Introduction to analysis: Math 218
Instructor: Peter Ozsváth
phone: 609-258-4222
email:
petero@math.princeton.edu
office: 1106
Office Hours: 8:10AM-9:10AM on Tuesdays
Graders:
Alper Gunes
Office: TBA
Office Hours: TBA
Tuomas Tuukkanen
Office: TBA
Office Hours: TBA
Undergraduate course assistants:
Michael Cheng,
Brandon Cho,
Kareem Jaber
Atharva Pathak,
Zeyu Wang,
Owen Yang.
Problem Sessions: TBA
The course:
This course is called An Introduction to Analysis, a continuation of
the rigorous introduction to analysis from Math 216.
We will be mostly following Robert Gunning's book by the same name, Chapters 4-7.
Recommended further reading:
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I. N. Herstein Topics in algebra. Chapter 6, for a more leisurely treatment of abstract linear algebra.
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M. Spivak Calculus on manifolds. Further reading on differential forms.
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J. Milnor Topology from a differentiable point of view,
for a rapid and very elegant introduction to differential topology.
Announcements:
Grading:
The course grade is calculated as follows:
-
Final: 40%
-
Midterm: 30%
-
Homework: 30%
Homework:
There will be weekly homework assignments, due each Thursday, concerning the topics covered in the previous week.
Group I assignments are fairly straightforward; Group II require a bit more thought.
You may discuss the problems with one another, but you should try
them on your own at first. Also, you must write up your own
solutions yourself.
Late homework will not be accepted, except under special
circumstances. In such cases, make arrangments in advance with the
grader.
Assignments:
Homework 1 due Thursday, Feb 8 at 1:30PM.
Section 4.1: Problems 1-8; 13-15.
Homework 2 due Thursday, Feb 15 at 1:30PM.
Section 4.2: Problems 2-7*; 13-15; 17.
*For Problem 3, change the upper left entry in the matrix from 1 to 2
Homework 3 due Thursday, Feb 22 at 1:30PM.
Section 5.1: Problems 1-8.
Homework 4 due Thursday, Feb 29 at 1:30PM.
Section 5.2: Problems 1-2; 4-6; 8-9.
Homework 5 due Thursday, Mar 28 at 1:30PM.
Section 6.1: Problems 3-13.
Midterm Exam:
I will hand out a 3 hour self-timed midterm on Monday, March 4th, due March 8th at 11:59PM.
Final Exam:
There will be a take-home final.