Course information
Instructor: Prof. John Hunter
Lectures: MWF 2:10–3:00 p.m., Wellman 230
Discussion sections:
A01. Tue 5:10–6:00 a.m., Storer 1342
A02. Tue 6:10–7:00 p.m., Storer 1342
Office hours: MW 3:15–4:30 p.m.
CRN: 59250 (A01); 59251 (A02)
Office: MSB 3202
Office hours: R 2:00–4:00 p.m.
University of California
Davis, CA 95616, USA
email: jkhunter@ucdavis.edu
Office Phone: (530) 6014444x4016
Office: Mathematical Sciences Building 3230
Smart Site: The Smartsite for the class is here
Announcement: Final
Course grades have been submitted. Final solutions are here.The Final exam will be in class:
 Final: Thursday, Dec 10, 1:00–3:00 p.m., Wellman 230.
It will cover all the material from this quarter, except that double series will not be on the final.
Some sample final questions are here.
Solutions to the sample final questions are here.
Important Dates
 Instruction begins: Friday, September 25
 Last day to add: Friday, October 9
 Last day to drop: Wednesday, October 21
 Last class: Friday, December 4
 Academic holidays: Wednesday, November 11; Thursday–Friday, November 26–27
Exams
There will be two Midterms and a Final
 Midterm 1: Wednesday, Oct 21 (in class)
 Midterm 2: Wednesday, Nov 18 (in class)
 Final: Thursday, Dec 10, 1:00–3:00 p.m. (Exam Code R)
Midterm 1
Solutions to the midterm are here.
Midterm 1 is in class on Wednesday, October 21st. It will be closed book. An outline of the topics is as follows:
 Proofs, including proof by induction
 Functions and sets
 Algebraic and order properties of the real numbers
 Definition of the supremum and infimum and their properties
 Completeness axiom of the real numbers
 Sequences, convergence, and limits
 Properties of limits
 Convergence of monotone sequences
 Definition of the limsup and liminf of a bounded sequence
 Relations between the limsup, liminf, and the limit of a sequence
These topics are covered in Sections 1.1–1.4, 2.1–2.4 of the text and Sections 2.1–2.7, 3.1–3.6 of the course lecture notes.
Some sample midterm questions are here. Solutions to the sample midterm questions are here.
Midterm 2
Solutions to Midterm 2 are here.
Midterm 2 is in class on Wednesday, November 18. It will cover sequences (starting with the material since Midterm 1) and series. Topology will not be on the exam. An outline of the topics is as follows:
 Cauchy sequences
 Subsequences
 The BolzanoWeierstrass theorem
 Convergence of series
 Geometric, telescoping, and pseries
 Cauchy condition for series
 Absolutely and conditionally convergent series
 The comparison test
 The alternating series test
 Rearrangements of series
 Double series as iterated sums
These topics are covered in Sections 2.5–2.8 of the text and in the course lecture notes (with more material than we covered in the lectures).
Some sample midterm questions are here. Solutions to the sample midterm questions are here.
Grade
Grade will based on exams and homework, weighted as follows:
 15%: Homework
 25%: Each Midterm
 35%: Final
Text
Understanding Analysis, Stephen Abbott, Second Edition, 2015.
This class will cover the first three chapters of the text:
 Chapter 1: The Real Numbers
 Chapter 2: Sequences and Series
 Chapter 3: Topology of the Real Numbers
The department syllabus and list of topics for the class is here.
Lecture Notes
In addition to the text, I will use my own lecture notes available online here:
An Introduction to Real Analysis
Background material is in:
The class will cover Chapters 2–5 of the notes:
Homework
Homework will be assigned weekly and a hard copy will be due in class on Friday. Please write clearly, or type, and staple your solutions.
In addition, please put your name and section number on your homework.
The standard tool for writing mathematical papers is LaTeX, or one of its many variants. If you want to learn how to use it, see here to get started. (This suggestion is only if you're interested  you're not required to use latex for your homework.)
Problem numbers refer to the exercises in the text (2nd edition).

Set 1 (Fri, Oct 2)
Sec 1.2, p. 11: 1.2.1, 1.2.3, 1.2.4, 1.2.5, 1.2.6, 1.2.8, 1.2.9, 1.2.10, 1.2.11, 1.2.12Set 2 (Fri, Oct 9)
Sec 1.3, p. 18: 1.3.1, 1.3.2, 1.3.3, 1.3.4, 1.3.5, 1.3.8, 1.3.9, 1.3.11
Sec 1.4, p. 24: 1.4.2, 1.4.4Set 3 (Fri, Oct 16)
Sec 2.2, p. 47: 2.2.2, 2.2.4,
Sec 2.3, p. 54: 2.3.1, 2.3.3, 2.3.6, 2.3.10
Sec 2.4, p. 59: 2.4.1, 2.4.2, 2.4.3, 2.4.7Set 4 (Fri, Oct 30)
Sec 2.5, p. 65: 2.5.1, 2.5.2, 2.5.4, 2.5.5, 2.5.8, 2.5.9
Sec 2.6, p. 70: 2.6.2, 2.6.4, 2.6.7Set 5 (Fri, Nov 6)
Sec 2.4, p. 59: 2.4.8, 2.4.9
Sec 2.7, p. 76: 2.7.2, 2.7.4, 2.7.7, 2.7.8, 2.7.9, 2.7.12, 2.7.13Set 6 (Fri, Nov 13)
Sec 2.7, p. 76: 2.7.1
Sec 2.8, p. 80: 2.8.1, 2.8.2, 2.8.3, 2.8.4, 2.8.5, 2.8.6, 2.8.7Set 7 (Fri, Dec 4)
Sec 3.2, p. 93: 3.2.2, 3.2.3, 3.2.4, 3.2.6, 3.2.8, 3.2.14, 3.2.15
Sec 3.3, p. 99: 3.3.1, 3.3.2, 3.3.5, 3.3.6, 3.3.8, 3.3.11