Course: Honors Advanced Analysis, Math 425, Section A
Time: MWF 12:00--12:50pm
Location: 443 Atlgeld Hall
Instructor: Prof. Leininger
Phone: 265-6763
Email: clein (at) math.uiuc.edu
Office: 265 Altgeld Hall
Office hours (my office): TBA
Text: J. R. Munkres, Analysis on Manifolds
About the course: This course gives a rigorous (proof based) treatment of calculus of several variables and the natural generalization to calculus on manifolds. It culminates in the differential form version of Stokes Theorem, with the classical Stokes, Green's and Divergence Theorems as special cases.
Grades: Grades for Math 425 will be based on homework [20%] one midterm [40%] and a final [40%].
I will curve an exam score if absolutely necessary (e.g. the problems were legitimately too difficult or the exam was too long). The final grades will be assigned on the usual scale: 90--100 A, 80--90 B, 70--80 C, 60--70 D, below 60 Failing.
Homework: This will be assigned and collected periodically. I'll only be grading (some of) the problems, though you should turn them all in. I expect assignments handed in to be written neatly (or typed). Poorly written homework will be returned, ungraded.
Collaboration is allowed... In fact, I encourage it! However, I also expect that you attempt (with real effort) each problem on your own before discussing it in a group. Moreover, each individual must turn in their own assignment.
Midterm The midterm will be any two hour period between 5 and 8pm on March 17 in 145 Altgeld Hall. Here is a copy.
Missed exams/homework: A missed exam will count as ZERO, except under the most extreme circumstances. In an extreme situation, the exam score will be replaced with the remaining exam score (e.g. if the midterm is missed for a legitimate reason, then that score will be replaced by the final exam score).
Attendance: I will not take attendance, but I'll know who is coming to class and who is not. This will be relevant in making grade decisions for borderline cases.

Final Exam: Take home exam below.
Assignments:
Problem set 1: § 1: 1, 2; § 3: 6, 9; § 5: 2, 5; § 6: 5, 10. (due Wednesday, January 28).
Problem set 2: § 7: 1, 3, 4; § 8: 1, 3, 4, 5. (due Wednesday, February 4).
Problem set 3: § 9: 5, 6; § 10: 1, 2, 6; § 11: 1, 4 (for problem 1, you need only find an example). (due Wednesday, February 11).
Problem set 4: § 11: 8, 9, 10. § 12: 3, 4. § 13: 1, 4, 5. (due Wednesday, February 18).
Problem set 5: § 14: 1, 2, 3, 7. § 15: 1, 2, 7. (due Wednesday, February25).
Problem set 6: § 16: 2. § 17: 2, 6, 7; § 18: 1, 4. (due Wednesday, March 4).
Problem set 7; § 19: 1, 2, 5, 6. (due Wednesday, March 11)
Problem set 8; § 21: 1, 3. § 22: 2, 3. (due Wednesday, April 1)
Problem set 9; § 23: 1, 2, 4. § 24: 1, 4, 5, 6. (due Wednesday, April 8)
Problem set 10; § 25: 3, 4. § 26: 1, 3, 4, 8. (due Wednesday, April 15).
Problem set 11; § 27: 2--4. § 28: 2, 3, 5. (due Friday, April 24)
Problem set 12; § 29: 3. § 30: 1, 2, 4, 6. § 32: 3. (due Wednesday, April 29).
Problem set 13; § 34: 1, 8. § 35: 1, 3. § 37: 2, 3, 6 (not to turn in).
Take-home final exam: Here. I will be available for questions 5/8 and 5/18 in my office, and over email anytime. See exam for instructions.

Notes from class, 04/17 Typo on second to last page; it should be (\phi_I)^\sigma = \phi_{\sigma^{-1}(I)}
IMPORTANT INFO: LAS and engineering students in this class are permitted to drop from this course without academic penalty and without petition through the end of the 13th week of the semester. Thus, Friday, April 17, 2009 is the drop deadline for this course.
LAS students who wish to drop the course should see the receptionist in the LAS office and ask to be direted to a COAR user, who will process the late drop without a grade of "W". Engineering students should be directed to the Engineering College Office, 206 Engineering Hall, for assistance with the late drop. Students in other colleges may need to petition their college office for this policy to be applied, but the math department would support it.






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