Abbe Herzig

What does it mean to understand a mathematical concept? In this course, we will explore children’s mathematical thinking and how they develop understanding of foundational concepts like number, place value, counting, operations, whole numbers, fractions, proportion, and algebra. These ideas have profound and rich mathematics underlying them, sometimes in surprising ways. As you reflect on and communicate about your own mathematical thinking and beliefs, you will deepen your understanding of these ideas. We will also explore the math that children know and how they think about mathematics, how different groups of students experience mathematics learning, and what types of learning activities facilitate learning with understanding. This is not a methods course but does contain some essential elements of pedagogy and learning activities.

When used well, mathematics is a powerful set of tools for understanding the world. When used in other ways, mathematics can serve to uphold and perpetuate inequality and injustice. In this class, we will investigate how we can use mathematical tools to understand, document, and work against inequity and injustice, including topics such as voting rights, health disparities, access to education, “big data” algorithms that control aspects of our lives, the carceral system, and environmental justice. Students of all mathematical levels are welcome.

This course will explore mathematical foundations, including logic, set theory, combinatorics, function theory, probability, and statistics. Each of these topics bridges both theoretical mathematical structures and applications to a broad range of real-world problems. Applications of these theoretical mathematical results will be explored through problems from the biological, physical, and social sciences; education; politics; music; and visual arts (among others). This course includes a calculus-based introduction to the theory and applications of probability and statistics. Students primarily interested in a more general, single-semester introduction to the principles and practices of statistics should consider the lecture course, An Introduction to Statistical Methods and Analysis. Students should be comfortable with methods and concepts from single-variable differential and integral calculus (one year of high-school study or one semester of college study). Conference work can focus on any topic relating to mathematics, including theoretical mathematical ideas or their applications to problems outside of mathematics.

Variance, correlation coefficient, regression analysis, statistical significance, margin of error...you’ve heard these terms and other statistical phrases bantered about before, and you’ve seen them interspersed in news reports and research articles. But what do they mean? How are they used? And why are they so important? Serving as an introduction to the concepts, techniques, and reasoning central to the understanding of data, this lecture course focuses on the fundamental methods of statistical analysis used to gain insight into diverse areas of human interest. The use, misuse, and abuse of statistics will be the central focus of the course; specific topics of exploration will be drawn from experimental design theory, sampling theory, data analysis, and statistical inference. Applications will be considered in current events, business, psychology, politics, medicine, and many other areas of the natural and social sciences. Statistical (spreadsheet) software will be introduced and used extensively in this course, but no prior experience with the technology is assumed. Group conferences, conducted in workshop mode, will serve to reinforce student understanding of the course material. This lecture is recommended for anybody wishing to be a better-informed consumer of data and strongly recommended for those planning to pursue advanced undergraduate or graduate research in the natural sciences or social sciences. Enrolled students are expected to have an understanding of basic high-school algebra and plane coordinate geometry.

This course continues the thread of mathematical inquiry, following an initial study of the dual topics of differentiation and integration (see Calculus I course description). Topics to be explored in this course include the calculus of exponential and logarithmic functions, applications of integration theory to geometry, alternative coordinate systems, infinite series, and power series representations of functions. For conference work, students may choose to undertake a deeper investigation of a single topic or application of the calculus or conduct a study of some other mathematically-related topic, including artistic projects. This seminar is intended for students interested in advanced study in mathematics or science, preparing for careers in the health sciences or engineering, or simply wishing to broaden and enrich the life of the mind.