Math 3100 - Sequences and Series - Spring 2017

An Introduction to Analysis

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

9:30-10:45 (Boyd 322/323)

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

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.
Quizzes: There will be periodic short quizzes 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 (of course) a final exam.
 ** dates to be determined **

Exam 1: February 16th  Exam 1    Exam 1 Review    Old Exam 1
Exam 2: March 30th
 Exam 2    Exam 2 Review    Old Exam 2
         Exam 3: April 20th                         Practice Exam 3
Final Exam:
Tuesday 2nd of May 8:00-11:00

Grading: Homework/Quizzes: 15/5%                   
Tests: 45% (15% each)
Final: 35%

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 A student who incurs an excessive number of absences may be withdrawn from a class at the discretion of the professor (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 two or more unexcused absences. A student withdrawing after the first exam.

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


Induction, Inequalities and the
Binomial Theorem

Sequences, Boundedness and Monotonicity
Convergence (and Subsequences)

Consequences of Convergence
Quiz 1
Limit Laws and Squeeze Theorem

Proof of Limit Laws
Quiz 2
Special Limits and Ratio Test (for sequences)

"Order Limit Laws" and Infinite Limits
Monotone Convergence Theorem and the Bolzano-Weierstras
s Theorem
Suprema, Infima, and the Axiom of Completeness
Archimedean Property and Density of Rationals in the Reals


Cauchy Sequences and the Cauchy Criterion
Limit Superior and Limit Inferior
Quiz 3

Exam 1
Sequential Characterization
Quiz 4
Intermediate and Extreme Value Theorems

Spring Break
Functional Limits and Differentiation Mean Value Theorem and Consequences
Review of Infinite Series
Proof of the Convergence Tests

Review Exam 2

Power Series and "differentiation term-by-term"
Taylor Series and Examples
Uniform Convergence and Continuity
More on Uniform Convergence
Quiz 5

Review Exam 3


Homework Assignments
  date due 
Recommended Questions
Questions to be handed in
Thursday January 19
(by 5:00pm)
Ross: Sections 7 and 8
Adams: Sections 1.2-1.4
All questions from both texts

Section 7:     4
Section 8:     1(b)(d), 2(b)(d), 4, 6, 8, 9, 10
Section 1.2:  12
Section 1.3:  20

Thursday January 19
(by 5:00pm)
Ross: Section 9
Adams: Sections 1.4-1.5
All questions from Ross' text
(except those involving infinite limits)
All questions from Adams' text

Section 9:     1(c), 2, 4, 6, 12(a), 15, 18(a)-(c)
Section 1.4:  22

3 & 4
Tuesday February 7
(by 5:00pm)
Ross: Sections 4, 5, 9, 10
Adams: Sections 1.6
All questions from Ross' text
All questions from Adams' text

Section 4:     [1, 2, 3, 4 only right column], 5, 6, 9, 12, 16
Section 5:    
1, 2, 3, 4, 6                  
Section 9:     10, 16
Section 10:   4 (only for Theorem 10.2), 5, 7, 10

Tuesday February 14
(by 5:00pm)
Ross: Sections 4, 5, 7-12
Adams: Sections 1.2-1.6
All questions from Ross' text
All questions from Adams' text
    Homework 5

Thursday March 2
(by 5:00pm)
Ross: Sections 17-18
Adams: Section 1.7
All questions from Ross' text
All questions from Adams' text

Section 17:     9(d), 10(a), 12, 13, 14
Section 18:    
2, 4, 5, 6, 7, 9, 10                    

Tuesday March 21
(by 5:00pm)
Ross: Sections 20, 28-29
All questions from Sections 28 and 29

Section 20:     11(b), 18
Section 28:    
3, 4, 6, 7, 8, 14     
Section 29:     3(a), 4, 5, 7(b), 8, 11           

Friday March 24
(by 5:00pm)
Ross: Sections 14-15
Adams: Sections 2.1-2.3
All questions from Ross' text
All questions from Adams' text
    Homework 8

Tuesday April 11
(by 5:00pm)
Ross: Sections 23, 31
Adams: Sections 3.2.4, 3.3
All questions from Ross' text
All questions from Adams' text
    Homework 9

Tuesday April 18
(by 5:00pm)
Ross: Sections 24-25
Adams: Sections 3.1-3.2
All questions from Ross' text
All questions from Adams' text

Section 24:     2, 3, 4, 5, 6, 9, 14, 15, 16
Section 25:     2, 6, 7, 8, 9, 10