MA  425,    Fall 2008

MWHF 10:15-11:05,    HA

1.    Instructor:  Demetrio Labate
Instructor Office:  HA 332
Office Hours:    MW or by appointment
Phone Number:  513-7443
E-mail address:  dlabate@math.ncsu.edu
Homepage:  http://www.math.ncsu.edu/~dlabate
2. Goals and Objectives:
  The study of real analysis is fundamental for a prospective student in mathematics, as well as for those students in applied sciences who wish to go beyond the basic manipulation of calculus formulas. Students of real analysis will develop their ability to think deductively, analyze mathematical statements, and apply mathematical ideas to the solution of new problems. The material covered during the course is centered on the theory underpinning one-dimensional calculus, and includes the concepts of real number system, function, limit, continuity, differential and integral calculus.
Notice that the emphasis of this course is on MATHEMATICAL PROOFS. During this course, students will learn to analyze proofs of theorems and to write (simple) proofs of mathematical statements related to the topics covered during the lectures.
3. Textbook:
Introduction to Real Analysis, Third Edition, by Robert G. Bartle and Donald R. Sherbert.
 
Lecture Notes:

Chapter 1 ,   Chapter 2 (part1),   Chapter 2 (part2),   Chapter 3 (part1),   Chapter 3 (part2),   Chapter 3 (part3),   Chapter 4 ,  

Chapter 5 (part1) ,   Chapter 5 (part2) ,   Chapter 6 ,   Chapter 7 (part1) ,   Chapter 7 (part2) ,   Chapter 8 ,  

4. Homework and Examinations:
I encourage you to work the homework assignements regularly and carefully. You will only learn to write proofs (and hence truly understand the mathematical concepts involved) by doing it on your own, and not by watching someone else doing it for you. There will be weekly homework assignments or quizzes counting 30% towards the final grade. These assignements will require for you to write simple proofs based on the material of the lectures. You are encouraged to discuss the homework with other students or with me (preferably in my office). However, be aware that you should be able to work on your own to master the material and be able to solve the test problems in class.

Homework problems

There will be two tests in class counting 40% towards the final grade (on Fri September 28 and on Mon November 19 ).
The final exam counts 30% towards the final grade (Wed Dec 12, 8:00-11:00).
Makeup tests will be allowed for justified and unavoidable absences. In all other cases, you will get a zero score for a missed test.
Old Tests with solutions:

Test 1 ,   Test 2 .

Current tests with solutions:

Test 1 ,   Test 2 .


 
    Grading:
The grade will be determined according to a set point scale: 90%-100%: A, 80%-89%: B, 70%-79%: C, 60-69% D; F is less than 60% (+ and - will also be used).
 
5. Topics and estimated days allocated to each topics:
 
 
 Chapter  Sections Lectures   Topics
1  1.1-1.3 & Appendix A
 2 Preliminaries and prerequisites
2  2.1-2.5 6 Real Numbers
3 3.1-3.5 (3.7 optional)
 8 Sequences
4 4.1-4.3 3 Limits
5 5.1-5.4, 5.6 7
 Continuous Functions 
6 6.1-6.2 (6.4 optional)
 5
 Differentiation
7 7.1-7.3 6 The Riemann Integral
8 8.1-8.2 2 Sequences of Functions
9
 9.1-9.4
 If time permits
 Series

 

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Students with disabilities: Written requests issued by the Office of Disability Services will be honored.