**Advanced Calculus - MA 3831 - Term A 2009**

**Lecturer:**- Irina Mitrea, 305D Stratton Hall, imitrea@wpi.edu, Phone: 831-5321.

**Teaching Assistant:**- Liang Haodong, 204 Stratton Hall, hdliang@wpi.edu, Phone: 831-5546

**General description:***Advanced Calculus is a two-part course giving a rigorous presentation of the important concepts of classical real analysis. Topics covered in the two-course sequence include: basic set theory, elementary topology of Euclidean spaces, limits and continuity, differentiation Reimann-Stieltjes integration, infinite series, sequences of functions, and topics in multivariate calculus.*

**Recommended Background:**MA 2051 and MA 2071

**Textbook:**- Walter Rudin,
**Principles of Mathematical Analysis**, third edition.

**Course web page:**- http://users.wpi.edu/~imitrea/MA3831page.html

**Examinations:**- Preliminary Examination 1: Monday, September 14th, from 3:00 pm to 3:50pm.
- Preliminary Examination 2: Monday, September 28th, from 3:00 pm to 3:50pm.
- Final Examination: Thursday, October 15th, from 3:00pm to 3:50pm.
*Notes, textbooks and calculators are not allowed during prelims and the final examination. All examinations take place in Stratton Hall 106.*

**Lectures:**

**Office Hours:**

**Grading:**Preliminary examinations count 20% each, the final 35%, and the remaining 25% is apportioned among homework, quizzes and class participation. 1% bonus points up to a maximum of 5% is awarded for each participation in the extracurricular mathematical activities (1) Math Club and (2) WPI Undergraduate Mathematics Lecture Series. Up to 5% bonus points are awarded for the completion of mini-projects in analysis (these will be posted on this website soon and are due at the end of the term, you may work in teams of three).

Grades of A,B,C are guaranteed by final averages of 90%, 75% and 60%, respectively. A grade of NR will be assigned to overall performances in the course which below the 60% treshold.

**Homework:**Homework will be assigned weekly. It will be collected on Mondays during lecture and returned to you on Thursdays during lecture. Do all problems assigned, though only some will be graded. Please be sure that (1) your work is legible; (2) the problems are listed in the order they were assigned; (3) the solution of each problem is written on a separate page/pages. The assignments will be posted on this website.

**Homework 1 (due September 8)****Homework 2 (due September 14)****Homework 3 (due September 28)****Homework 4 (due October 12)****No late homework will be accepted.**You may work cooperatively on assignments provided that:- You write up the solution yourself.
- You put a note on your homework indicating the names of anyone you worked with.

**Quizzes:***There will be a short quiz every Tuesday,unless otherwise announced. It will be returned to you on Thursday.*

**Incomplete**:*An incomplete will be given only in those rare circumstances where a student has completed all but a small portion of the course with a grade C or better and a severe, unexpected event prevents him/her from completing the course. In particular, if you get behind in the course you cannot ``bail out" by taking an incomplete.*

**Attendance and absences**:*You are responsible for the material covered in class, whether you attend or not. You are also responsible for the announcements made during class; these may include changes in the syllabus.*

**Academic honesty***is fundamental to the activities and principles of a University. Any effort to gain an advantage not given to all students is dishonest whether or not the effort is successful. Each student is expected to familiarize him/herself with WPI's Academic Honesty policies which can be found at http://www.wpi.edu/Pubs/Policies/Honesty**All acts of fabrication, plagiarism, cheating, and facilitation will be prosecuted according to the university's policy. If you are ever unsure as to whether your intended actions are considered academically honest or not, please see the course instructor. When in doubt about plagiarism or collaboration, consult the course instructor.*

**If you need accommodations because of a disability:***Students with disabilities who believe that they may need accommodations in this class are encouraged to contact the Disability Services Office (DSO) as soon as possible to ensure that such accommodations are implemented in a timely fashion. The DSO is located in Daniels Hall, (508) 831-5235.**If you are eligible for course adaptations or accommodations because of a disability (whether or not you choose to use these accomodations), or if you have medical information that I should know about please make an appointment with me immediately.*

**Words of advice:***I encourage you to ask questions about the HW.***Keep up with the latest materials covered**; experience shows that, otherwise, you are likely to get poor grades on the exams. If you miss a class, make sure you get the notes from someone else who attended it. The professor will not assist any absentee to find out what happened in his/her absence. Hard work and regular attendance will get you through this course.