V63.0325-003: Analysis I

Term:	Spring 2011
Meeting times:	2:00 - 3:15 p.m. MW in WWH 102 Recitation (V63.0325-004): 9:30 - 10:45 a.m. R in Room TBD
Instructor:	Prof. Assaf Naor
Office:	1113 WWH
Office hours:	TBA
Phone:	212-998-3382
Email:	naor@cims.nyu.edu

Prerequisites

Prerequisite: V63.0123 Calculus III and V63.0140 Linear Algebra or the equivalent.

Goals and Topics

The main purpose of this class is to study rigorously functions of one real variable, starting from the construction of real numbers
Topics to be covered: The real number system. Convergence of sequences and series. Rigorous study of functions of one real variable: continuity, connectedness, compactness, metric spaces, power series, uniform convergence and continuity.

Course Details

Textbook and Materials

An Introduction to Analysis by William R. Wade, 4th Edition, Pearson Prentice Hall.

Homework

Homework will be assigned weekly, and collected during recitations (and
handed back also during recitations, the week after). For fairness reasons, late homework
will not be accepted, but the lowest homework grade will be dropped to compute the nal
grade.

Exams

Midterm Exam: The midterm exam will be during a regular class period; the exact date is to be determined.

Final Exam: The final exam is currently scheduled on May 16th, 2:00 p.m. - 3:50 p.m.
[NOTE: The room will be determined later [MAY NOT BE IN THE USUAL ROOM]. Note that we will not be able to accommodate early finals for non-academic, non-emergency reasons: please plan your travel schedule accordingly.

Grading policy

Homework, Midterm Exam and Final Exam will all count. A more precise grading policy is to be determined.

Tentative Calendar

Week	Topic
1, 2, 3	the set of real numbers: construction properties
4, 5, 6	convergence of sequences, compactness
7, 8, 9	functions of one real variable: continuity, differentiation, Riemann integration (the simplest notion of integration
10, 11, 12	series: convergence, properties
13, 14, 15	convergence of functions: pointwise and uniform convergence