Math 104 - Introduction to Analysis

InstructorPaul Vojta
LecturesMWF 2–3, Cory 247
Class Number40152
Office883 Evans
Office HoursMondays 12:30–1:30, Wednesdays 1–2, Fridays 1–2,
excluding spring break and university holidays.
Please email me to set up a time to meet if you cannot make any of these times.
GSI Office HoursThe GSI for Math 104 (all sections) is Ben Wormleighton. He will also hold office hours this semester for Math 104 students. His office hours will be:
Monday1–3 Evans 869
4–6Evans 891
Thursday9–12 Evans 891
Friday9–12 Evans 891
PrerequisitesMath 53 and 54
Required Text Jiří Lebl, Basic Analysis: Introduction to Real Analysis. See below for availability.
Catalog DescriptionThe real number system. Sequences, limits, and continuous functions in R and Rn. The concept of a metric space. Uniform convergence, interchange of limit operations. Infinite series. Mean value theorem and applications. The Riemann integral.
Syllabus TBD
GradingGrading will be based on:
30%Homework Assigned weeklyDue in class, usually on Wednesdays
15%First midterm February 282:00–3:00 pm
20%Second midterm April 42:00–3:00 pm
35%Final examTuesday, May 8 11:30 am–2:30 pm
HomeworkAssigned weekly, generally due on Wednesdays. Assignments are given below. Solutions will be posted on bCourses.
CommentsI tend to follow the book rather closely, but try to give interesting exercises and examples.
This course is a bit harder than some of the other basic upper-division math courses, such as Math 110 or perhaps 113. I recommend against taking this course if you haven't had some other upper-division math course or Math 55.
Note the final exam date given above (exam group 6). Do not enroll in this course if you cannot take the exam at that date and time, whether because of a conflict, too many exams on that day, or any other reason. The schedule of final exams is available at

The Textbook

The textbook is Basic Analysis: Introduction to Real Analysis, by Jiří Lebl, and is available for free on the web. For this class we will use the edition of February 29, 2016 (version 4.0). You can get it either:

Note that a list of errata for the book is available.

Homework Assignments

General rules on homework assignments are:

Homework assignments are due in class on the days indicated below.

January 24 pdf dvi
January 31 pdf dvi
February 7 pdf dvi
February 14 pdf dvi
February 21 pdf dvi
March 2 pdf dvi

Course Handouts

January 17 Equivalence of three variations on induction pdf dvi
February 2 Infinite limits pdf dvi

Exams (Generally)

Policies for exams are as follows.

The two midterms will be given during the normal class hours (2–3 pm), and will be in our normal classroom (Cory 247).

Generally, about a week before each exam, a sample exam will be distributed in class and posted on bCourses. This will usually be an exam from an earlier Math 104 class that I've taught. Sample exams should be used to get a general idea of the likely length of an exam and the general nature of questions to be asked (e.g., the balance between computational and more theoretical questions). However, one should not (for example) note that a sample exam contains questions on material from Sections 1.5, 2.1, 2.7, 3.1, 3.4, etc., and expect to see questions from those sections on the actual exam.

Exams are cumulative, so the second midterm may have questions from material prior to the first midterm. Of course, the final exam will cover the whole course, but will have increased emphasis on the material not covered on the midterms.

Here is a link "How to lose marks on math exams" (by a former GSI Andrew Critch).

The Math Department maintains an archive of old exams (usually without answers). Here is the link for Math 104.

And finally, a word about regrades: Grade calculation errors are welcome for discussion or review. Whether this solution should be worth 4 or 5 points is not.

First Midterm

The first midterm will be given on Wednesday, February 28, from 2:10 to 3:00, in our usual classroom. It will cover everything in the textbook up to and including Example 2.5.4 (page 77), plus added topics from the lecture (notably, infinite limits, infinite lim sups, etc.), minus Section 1.5 (decimal representations of real numbers). You will also be responsible for material in lectures and handouts up to and including February 16, and homework assignments up to and including Homework #5.

A sample midterm was distributed in class on February 21, and is available on bCourses. Solutions to the sample midterm will be posted on bCourses on or about Monday, February 26.

Last updated 22 February 2018