Fall 2007 Math 315
What, When, and Where:
Course Description:
Theory of Analysis
Text:
Rudin, W., Principles of Mathematical Analysis, Third Edition
Lectures:
MWF 8:00-8:50 133 TMCB
Office Hours:
MWF 10:00-10:50 306 TMCB
Grading Scheme:
40% Homework
20% Exam I
20% Exam II
20% Exam III (Final Exam)
Course Schedule: (subject to change)
Sep 05 Introduction
Sep 07 Ordered Sets
Sep 10 Fields I
Sep 12 Fields II
Sep 14 Constructing the Reals I
Sep 17 Constructing the Reals II
Sep 19 Extended Reals, Complex Field
Sep 21 Cardinality I
Sep 24 Cardinality II
Sep 26 Metric Spaces I
Sep 28 Metric Spaces II
Oct 01 Compact Sets I
Oct 03 Compact Sets II
Oct 05 Connected Sets
Oct 08 Convergent Sequences
Oct 10 Subsequences
Oct 12 Cauchy Sequences I
Oct 15 Cauchy Sequences II
Oct 17 Cauchy Sequecnes III
Oct 19 Upper and Lower Sequences
Oct 22 Series I
Oct 24 Series II
Oct 26 Series III
Oct 29 Continuity
Oct 31 Continuity and Topology
Nov 02 Continuity and Compact Sets
Nov 05 Continuity and Connected Sets
Nov 07 Differentiation I
Nov 09 Differentiation II
Nov 12 Differentiation III
Nov 14 Differentiation IV
Nov 16 Integrarion I
Nov 19 Integration II
Nov 26 Integration III
Nov 28 Integration IV
Nov 30 Sequences and Series of Functions I
Dec 03 Sequences and Series of Functions II
Dec 05 Sequences and Series of Functions III
Dec 07 Sequences and Series of Functions IV
Dec 10 Sequences and Series of Functions V
Dec 12 Sequences and Series of Functions VI
Assignments:
Sep 14 Chapter 1: 01-10
Sep 21 Chapter 1: 11-19
Sep 28 Chapter 2: 01-11
Oct 05 Chapter 2: 12-21
Exam I over Chapters 1-2
Oct 29 Chapter 3: 01-10
Nov 09 Chapter 3: 11,12,14,16,17
Nov 16 Chapter 4: 1,2,3,9,14,18,23,24
Exam II over Chapters 3-4
Dec 03 Chapter 5: 1,2,6,14,22,24,25,26
Dec 12 Chapter 6: 1,2,4,10(a-c),11 and Chapter 7: 2,3
Exam III over Chapters 5-7