Mathematics 6580       Calculus III       Course Description

Fall, 2009 (MWF 11:00 in the Instructional Center, Room 215)

Instructor: Evans Harrell, Office Skiles 218D, 894 3300, harrell at math.gatech.edu
Instructor's office periods: MW, 1:30-2:30 pm, in Skiles 218D. Ordinarily I will also be available for 20 minutes after each class.

Course Description

In the early years of this century, David Hilbert formalized the concept of an infinite-dimensional vector space in order to understand topics in mathematical analysis such as integral equations and Fourier series. Remarkably, Hilbert space turned out later to play a central role in quantum mechanics, signal processing, and many other areas of science and engineering. In this class we develop the theory of Hilbert space, as well as applications in physics and engineering.

In the first part of the course we will use Introduction to Hilbert spaces, by S. Berberian, and web resources such as the on-line text by James Herod. Also helpful may be the first few chapters of the on-line text by Evans Harrell and James Herod. In the latter part of the course we will use parts of Theory of linear operators in Hilbert space, by Akhiezer and Glazman, and materials distributed by the instructor. The textbook by Berberian is a short text of essentially pure mathematics, which we will finish about 2/3 of the way through the course, after which we will discuss the theory of linear operators and applications of Hilbert space. The instructor will tailor the last part of the class to the interests of the enrolled students.

Prerequisites

Students should be familiar with linear algebra and ordinary differential equations, as represented by Math 2403 and one of Math 2406 or Math 4305 at Georgia Tech. Helpful, but not required, background would include a knowledge of advanced undergraduate analysis and of some parts of science or engineering where Hilbert space arises.

Class web page

The class will be coordinated through T-Square, but you can also consult the Class web page directly. It is your responsibility to consult T-Square or the web page regularly for information about the class, such as homework assignments.

Grading and requirements

There will be exams on
  1. Monday, 14 September, and
  2. Wednesday, 14 October,
as well as a final exam, and there may be short pop quizzes on other days. You will be able to review your class standing after each test from the Web page. In addition there will be a project or term paper on an application of Hilbert-space theory, with a half-page proposal due on Monday, 19 October and a final deadline of Monday, 23 November. Homework problems will be posed in the lectures or on the Web, and will be collected on Mondays, or Wednesdays when Monday is a holiday.

Missed tests, special accommodation, etc

There will be never be an opportunity to retake a missed exam after the event. Any special accommodations must be requested by electronic mail two weeks in advance of any scheduled event. It is the student's responsibility to take the initiative for all such accommodations.

Tests may vary as to what materials are permitted, and whether part of the test can be prepared at home. In all cases work on the test is to be done by the student without collaboration and without consultation of materials other than those explicitly permitted. The term paper or project must be entirely the student's own writing. To the extent that it is a review of others' research, uses software developed by others, etc., proper citation and scholarly standards will be expected.

Learning Disabilities

It is the right of any student with a certified learning disability to request necessary accommodation. Such requests must be made well in advance of the time that the accommodation is required and a letter of documentation from the ADAPTS office must be presented at the time of any request.

Academic Integrity

Students are expected to abide by the Georgia Tech Academic Honor Code. You are encouraged to discuss the homework and solutions with classmates, but you must later write up the work independently, without consultation or copying. No collaboration is permitted on quizzes or exams. 

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