces of functions, discrete spaces, and more. Second, about how this extension of "geometry" can allow us to apply our powerful geometric intuition to a wide range of
Formal logic is the study of the structure of reasoning itself—how arguments are built, when they succeed, and why they fail. In an age of information overload, knowing how to dissect an argument, detect reasoning errors, and construct rigorous proofs is a superpower. This course introduces the foundations of formal logic, with an emphasis on precision, clarity, and critical
Multivariable calculus is one of the core parts of an undergraduate mathematics curriculum. Introductory calculus mostly concentrates on situations where there is one input and one output variable; multivariable extends differentiation, integration, and differential equations to cases where there are multiple input and output variables. In this way, multivariable calculus
This rigorous course provides a comprehensive introduction of the nervous system, including its structure, function, and development. Students will explore the principles of the cellular and molecular mechanisms that allow neurons and other specialized nervous cells to detect, encode, and transmit information; including signaling, synaptic transmission, and neuroplasticity.
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,
