640:311:04

Introduction to Real Analysis I

SPRING 2016

Basic information

• Instructor: Professor Eugene Speer
  • Hill Center 520
  • 848–445–7974
  • speer at math.rutgers.edu

• Office hours:
  • Tuesday, 9:00–10:00 AM, Hill 520
  • Thursday, 10:20–11:40 AM, Hill 520
  • Friday, 9:00–10:00 AM, Hill 520
  • Or by appointment or chance in Hill 520

• Detailed course information and policies (revised January 31): As web page and as a PDF file.
• Hints on writing proofs:
  • From your instructor: As web page and as a PDF file.
  • From Professor James Munkres, the author of the text used in Math 441, Introductory Topology. (The copy here was obtained from Prof. Jim Wiseman at Agnes Scott College; I do not know who wrote the prefatory remarks.)
• Homework assignments: Click here for assignments.

Announcements and additional resources

• 1/19/2016: Here is a scan of the problems which are assigned for Wednesday, January 20.
• 1/25/2016: Here are the notes on the integers as a subset of the real numbers which were discussed in class on January 22
• 1/27/2016: Here is the proof of a theorem (this proof was left incomplete in class on January 26).
• 1/31/2016: There is an error in the information sheet posted on this web page ind distributed in class on the first day of the course. The first exam is scheduled for Friday, February 19 (not February 16). The sheet posted here has been corrected.
• 2/5/2016: Throughout the term there will be some differences between our presentation of real analysis and that of our text, Gaughan's Introduction to Analysis. Here are some notes that provide a record of the most significant of these differences. Updates will be posted as necessary throughout the term.
• 3/2/2016: Here is an up-to-date version of the notes on differences between our treatment and that of Gaughan.
• 4/4/2016: Here are further notes on differences between our treatment and that of Gaughan; these are a continuation of the notes posted on 3/2/2016. Here is a complete version containing all the notes.
• 4/27/2016: Here are yet more notes on differences between our treatment and that of Gaughan; these are a continuation of the notes posted on 4/4/2016. This installment covers our treatments of l'Hospital's rule, of the intermediate value property of derivatives, and of Taylor's Theorem. Here is a complete version containing all the notes.

Final exam: schedule, coverage, review problems, review session, and office hours

• The exam is cumulative. It will cover all the material in the course except for the discussion of Taylor's Theorem given in the last week. This corresponds to Chapters 0--4 of our text by Gaughan, but we omitted Theorems 3.12, 3.19, and 4.14.
• Review: There will be a review/problem session on Wednesday, May 4, from 10:00 AM to 12:00 PM, in Hill Center 423. Here is a set of review problems intended to help you prepare for the exam; they are probably best used in conjunction with the two midterm exams, the assigned homework problems, and the workshop problems. As well as problems like these, the final exam may ask for statements of definitions and/or of results proved in class, and for proofs of the latter.
• Office hours: I will not hold my normal office hours during reading perioid and exams, but will have an office hour Tuesday, May 10, 10:00–11:30 AM, in Hill 520.
• Nathaniel's review session: Nathaniel will be hosting a review session on Wednesday, April 27, from 6:00 PM to 8:00 PM, in Hill 525.

Exam 2

• The second midterm exam will be held on Friday, April 1.
• The exam will cover our work from the first exam through Friday, March 25, which means Chapter 2 and Sections 3.1–3.3. More precisely: although the exam will not ask questions specifically about Chapters 0 and 1, many of the concepts there are relevant to the later material, and questions on the exam may involve such concepts.
• Here are three hints:
  • The exam will have a problem very similar to the first problem on Exam 1, but involving limits of functions rather than limits of sequences.
  • The exam will have a problem which is taken straight from a homework problem (one which was turned in), possibly with minor rewording.
  • There will be a short-answer section, probably True/False.
• The class meeting Wednesday, February 17, will not have a workshop; rather, Nathaniel will answer questions and do problems from this assignment, earlier assignments, past workshops, etc.
• I will hold extra office hours on Thursday, March 31; my office hours that day will be 9:00-10:00 AM, 10:20-11:40 AM, and 3:20-4:20 PM.