Syllabus for MAT 319 and MAT 320 - Fall 2002

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

  Analysis, one of the pillars of modern mathematics, begins with a rigorous development of single-variable calculus. Thus, these courses serve 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 will be more comprehensive and will provide a firm grounding for further study. MAT 319 will have 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.

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

• Lecturers:
  Daryl Geller, 4-100B Math Building, phone 632-8327.
  E-mail daryl@math.sunysb.edu - Internet http://www.math.sunysb.edu/~daryl
  Office hours: TuTh 12:45-2:15, 3:45-4, and 5:15-6, in P-143 Math.
  
  Detlef Gromoll, 5-117 Math Building, phone 632-9290.
  E-mail detlef@math.sunysb.edu - Internet http://www.math.sunysb.edu/~detlef
  
  Check for announcements or postings on the web regularly!

• Teaching Assistants:
  Vincent Graziano, 2-116 Math Building. E-mail graziano@math.sunysb.edu
  
  Wonkuk Kim, 3-118 Math Building. E-mail wkim@math.sunysb.edu

• Teaching Assistant Office Hours: To be announced.
• Text: D. Geller, A Bridge to Analysis, available only at Kinko's Copies on campus. There will be additional handouts.
• Grading System: The first test, on the first three chapters of the book (up to page 117) will be given in class on Thursday, October 10. It will be graded by Monday, October 14, at which time the classes will split. You will be allowed to switch your registration (from MAT 319 to MAT 320, or vice versa) at that time. Your results on the test will help you to make an informed decision.

  After October 14, Professor Geller will lecture in MAT 319 and Professor Gromoll will lecture in MAT 320.

  The second test will be given in class on Tuesday, November 19.

  The final examination will be held on Tuesday, Dec. 17, from 2 - 4:30 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 15%, two midterms 25% each, final exam 35%.
  In MAT 320, there will be up to 10% extra credit for independent study type projects.

  The grades of A^- and A will be reserved for students who demonstrate a substantial ability to apply the concepts of these courses in new and somewhat creative ways.

  Please note that, on midterms and exams, ``proofs'' that contain errors will receive only a limited amount of partial credit, if any at all. Also please note that there will be no curve in these courses 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 class. If you do so, please indicate on your homework who you worked with. At times, your friends may understand a solution better than you do; when this happens, do not hesitate to ask us for help.

  If someone regularly ``does'' the homework by copying from friends, 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 staff's meticulous grading will provide.

• Approximate Course Schedule:
  Chapter 1: Sep. 3 - Sep. 13
  Chapter 2: Sep. 17 - Oct. 1
  Chapter 3: Oct. 2 - Oct. 7
  Sections 4.1 and 4.2: Oct. 8
  First Test (on Chapters 1-3): Oct. 10
  
  After the split, MAT 320 continues:
  Rest of Chapter 4: Oct. 14 - Oct. 25
  Chapter 5: Oct. 28 - Nov. 12
  Second Test (on Chapters 4-5): Nov. 19
  Chapter 6: Nov. 14 - Dec. 13
  
  After the split, MAT 319 continues:
  Sections 4.2.1, 4.3, 4.3.1: Oct. 14 - Oct. 18
  Chapter 5 (omit pages 216 -224): Oct. 21 - Nov. 12
  Second Test (on Chapters 4-5): Nov. 19
  Chapter 6 (omit section 6.5): Nov. 14 - Dec. 13.

• Special Needs: If you have a physical, psychological, medical or learning disability that may impact on your ability to carry out assigned course work, I would urge that you contact the staff in the Disabled Student Services office (DSS), Room 133 Humanities, 632-6748/TDD. DSS will review your concerns and determine, with you, what accommodations are necessary and appropriate. All information and documentation of disability is confidential.