Instructor: Office: Email: 
Neil Lyall Boyd GSRC 602A lyall (followed by @uga.edu) 
Time/Location: Office Hours: 
TR TR W 
9:3010:45 (Boyd 322/323) 8:309:30 10:0011:00 
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: 
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 inclass
"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 8:0011:00 
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 A student who incurs an excessive number of absences may be withdrawn from a class at the discretion of the professor (http://bulletin.uga.edu/bulletin/ind/attendance.html) In this class, we interpret "excessive" to mean two or more unexcused absences. A student withdrawing after the first exam. 
Week Commencing on Monday 
Tuesday 
Thursday 

01/02  Induction,
Inequalities and the Binomial Theorem 

01/09  Sequences, Boundedness and
Monotonicity 
Convergence (and Subsequences)  
01/16 
Consequences of
Convergence Quiz 1 
Limit Laws and Squeeze Theorem  
01/23 
Proof of
Limit Laws Quiz 2 
Special Limits and Ratio
Test (for sequences) 

01/30 
"Order Limit Laws"
and Infinite Limits Monotone Convergence Theorem and the BolzanoWeierstrass Theorem 
Suprema,
Infima, and the Axiom of Completeness Archimedean Property and Density of Rationals in the Reals 

02/06 
Cauchy Sequences and the
Cauchy Criterion 
Limit Superior and
Limit Inferior Quiz 3 

02/13 
Review 
Exam 1  
02/20  Continuity 
Sequential Characterization Quiz 4 

02/27  Intermediate and Extreme
Value Theorems 
Examples 

03/06 
Spring Break 

03/13  Functional Limits and Differentiation  Mean Value Theorem and Consequences 

03/20 
Review of Infinite Series 
Proof of the
Convergence Tests 

03/27 
Review  Exam 2  
04/03 
Power Series and
"differentiation termbyterm" 
Taylor Series and Examples 

04/10  Uniform Convergence and Continuity 
More on Uniform Convergence
Quiz 5


04/17 
Review  Exam 3  
04/24 
Review  
Homework Assignments 

Assignment 
date due 
Section 
Recommended Questions 
Questions to be handed in  
1 
Thursday
January 19 (by 5:00pm) 
Ross:
Sections 7 and 8 Adams: Sections 1.21.4 
All
questions from both texts 


2 
Thursday January 19 (by 5:00pm)

Ross: Section 9
Adams: Sections 1.41.5

All
questions from Ross' text (except those involving infinite limits) All questions from Adams' text 


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 


5 
Tuesday February 14 (by 5:00pm)

Ross: Sections 4, 5, 712
Adams: Sections 1.21.6 
All questions from Ross' text
All questions from Adams' text

Homework
5 

6 
Thursday March 2
(by 5:00pm)

Ross: Sections 1718 Adams: Section 1.7 
All questions from Ross' text
All questions from Adams' text



7 
Tuesday March 21
(by 5:00pm)

Ross: Sections 20, 2829 
All
questions from Sections 28 and 29 


8 
Friday March 24 (by 5:00pm) 
Ross: Sections 1415 Adams: Sections 2.12.3 
All questions from Ross' text
All questions from Adams' text

Homework
8 

9 
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 

10 
Tuesday April 18
(by 5:00pm)

Ross: Sections 2425 Adams: Sections 3.13.2 
All
questions from Ross' text All questions from Adams' text 
