MAT 319/320 "Foundations of Analysis/Introduction to Analysis" Fall 2005

General Information

Description and goals: Both MAT 319 and 320 provide a closer, more rigorous look at the fundamental concepts of one-variable calculus. The main focus will be on the key notions of convergence and continuity; the basic facts about differentiation and integration will be presented as examples of how these notions are used. The course provides a good opportunity for students to learn how to read and write rigorous proofs. MAT 320 prepares them for further studies in analysis. Both courses are writing intensive; all students will have the opportunity to complete the proof-oriented component of the Department of Mathematics upper division writing requirement.

Relation between MAT 319 and MAT 320: These two courses will be taught together to begin with. The first Midterm will be taken by all students in class on September 29. The lecture in the following week will still be joint, but after that the classes will split. Students will divide into sections depending on their aptitude and choice and the lecturers' recommendations. (Special arrangements have been made with the Registrar to permit this late change of registration.)
Since the syllabus of MAT 319 is less crowded than that of MAT 320 this course will go more slowly. It is intended primarily for students in the Teacher Preparation Program, and will therefore discuss some topics relevant to future teachers. Students in MAT 319 will also be expected to complete a project. However MAT 319 will not provide as good a foundation for the more advanced subsequent courses in the major such as MAT 322, MAT 324, MAT 364 and MAT 401/2. Any student who is contemplating going to graduate school in a mathematics related field is strongly advised to take MAT 320.

Schedule for the first few weeks: Both classes will meet for lectures on Tuesday and Thursday 2:20-3:40 in HH112. The recitations/workshops meet on Monday and Wednesday 2:20-3:15, initially in Physics P112 and P117. . (Come first to P112; we will treat P117 as an overflow room.) There will be workshops on Monday Aug 29 and Wednesday Sept 7, and a recitation on Wednesday Aug 31. For the rest of September, workshops will be on Mondays and recitations on Wednesdays.

Instructor for MAT 319: Professor Dusa McDuff.
Office Hours: Tuesday 1-2:15 in Math Undergraduate Office, Wed 11:50-12:45 in office, and by appointment.
Office: 3-111 Mathematics Department. SUNY at Stony Brook.
e-mail: dusa at

TA: Tanvir Prince
Office Hours: Mon 1:15-2:15 in office, Tuesd 7--9pm in MLC,
e-mail: prince at

Textbook: Introduction to Real Analysis, by R. Bartle and D. Sherbert, Third ed, Wiley.

Grading Policy for MAT 319: Homework 25%. Project 15%. Midterms (two) 15% each. Final Exam 30%.

Exam Schedule: Midterm 1: Thu Sept 29 (in class). Midterm 2: TBA (in class). Final: Tuesday Dec 20, 5:00--7:30pm.

Recitations and Workshops: Students are expected to go to both the Monday and Wednesday class until the first Midterm. The workshops are required: students will be working in groups on a problem set that will be handed in and graded. These workshops are intended for the most part to help students learn and review concepts taught in previous classes. However they will count a little towards the homework part of the grade: they will each be worth approximately 1/3 of a homework. The recitations will be more traditional --- problems similar to the homework problems will be discussed. After the class splits, there will be one recitation per week for each class: the MAT 320 recitation on Monday and the MAT 319 class on Wednesday.

Scheduling conflicts: Any student with a scheduling conflict should make appropriate arrangements with their professor. Please tell us about any conflicts as soon as possible.

Homework This is an essential part of the class and is worth a considerable amount of the grade. The homework sets will be posted on the web in PDF format and will be due at 5pm on the due date. Solutions can be handed in to the TA or to the appropriate professor. (Put it under their office door if they are not there.) Late work will receive reduced credit, and will not be accepted after solutions are posted. You may work on your homework with other people (in fact, this is often a good idea), but the work you hand in must be your own, not copied directly from others. You should also list your working partners on the homework you hand in. The first homework will be due on Thursday Sept 8.

MAT 319 Project Each student in MAT 319 will work on a project (typically with one or two other students). The exact form of this project will depend on how many students are in the class and will be announced later. It will involve a 5 minute oral presentation backed up by a written paper.

Schedule for presentations I have written your names in alphabetical order within the groups; you should decide yourselves what is the best order for your presentations. The order is more or less (but not exactly) what you asked for on Thursday.
Dec 8
1. Garritano, Hughes, Panoussis
2. Guastavino, Miller, Scapellati
3. Pak, Samaroo, Yeung
4. Bennett, Gounaris
5. Xu
Dec 12
1. Estrada, Kosta, Langdon
2. Chen, Tsang
3. Cohen, Melchin, Samuel
4. Cheng, Wu
Dec 13
1. Baker, Willie
2. Agcaian, Falco, Hachmann, VanAcker
3. Hsieh
4. McConnell, Oblein
5. Lauber
6. Eaton, Gosselin, Phelan

Homeworks etc These will be posted below in pdf format.
Worksheet 1
Worksheet 2
Worksheet 3
Worksheet 4
Homework 1
Homework 2
Homework 3 (revised)
Homework 4 (due TUESD 9/27)
Review for Midterm 1
Homework 5 (for MAT 319)
Midterm I
Homework 6
Homework 7
Homework 8
Homework 9
Midterm II
Homework 10


  • The final exam will be on Tuesday Dec 20 in the usual lecture room HH 112, at 5pm -7:30pm. There are 6 questions worth 15-20 points each. See you there!.

  • Here is a review sheet for the final and here is last year's final . I may revise the review sheet over the weekend (I have had to post these in a hurry), but I am not planning to make any serious changes. Just -- watch this space!

  • I will have office hours on MONDAY DEc 19 2:30--3:30 in my office and again on Tuesday Dec 20 1--2 in my office.

  • You may email me with any questions, if you want your grade for the project etc (though that won't be ready until the end of next week.)

  • When you hand in the final version of your project, please also hand in the draft with its comments so I can see how well you addressed them.

  • Tanvir will hand back the drafts on Monday Dec 5 2:20-3:15 in his office, and also on Tuesday Dec 6 in HH112 at 2:20--3:40. NOTE: there is no lecture on this Tuesday: instead Tanvir will be in the usual lecture room ready to answer questions.

  • Tanvir's extra office hours: today (Thursday Dec 1) at 6-7pm and Friday Dec 2 at 12--1 and 6--7; both in his office. Deadline for project draft is 7pm on Friday in Tanvir's office. (DO NOT hand it in to me -- I will be away.)

  • Review session for final exam: Tanvir has booked P 131 (Math) on THURSDAY Dec 15 7-8:30 pm. I will hold some extra office hours on Monday Dec 19, and will also post a review sheet for the exam. (Exam is Tuesday Dec 20.)

  • Here is the quiz.

  • Here is the list of suggested projects. Email me as soon as you can what your choice of project. Deadline for submission of first draft of paper is Dec 2. The final draft is due Dec 13. There are many other details on the project list.

  • Here is the list of theorems and definitions for Midterm 2. Here is a review sheet for the midterm.

  • One of you asked about the syllabus for MAT 319. We will do secs 3.1 - 3.4, 3.6, 4.1-4.2, 5.1-5.3 very carefully in lectures and also 6.1-6.2 if time permits. Many of the other topics in the initial chapters of the textbook will be covered in the projects and presentations. In October we will concentrate on Chapters 3 and 4, with lots of homework and an exam (somewhat like Midterm I) in mid November.

  • The exam will be in class on Thursday Nov 10. We will start work on the projects the week after that.

  • For people with disabilities
    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, room 128, (631) 632-6748. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. Students requiring emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information, go to the following web site:

    Last modified: 12/1/2005