SUNY at Stony Brook MAT 322: Analysis in Several Dimensions
Spring 2015

General Information

Place and time: TuTh 11:30am-12:50pm in Earth & Space 183.

Professor: Leon Takhtajan, Office: Math Tower 5-111.

Office hours: Mon 3:00-4:00pm and Wed 3:00-4:00pm in 5-111.

Grader: Yuhan Sun, Office: MLC.

Office hours: Mon, 1:00-2:00pm, 4:00-5:00pm and Wed 1:00-2:00pm in MLC.

Course description: This is a mathematically rigorous course with complete proofs. Topics covered will include topology of , derivatives, the inverse function theorem, the Riemann integral, the change of variables theorem for multiple integrals, manifolds and differential forms in , Stokes's theorem and applications.

Prerequisites: The course will heavily rely on MAT 211: Introduction to Linear Algebra or MAT 310: Linear Algebra and MAT 320: Introduction to Analysis.

Textbook: "Analysis on Manifolds" by James R. Munkres, Westview Press, 1997.

Homework: The homework is a compulsory part of the course and will be assigned every week and will be due next Tuesday in class. Doing the homework is fundamental for understanding the course material. To do well in class students are strongly encouraged to read the section to be covered before class, plan to work on reading and homework for 6-8 hours a week and start preparing for tests well in advance.

Exams: Midterm 1: Thursday, March 12, in class; Midterm 2: Thursday, April 23, in class. Final Exam: Wednesday, May 13, 5:30-8:00pm.

Grading policy: The overall numerical grade will be computed by the formula Homework 20% + Midterm Exam 1 20% + Midterm Exam 2 20% + Final Exam 40%. Make sure that you can attend the exams at the scheduled times; make-ups will not be given. Resolve any conficts now. If one midterm exam is missed because of a serious (documented) illness or emergency, the semester grade will be determined based on the balance of the work in the course.

Information for students with disabilities: If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact Disability Support Services at (631) 632-6748 or They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following website:

Academic integrity: 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 integrity website at

Critical incident management: 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' ability to learn.