Math 311H - Intro. to Real Analysis I (Spring 2020)

Instructor / Office hours

Dr. Iian Smythe (i.smythe@rutgers.edu) / W 10:20pm - 11:40pm in 511 Hill Center or by appointment

Teaching assistant / Office Hours

Yonah Biers-Ariel (yb165@math.rutgers.edu) / M 1:30pm - 2:30pm & Th 12:00pm - 1:00pm in 620 Hill Center

Lecture

MTh 10:20am - 11:40am in 108 Allison Road Classroom (ARC) Building

Workshop

W 8:40am - 10:00am in 009 Hill Center

Course description

An introduction to real analysis, the study of the real line and real-valued functions of a single-variable, the rigorous foundations of calculus. We will cover the material in Chapters 1-5 of Abbott (see below), including: the real numbers and their properties, limits of sequences and series, the topology of the real line, limits and continuity of functions, the derivative and differentiability. Other topics (e.g., sequences and series of functions, metric spaces, construction of the real numbers) will be covered if time allows. An emphasis will be placed on theoretical understanding and examples which stretch intuitions beyond that developed in calculus. Students will be expected to understand, write, and present proofs.

Our course is discussion based: Students will be assigned readings from the text as well as brief quizzes about the readings. The readings will be discussed and expanded upon during lecture.

See the course syllabus for more information regarding grade evaluation, homework standards, workshops, important dates, etc.

Textbooks & Resources

Our required textbook is Understanding Analysis (2e) by Stephen Abbott. The book is freely available as an ebook from Rutgers Libraries.

Course material (announcements, homework, lecture notes, etc) will be posted on Canvas.