MATH 201A Fall 2013

Course Information

Lectures: MW 9:00am - 9:50am held in Physics 148.
Lectures: F 9:00am - 9:50am held in Physics 140.
Section: Thur 9:00am - 9:50am held in Physics 140.
The first section (Thursday, September 26) will meet but will be introductory.
Final: Thur Dec 12 6:00pm - 8:00pm held in Physics 148.
Instructor: Babson
Teaching Assistant:Schenthal
`Email: b a b s o
Text: Applied Analysis by John Hunter and Bruno Nachtergaele (available from various sources, eg).
Grading: 40% Homework, 30% Midterm, 30% Final.
Syllabus: Department Syllabus.

Office Hours:
Babson: 10 Monday
Schenthal: 11 Thursday

Midterm solutions

Final problems

Course Outline: The course will cover chapters 1 through 6.

The prerequisites for this course are (from the course catalog): Graduate standing in Mathematics or Applied Mathematics, or consent of instructor

This is a rough outline of when topics will be covered and will be edited as the term progresses. The exam scheduling will not change. Homework problems will also be added with assignments collected on Fridays.

DayDateSection(s) coveredHomework
FridaySeptember 271.1 Metric and Normed Spaces
MondaySeptember 301.2, 1.3 Cauchy and convergent sequences
WednesdayOctober 21.5 topological spaces
FridayOctober 41.4 ContinuityHW1
MondayOctober 71.6 strong/weak topologies
WednesdayOctober 91.6 Completion
FridayOctober 111.6 CompletionHW2
MondayOctober 141.3 RS Borel and Measure
WednesdayOctober 161.3 RS L^1 completeness
FridayOctober 181.7, 1.8 CompactnessProblems 1, 5 and 6 from HW3 and problems 17, 18 and 28 from chapter 1, volume 1 of Reed and Simon (handed out in class)
MondayOctober 212.2 C(K) completeness
WednesdayOctober 234.7 Fol Stone-Wieistrass
FridayOctober 252.4: Arzela-Ascoli Problems 2,3 and 4 from HW3 and Problems 1 and 2 from HW4 and Problem 1.15 from Hunter and Nachtergaele
MondayOctober 283.1,3.2, 3.3: Lipschitz and Contraction
WednesdayOctober 303.4: Integral Ops and Green's functions
FridayNovember 1Review Problems 3, 4, 5, 6 and 7 from HW4 and Problems 1, 2 and 3 from HW5 These problems are on material which will be covered on the midterm, but they will not be collected for another week.
MondayNovember 4Midterm Try:Hunter's Midterm 1,3,4, Hunter's Final 1,2,3,4 and Thomases' Midterm 1,3,4,5
WednesdayNovember 63.5, 2.5: ODE
FridayNovember 84.6 Fol Tychonoff
MondayNovember 11 Veteran's Day: No Class
WednesdayNovember 135.1 Banach
FridayNovember 155.1-5.2 BanachProblem 3.7 from Hunter and Nachtergaele, Problem 60 on page 132 in Folland (Use the diagonal trick to show that the product of countably many sequentially compact spaces is sequentially compact.) and Problems 1, 2 and 3 from HW6
MondayNovember 185 Bases, Equivalence, Fin Dim
WednesdayNovember 205 Ker, Examples
FridayNovember 225 Closed Embedding, Duals
MondayNovember 255 Compact Operators, Norm/Pointwise Top
WednesdayNovember 276 Hilbert Problem 5.3 in Hunter-Nachtergaele and HW7
FridayNovember 29 Thanksgiving: No Class
MondayDecember 26 Projection and Sum
WednesdayDecember 46 ONB
FridayDecember 66 Sep Hilb, QM HW8
ThursdayDecember 12 Final Exam:6:00pm-8:00 PHY 148