Math 3100 - Sequences and Series - Fall 2018

An Introduction to Analysis

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

10:10-11:00 (Boyd 323)

 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 Monday August 20th)
  2. Homework 2 (due on Wednesday August 29th)
  3. Homework 3 (due on Wednesday September 5th)
  4. Homework 4 (due on Monday September 17th)
  1. Homework 5 (due on Monday October 1st)
  2. Homework 6 (due on Friday October 5th)
  3. Homework 7 (due on Friday October 12th)
  1. Homework 8 (due on Friday November 2nd)
  2. Homework 9 (due on Friday November 9th)
  1. Homework 10 (due on Monday December 3rd)
Quizzes: There will be a short quiz two or three times during the semester, these will be announced ahead of time in class.
No make up quizzes will be given.
Exams: There will be three in-class "midterm" exams and a final exam.
 ** dates are provisional and subject to change **

Exam 1:   Friday the 21st of September
 Exam 1 
 Exam 1 Study Guide    Sample Old Exams:  Version 1    Version 2    Version 3 
Exam 2:   Wednesday the 17th of October
Exam 2
 Exam 2 Study Guide    Sample Old Exams:  Version 1    Version 2
         Exam 3:   Wednesday the 14th of November (Provisionally) Exam 3
 Exam 3 Study Guide    Sample Old Exams:  Version 1    Version 2          
Final Exam:
  Friday the 7th of December from 8:00-11:00

Grading: Homework/Quizzes: 15%                   
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  
Absolute Value, Inequalities and Induction Binomial Theorem
Boundedness and Monotonicity of Sequences
Convergence of Sequences   
More on Convergence
Consequences of Convergence Limits Laws and "Baby Squeeze" Proof of Limit Laws
 Labor Day
Special Limits    Subsequences

 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
Continuity Examples and the Sequential Characterization Proof of Sequential Characterizations and More Applications
Review Exam 2    Integral Test, Alternating Harmonic Series, and Rearrangements
Intermediate Value and Extreme Value Theorems 
Functional Limits and Differentiation Fall Break
  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 
Examples Some proofs

Review Exam 3 Uniform Convergence
Thanksgiving Break

More on Uniform Convergence  Examples More Examples

Review (class held on Tuesday)