MATH 3100: Sequences and series

Spring 2013

MWF 1:25-2:15 PM, Boyd Graduate Studies Building, Room 303
Instructor: Paul Pollack

< URL: http://www.math.uga.edu/~pollack/3100s13/ >
This page is an online copy of the syllabus. The web page will occasionally be updated with additional course materials.

Current assignments/other course material

Other course materials:

Course summary

The UGA bulletin describes the content of this course as follows:

Precise definitions of limit and convergence concepts; practical tests for convergence of infinite series; power series representations and numerical error estimates; applications to calculus and explicit summation formulae; trigonometric series.

This isn't wrong (although we might not cover all of these topics), but it fails to capture the spirit of the course. You should view this class as a re-introduction to sequences and series (and to the real numbers). You have surely met these topics in calculus, but the rushed pace of a calculus course makes it doubtful that your introduction got off on the right foot. We will move at a more leisurely pace, with an emphasis on developing a deep understanding of what's `really going on'. It is hoped that by the end of the course, any residual SSAD (Sequences and Series Anxiety Disorder) will have vanished, allowing you to look ε's, δ's , and N0s straight in the eye.

A second raison d'ĂȘtre of this course is that you continue the mathematical apprenticeship which you begun in MATH 3200. This includes the construction of carefully reasoned mathematical proofs. You should not expect this to be easy; indeed, as you mature as a mathematician, you will find yourself confused a good deal of the time! (By the time you get to be a professional mathematician, you are constantly confused.) I will do my best to guide you through the difficulties and to help you come out the other side. Of course, this depends a great deal on your own engagement with the material -- both in class and in office hours.

Textbook

We will use the course notes by UGA's own Professor Malcolm Adams, which are freely available online at <URL: http://www.math.uga.edu/%7Eadams/SANDS13.pdf>. These notes were written with this course in mind, and so we will aim to make it all the way through.

Office hours

Monday, Wednesday, and Thursday: 2:30-3:30 PM

Instructor: Paul Pollack
E-mail: pollack at math dot uga dot edu

Office: 318 Boyd Graduate Studies Building

Office hours:
Monday, 2:30--3:25 PM
Wednesday, 2:30--3:30 PM
Thursday, 2--3:00 PM

Exam dates

There are three in-class midterm exams as well as a final exam.

No make-up exams will be given. The final exam is cumulative.

Attendance/Homework/Exam Policies

Your grade is made up of the following weighted components:

You are expected to participate in class. In particular, attendance in this course is required. More than four unexcused absences may result in you receiving a WF. Keep me posted whenever you have a conflict that requires you to miss class and this should not be an issue.

All exams are in-class, closed book and closed notes.

Homework will be collected in class, about once each week. Late homework will not be accepted. (If you have a need to turn in HW early, that can be arranged.) Your lowest HW score will be dropped at the end of the term.

On homework, collaboration is allowed and in fact is very much encouraged. Mathematics wouldn't be nearly as much fun if we couldn't talk about it with other people! However, However, copying (from a textbook or another student) and web searches are not allowed, and you must write your own final solutions independently. Keep in mind that by entering UGA, you have already agreed to abide by the UGA Honor code described in detail at <URL: http://honesty.uga.edu/ahpd/culture_honesty.htm>.

In practice, what this means that you may discuss homework problems and their solutions with your classmates, but you may not turn in a solution unless you understand it yourself. A reasonable rule of thumb is that you should be able to explain your solutions verbally to me (in all their gory detail) if requested to do so.

The withdrawal policy for this course is that if you withdraw within a week of the date the first midterm is handed back, you automatically qualify for a WP (assuming you are eligible by UGA's standards). After that point, it is at the discretion of the instructor (i.e., me) who will take your performance in the class to-date into account.

Special accommodations

Students with disabilities who may require special accommodations should talk to me as soon as possible. Appropriate documentation concerning disabilities may be required. For further information, please visit the Disabilities Resource Center page at <URL: http://drc.uga.edu/>.

Disclaimer

This course syllabus provides a general plan for the course; deviations may be necessary.


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