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This course covers the breadth of university calculus: differentiation, integration, infinite series, and ordinary differential equations. It focuses on concepts and interconnections. In order to cover this much material, computational techniques are de-emphasized. The approach is historically based and classical, following original texts where possible.
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 combines calculus and linear algebra; the subject can also be called vector and matrix calculus.
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 problems that might not initially seem geometric, both within mathematics, and in physics, computer science, and elsewhere.
In this course, we will focus on developing the statistical skills needed to answer questions by collecting data, designing experimental studies, and analyzing large publicly available datasets. The skills learned will also help students to be critical consumers of statistical results. We will use a variety of datasets to develop skills in data management, analysis, and effective presentation of results.
Discrete mathematics studies problems that can be broken up into distinct pieces. Some examples of these sorts of systems are letters or numbers in a password, pixels on a computer screen, the connections between friends on Facebook, and driving directions (along established roads) between two cities. In this course we will develop the tools needed to solve relevant, real-world problems. Topics will include: combinatorics (clever ways of counting things), number theory and graph theory. Possible applications include probability, social networks, optimization, and cryptography.
Throughout history, people have played games — games of chance and games of skill. Many of us grew up playing all kinds of different games, and most of those are infused with the core tenets of statistical reasoning and understanding: probability, risk assessment, expected value, and game theory. This course will look at statistics and probability through this lens. We will consider dice, cards, and several ‘classic’ board games. We will consider situations with both complete and hidden information and how to analyze those.
How are language and thought connected, and does speaking multiple languages affect these connections? Most people have had the experience of struggling to come up with a particular word or phrase, sometimes recalling it after a substantial delay. This course will unpack the mental processes involved in that experience and explore the ways that cognitive psychology -- the study of thought -- has been broadened by investigations of monolingual and multilingual language use.
What do we remember about our lives, and how do these memories contribute to our sense of self? This course will begin with an introduction to the scientific study of human memory to better understand how autobiographical memory brings episodic, semantic, and other types of memory together. We will then explore what autobiographical memory has revealed about the development of memory in childhood at brain and behavioral levels. Cross-cultural research has substantially reshaped the scientific understanding of autobiographical memory, and we will focus particularly on groun
Social psychology is the scientific study of how people think about, influence, and relate to one another. This course will explore social thinking, influence, and social relations that shape our lived experiences through a U.S. contextual lens. Social psychologists are increasingly concerned with the effects of the various systems of domination on outcomes such as health and wellbeing, relationships with others, personal and social identities, as well as political views and participation.