Math 311 - Intro. to Real Analysis I (Fall 2018)

Instructor / Office hours

Dr. Iian Smythe (i.smythe@rutgers.edu) / W 1:00pm-2:30pm in 511 Hill Center or by appointment

Teaching assistant / Office Hours

Marco Castronovo (marco.castronovo@rutgers.edu) / T 10:00am-11:20am in 626 Hill Center

Lecture

TTh 6:40pm-8:00pm in 525 Hill Center

Workshop

T 8:10pm-9:30pm in 525 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 0-4 of Gaughan (see below), including: basic set theory, mathematical induction, the real numbers, sequences and convergence, limits, continuity, differentiation and the basic theorems of differential calculus. Students will be expected to understand and write proofs.

Our course will be "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 in class. Students will be expected to answer questions about the readings in class.

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

Textbooks & Resources

Course material (homework, worksheets, solutions, etc) will be posted on Sakai.

Our required textbook is Introduction to Analysis, 5th edition, by E. D. Gaughan. It will be available on course reserve in the Mathematical Sciences and Physics Library.

The following are additional resources you may find useful:

• Understanding Analysis, 2nd edition, by S. Abbott (available online via Rutgers Libraries)
• Elementary Analysis, 2nd edition, by K. A. Ross (available online via Rutgers Libraries)
• Basic Analysis: Introduction to Real Analysis, by Jiří Lebl (freely available from the author)
• Introduction to Real Analysis, 4th edition, by R. G. Bartle and D. R. Sherbert