Boyd GSRC 602A
lyall (followed by @uga.edu)
(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:
|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.
|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 Study Guide
Sample Old Exams: Version
1 Version 2
||Monday 30th of April 8:00-11:00|
||Tests: 45% (15% each)
|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.|
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 A student who incurs an excessive number of absences may be withdrawn from a class at the discretion of the professor (http://bulletin.uga.edu/bulletin/ind/attendance.html)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 four or more unexcused absences.
|Week Commencing on Monday
of root 2, and
some properties of the reals
Absolute Value, Inequalities and Induction
| "Snow Day"
||Boundedness and Monotonicity of Sequences|
||More on Convergence
||Consequences of Convergence|
||Limits Laws and "Baby Squeeze"|| Proof of Limit
||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
|02/19||Introduction to Infinite
Test and Examples
||More Convergence Tests