Analysis, one of the pillars (along with algebra and topology) of modern mathematics, begins with a rigorous development of single-variable calculus. Thus, this course serves the important purpose of teaching you how to rigorously prove and apply results in calculus, including results related to the notions of limit, continuity, derivative, integral, and infinite series. Inherent in all of these notions is the concept of approximation. As we shall see, a good grasp of this latter concept is essential not only in proving ''pure'' results in analysis, but is also crucial in ''applied'' problems requiring estimations. In any approximation a key question is ``how do you estimate the error''? In the first part of this course, we will look at some types of algebraic manipulations that can be used in error estimation; we will also look at more powerful methods involving the mean value theorem for derivatives.
Students planning to go on to graduate school in mathematics are advised to take MAT 322 and MAT 324 as well. Students wanting to take MAT 322 or MAT 324 (or the seminars MAT 401 or MAT 402) will need to take MAT 320, not MAT 319. Students who want to take these courses after MAT 319 instead will need to do some extra work, and get permission from the relevant instructor.
The second test will be given in class on Friday, April 9..
The final examination will be held on Wednesday, May 12, from 11:15 a.m. - 1:45 p.m. Students are expected to ensure when they register for the courses that they will be available for the final examination, and that they do not have too many final exams on that date.
The final course grades will be determined as follows:
homework 10%, two midterms 25% each, final exam 40%.
On each midterm and exam, you will receive two grades: a point total,
and a ``perfection score'', which is the number of problems which you
have done "essentially" completely correctly. The "perfection score"
will be an important consideration in deciding which students receive A,
A-, B+ or B. If a student is going to get a lower grade than B, the
perfection score will not be utilized.
The purpose of the perfection score is to motivate students to try to do the proofs
without error, so that we have a solid foundation to build upon as we
continue through the course.
The grades of A^{-} and A will be reserved for students who demonstrate a
substantial ability to apply the concepts of the course in new and
somewhat creative ways.
Please note that there will be no curve in this course in determining grades.
Incompletes will be granted only if documented circumstances beyond your control prevent you from completing the course work.
Homework is a means to an end, the ``end'' being for you to
learn the material. We encourage you to work on homework together
with friends. In this course, we will never prosecute anyone for
academic dishonesty on any issue relating to homework.
If you hand in complete, correct solutions, you will get full
credit for them, no matter how you obtained them.
When you hand in homework in this course, you are not claiming that
it is your own work.
If someone
regularly ``does''
the homework by copying from friends or from solution manuals, they are
only cheating themselves, since this is not a way to learn the material.
Moreover, they will not receive the benefits of the feedback that our
meticulous grading will provide.
Never be shy to ask us how to do a homework problem, even if you
handed in a copied solution that you do not understand. You will not be
prosecuted or condemned for this, and we will be only too glad to help
you.
If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room128, (631) 632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential. Arrangements should be made early in the semester (before the first exam) so that your needs can be accommodated.
Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary
Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' procedures.