Math 3100 - Sequences and Series - Spring 2018

An Introduction to Analysis

Neil Lyall
Boyd GSRC 602A
lyall (followed by
  (Provisional) Office Hours:

9:05-9:55 (Boyd 323)
8:20-9:00 & 10:00-10:30

 Lecture notes based on the material covered in class will be produced as we proceed through the semester:

Lecture Notes

Additional References:    1. Sequences and Series, by Malcolm Adams
             pdf (last updated 11/14/16)
  2. Elementary Analysis, by Kenneth A. Ross (Second Edition)
             Free Online Version
  3. Understanding Analysis, by Stephen Abbott (Second Edition)
             Free Online Version

About this course: You will find this course to be very different from the more computationally based courses at the 2000 level (like Calculus). This course is meant to help the transition to the more abstract, theoretical courses at the 4000 level and above. Not only will you be expected to learn this material at the computational level, but you will also be studying the proofs of the theorems and learning to write in a rigorous mathematical style. Because you will be looking at mathematics at a much deeper level than you may have in the past, this course will be very challenging. You must never settle for just ending the right answer to a question, you must make sure that you really understand why that answer is correct, and then, you must strive to communicate that understanding in a clear and concise way.

Homework will be collected once a week.
  1. Homework 1 (due on Friday January 19th)
  2. Homework 2 (due on Friday January 26th)
  3. Homework 3 (due on Friday February 2nd)
  4. Homework 4 (due on Friday February 9th)
  1. Homework 5 (due on Monday February 26th)
  2. Homework 6 (due on Friday March 2nd)
  3. Homework 7 (due on Friday March 9th)
  1. Homework 8 (due on Friday April 6th)
  2. Homework 9 (due on Friday April 13th)

Quizzes: There will be a short quiz throughout the semester, these will be announced ahead of time in class.
No make up quizzes will be given. You will be able to drop your lowest quiz score.
Exams: There will be three in-class "midterm" exams and a final exam.
 ** dates to be determined **

Exam 1:   Friday 16th of February
  Exam 1  
 Exam 1 Study Guide    Sample Old Exams:  Version 1    Version 2    Version 3 
Exam 2:   Friday 23rd of March  Exam 2 
 Exam 2 Study Guide    Sample Old Exams:  Version 1    Version 2 
         Exam 3:   Friday 20th of April
  Exam 3 
 Exam 3 Study Guide    Sample Old Exams:  Version 1    Version 2           
Final Exam:
  Monday 30th of April 8:00-11:00
             Additional Final Exam Practice Questions

Grading: Homework/Quizzes: 10/5%                   
Tests: 45% (15% each)
Final: 40%

For full credit, full work must always be shown. Any absence on a test day will result in a test grade of 0. It will be possible to make up for a missed test only if documented justification for the absence is provided.

Attendence policy: The official attendance policy of the university states: 
Students are expected to attend classes regularly. A student who incurs an excessive number of absences may be withdrawn from a class at the discretion of the professor (

In this class, we interpret "excessive" to mean four or more unexcused absences.

Academic Honesty: As a University of Georgia student, you have agreed to abide by the University’s academic honesty policy, “A Culture of Honesty,” and the Student Honor Code. All academic work must meet the standards described in “A Culture of Honesty” found at: Lack of knowledge of the academic honesty policy is not a reasonable explanation for a violation. Questions related to course assignments and the academic honesty policy should be directed to the instructor.

The course syllabus is a general plan for the course; deviations announced to the class by the instructor may be necessary

Tentative Course Schedule (This will be continuously revised/modified as needed!)

Week Commencing on Monday

Wednesday Friday

Irrationality of root 2, and
  some properties of the reals 

"Snow Day"
 Absolute Value, Inequalities and Induction 
Binomial Theorem
"Snow Day"
    Boundedness and Monotonicity of Sequences   
 Convergence of Sequences 
More on Convergence
Consequences of Convergence

 Limits Laws and "Baby Squeeze"   Proof of Limit Laws
Ratio Test for Sequences

  Subsequences and Least Upper Bounds  
 Monotone Convergence and Bolzano-Weierstrass Theorems  
Cauchy Sequences

Limit Inferior and Limit Superior Review
Exam 1
Introduction to Infinite Series
Comparison Test and Examples
More Convergence Tests
Absolute and Conditional Convergence
Ratio Test and Examples
Root Test and Power Series
Sequential Characterization and Applications
Sequential Characterization and Examples
Spring Break
Review Exam 2

Integral Test, Alternating Harmonic Series, and Rearrangements
Intermediate Value and Extreme Value Theorems
Functional Limits and Differentiation

More Differentiation and Examples
Interior Extrema Theorem and
(Generalized) Mean Value Theorem
Differentiating Power Series and Taylor Series
Lagrange's Remainder Estimate for Taylor series and Examples

Some proofs
Review Exam 3

Review Review