Math 320, Section 4: Analysis I

Fall 2019


Dapeng Zhan


C327 Wells

Office Hours:

Dec 10: 11 am-noon, Dec 11-12: 1 – 2 pm, or by email appointment


zhan AT msu DOT edu

A printable copy of the syllabus is here. All course content lives on this website.

Location and Time

MWF 10:20-11:10 in A320 Wells Hall.


This course is a rigorous introduction to analysis on the real line, and covers sequences, limits, continuity, convergence of functions, and derivatives. It will focus on building skills for reading and writing proofs.


Ross, Elementary Analysis: The Theory of Calculus, Second Edition, Springer 2013. This textbook is available for free through MSU libraries.


(MTH 133 or MTH 153H or LB 119) and (MTH 299 or MTH 317H or approval of department).


Homework will be assigned weekly and due at the beginning of Friday’s lecture. There will be thirteen homeworks. (There will not be a homework due the week of Thanksgiving.) No late homework will be accepted. However, your lowest homework score will be dropped when computing your grade.

Typically three homework problems will be graded carefully, and some points will be given for completeness of the rest of the assignment. Full homework solutions will be posted online promptly.

You are encouraged to work in groups on your homework; this is generally beneficial to your understanding and helps you learn how to communicate clearly about mathematics. However, you must write up all solutions yourself. You should cite any other sources other than lecture and the textbook (another book, a blog about analysis, etc) you use.


There will be two short in-class quizzes at the beginning of lecture on Monday, September 16 and Monday, October 28. There will not be any make-up quizzes except in extreme and documented circumstances.


There will be two in-class midterms on Monday, October 7 and Monday, November 18. There will also be a final exam Friday, December 13, 7:45-9:45 am. There will not be any make-up exams except in extreme and documented circumstances. Note that department policy forbids early final exams for any reason.


Grades will be computed as follows:

A reasonable curve will be applied to the composite numerical scores. In past iterations of this class, typically about half of the class has received a grade of 3.5 or above.


We will cover Sections 1-5, 7-12, 14-15, 17-20, 23-25, and 28-30 of Ross. Precise reading for each week will be provided as the course goes on. You will get the most out of lecture if you do the reading before coming to class.

Lecture notes

[Notes of Sep 11-13]

[Notes of Sep 16-18]

[Notes of Sep 20]

[Notes of Oct 21 about uniform continuity]

[Notes of Nov 13 about derivative of inverse function]

[Notes of Nov 27 on complex numbers]

No lecture notes to be posted for the week Sep 23-27 since I almost follow the textbook (since the definitions of limsup and liminf 10.6 till the end of Section 11).


Homework 1 (Due September 6).

Homework 1 Solutions

Homework 2 (Due September 13).

Homework 2 Solutions

Homework 3 (Due September 20)

Homework 3 Solutions

Homework 4 (Due September 27)

Homework 4 Solutions

Homework 5 (Due October 4)

Homewrok 5 Solutions

Homework 6 (Due October 14, Mon)

Homework 6 Solutions

Homework 7 (Due October 18)

Homework 7 Solutions

Homework 8 (Due October 25)

Homework 8 Solutions

Homework 9 (Due November 1)

Homework 9 Solutions

Homework 10 (Due November 8)

Homework 10 Solutions

Homework 11 (Due November 15)

Homework 11 Solutions

Extra Problems

Extra Problems Solutions

Homework 12

Homework 12 Solutions

Homework 13

Homework 13 Solutions

Quizzes and Exams

Quiz1 Solutions

Midterm 1 Sample

Midterm 1 Sample Solutions

Midterm 1 Solutions

Quiz2 Solutions

Midterm 2 Sample

Midterm 2 Sample Solutions

Midterm 2 Solutions

Final Sample

Final Sample Solutions