### Department of Mathematics Stony Brook University

Announcements for the week of 8/30-9/3:
Homework (due in recitation on Monday 9/13): #8 .9 ,10, 11, 15, 17, 23.
Announcements for the week of 9/6-9/10:
Homework (due in recitation on Wednesday 9/15): #25, 26, 27, 30.
Announcements for the week of 9/13-9/17:
Homework (due in recitation on Wednesday 9/22): Chapter 1, #34, 35, Chapter 2, #1, 2, 5, 6
Announcements for the week of 9/20-9/24:
Homework (due in recitation on Wednesday 9/29): Chapter 2, #8, 10, 12, 15, 16, 17, 27
Announcements for the week of 9/27-10/1:
Homework (due in recitation on Wednesday 10/6): Chapter 2, #35, 36, 37
TEST on Thursday 10/7, covering up to the end of page 98.
The test will focus nn Chapter 2, (Chapter 1 being a "warmup" chapter). I handed out solutions covering to the end of page 86 in class on Thursday. You should know how to do all the problems, even those that were not assigned.
Announcements for the week of 10/4-10/8:
MAT 320 Homework (due in recitation on Wednesday 10/13): Chapter 2, #38, 39.
Pick up your test in class on Tuesday and decide if you would like to continue with MAT 320 or MAT 319.
Announcements for the week of 10/11-10/15:
Homework (due in recitation on Wednesday 10/20): Chapter 3, # 2, 8; Chapter 4, #2, 4, 6, 7, 8, 9
Announcements for the week of 10/18-10/22:
Homework (due in recitation on Wednesday 10/27): Chapter 4, #11, 13, 14, 16, 17, 18 (you can use the Mean Value Theorem and its consequences).
Announcements for the week of 10/25-10/29:
Homework (due in recitation on Wednesday 11/3): Chapter 4, #22, 23, 24, 25, 27
Announcements for the week of 11/1-11/5`:
Homework (due in recitation on Wednesday 11/10): Chapter 4, #29; Chapter 5, #1, 3, 7, 8, 9.
Announcements for the week of 11/8-11/12`:
Second midterm: in class, Tuesday, November 16.
Covers chapter 4, but math is cumulative, so there may be questions related to earlier sections.
Jan Gutt will have extra office hours on Friday, Nov. 12, in the MLC, from 10 a.m. - 2 p.m. and possibly later if needed.
Announcements for the week of 11/15-11/19`:
Homework (due in CLASS on Tuesday, Nov. 23): Chapter 5, #12, 15, 16, 18.
Announcements for the week of 11/22-11/26`:
Homework (due in recitation on Wednesday 12/1): Chapter 5, #20, 21, 22, 24, 29; Chapter 6, #1, 3.
Announcements for the week of 11/29-12/3`:
Homework (due in recitation on Wednesday 12/8): Chapter 6, #5, 6, 7, 8, 10(a)(b)(c), 12, 13.

# Syllabus for MAT 319 and MAT 320- Fall 2010

• Course Description: These are introductory courses in analysis, required for math majors. The courses will meet together for the first five weeks, then will split.

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.

• Difference between the courses: MAT 320 is more comprehensive and provides a firm grounding for further study. MAT 319 has more of an emphasis on topics which arise in high-school calculus.

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.

• Prerequisites: C or higher in MAT 200 or permission of instructor; plus one of the following: C or higher in MAT 203, 205, 211, AMS 261, or A- or higher in MAT 127, 132, 142 or AMS 161. Anyone lacking these prerequisites risks deregistration.

• Instructors:
Daryl Geller, 4-100B Math Building, phone 632-8327.
E-mail daryl@math.sunysb.edu - Website http://www.math.sunysb.edu/~daryl
Office hours: Tuesdays and Thursdays from 12:50-2:20.

Check for announcements or postings on the website regularly!

Michael Movshev, 4-109 Math Building, phone 632-8271.
E-mail mmovshev@math.sunysb.edu - Website http://www.math.sunysb.edu/~mmovshev
Office hours: to be announced.

• Teaching Assistants:
Jan Gutt
E-mail jgutt@math.sunysb.edu

Xiaojie Wang, 2-106 Math
E-mail wang@math.sunysb.edu
Office hours: Mondays and Wednesdays, 2-3 p.m. in the Math Learning Center, and Mondays 1-2 p.m. in 2-106 Math.

• Text for the first five weeks and for MAT 320: D. Geller, A Bridge to Analysis, available through lulu.com. You can click on this link to order the book: A Bridge to Analysis
Please select Ground shipping, as Mail may take too long.
lulu.com is a self-publishing website that makes books available very cheaply. Solutions will be distributed as the semester progresses. There are solutions for almost every problem in the book.

• Text for MAT 319, after the first five weeks: R.G. Bartle and D.R. Sherbert, Introduction to Real Analysis, 3rd edition, available in the university bookstore. You can buy it after the split.

Grading System: The first midterm, on the first three chapters of the book (up to page 117) will be given in class on Thursday, October 7. It will be graded by Monday, October 11, at which time the classes will split. You will be allowed to switch your registration from MAT 319 to MAT 320 at that time. Your results on the test will help you to make an informed decision.

There will also be a second midterm. In MAT 320, it will be held on Tuesday, November 16.

The final examination will be held on Thursday, December 16, 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%.

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: The only way to learn the material is to work problems for yourself. Each week, you should attempt to do all of the problems from the sections which are covered in class. We will ask you to hand some problems in. Your homework will be graded meticulously and will give you vital feedback on where you are making mistakes.

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.

• Approximate Course Schedule:
Chapter 1: Aug 31 -- Sep. 14>
Chapter 2: Sep. 16 -- Sep. 28
Chapter 3: Sep. 30 - Oct. 5
First Test (on Chapters 1-2): Oct. 7`

After the split, MAT 320 continues:
Chapter 4: Oct. 12 - Oct. 28
Chapter 5: Nov. 2 - Nov. 11
Second Test (on Chapter 4): Nov. 16
Chapter 6: Nov. 18 - Dec. 9

• After the split, MAT 319 continues:
To be announced.

• ## Americans with Disabilities Act:

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.