mat226sp02
Course Outline - Mat 604 - Fall 2005

Course meetings, Tues -Thurs 4:30-5:45 pm  Room Gillet 205


Text:1-Foundations of Analysis by Edmund Landau   English Edition 1966    This is available from the AMS on-line bookstore AMS for $17, Order Code: CHEL/79.H
Text:2- There is an unpublished book by Prof Fitting available in the bookstore or at Fitting Book

 Instructor:  Prof. Keen.  Office Gillet 137e  Phone 960 8867  email keenl@comet.lehman.cuny.edu   Office hours:  Tues, Thurs 2:30-4:00 and by appointment

Outline
In this course we will learn about number systems and learn how to prove theorems about them. We will cover:
1- The counting numbers
2- The whole numbers
3- Place Value notation and bases for number systems
4- The rational numbers
5- The real numbers
6- The complex numbers

There will be homework assigned on this page for each session.  There will be a 10 minute quiz each week on 1 or 2 of the
homework problems,  selected at random.   I will discuss selected homework problems during class time and will ask students to present solutions on the board.

There will be two class exams, one in the sixth week and one in the twelfth week.  There will be an optional* exam in the
last week and an optional final. The final grade will be based on the quizzes, two class exams and the final.

*I do NOT give make up exams for any reason.  Anyone who misses an exam must take the optional exam.
Those who wish to raise their grade may take the third exam and I will drop the lowest exam grade.

Tentative dates for the exams can be found below. Changes will be announced on this page well in advance.

Below is a tentative schedule of classes and assignments. Changes may be made, so check this page regularly.  
 
 
 


Class and Homework Assignments:
 
 
 


Date  Class Work Assignment
Aug 30  Introduction  Read the introduction in
  • Fitting Book
    		•
    Sept 1  Counting Numbers -- Axioms   Read Fitting sec 2.1-1.4
  • Do Exercises Fitting 2.3.2,2.3.3,2.4.1,2.4.2
    		•
    Sept 6  Addition, and Multiplication sec 2.6, 2.7  Read sections 2.8,2.9 
  • Do Exercises Fitting 2.6.2,2.6.3, 2.7.1,2.7.2
    • Sept 8   Multiplication and Exponents sec 2.8,2.9
    		 Read sections 2.10,2.11
  • Do exercises 2.8.3,2.8.4,2.8.5,2.9.1,2.9.2
    		•
    Sept 13  
  • 10 minute Quiz on exercises from 2.3,2.4
    • Order and well-ordering     		Read sec 2.12, 2.13
  • Exercises 2.11.1,2.11.2,2.11.3,2.11.4

    • Sept 15   Completion of Well-ordering
  • Exercises all in 2.12 and 2.13.1,2.13.2
    		•
    Sept 20  
  • 10 minute Quiz on secs 2.8,2.11;Chapter 3 The Number Zero. Subtraction
    		• Read Sections 3.1,3.2,3.3;
  • Exercises 3.3.1,3.3.3,3.4.2,3.4.4,3.5.4,3.5.9
    		•
    Sept 22   More on whole numbers and signed numbers Read Sections 3.4,3.5,3.8, 3.7;
  • Exercises 3.7.1,3.7.2,3.7.3,3.7.6,3.7.7,3.8.1
    		•
    Sept 27   Signed Numbers Chapter 8; Read 8.1,8.2,8.3
  • Exercises 8.2.1,8.2.2
    • Sept 29   Addition and Multiplication of signed numbers
  • 10 minute Quiz on secs 3.3,3,4;
    		•
    		Read Sections 8.4,8.5
  • Exercises 8.3.4,8.3.5,8.4.2,8.4.6,8.4.7
    		•
    Oct 6   Multiplication of signed numbers
    		Read Section 8.7
  • Exercises 8.5.2,8.5.3,8.7.1
    		•
    Oct 18    Rings and Fields
    		Section 8.7 Ex 8.7.1, 8.7.2, 8.7.3
    Oct 20   10 minute Quiz on secs 8.2,8.3
     Order Relation for rings
    		Sec 8.8
    Oct 25      Finish chap 8, begin chap 5
    		Ex 8.8.1, 8.9.1, 8.9.2, 8.9.3
    Oct 25   Chapter 5 Read sections 5.1-5.3
    Oct 27   Sec 5.1 - 5.3 Exercises 5.2.1,5.3.1,5.3.2
    Nov 1   Secs 5.3-5.7 Exercises 5.5.1,5.6.1,5.6.2
    Nov 3   Quiz Rational numbers, Review Bring in questions Sample Exam
    Nov 8  
  • Midterm Exam

    • Nov 10   The Euclidean Algorithm
    Nov 15   Farey diagrams and Continued Fractions Exercises 1,2 in Exercises on Continued Fractions and Geometry
    Nov 17
  • Fans and Umbrellas:

    • Continued Fractions     		Exercises 3,4,5,6
    Nov 22  
  • Quiz on Farey diagram and continued fractions.
    • Reading continued fractions off the Farey diagram, real numbers as limits of continued fractions     		Exercises 7, 8,9
    Nov 29  
  • Quiz on Farey diagram and continued fractions.
    • Reading continued fractions off the Farey diagram, real numbers as limits of continued fractions     		Infinite continued fractions and real numbers Exercise 10,11
    Dec 1   Real numbers Real numbers from the Farey diagram
    Dec 6
  • Exam on continued fractions and geometry and real numbers
    		• Sample exam
    Dec 8   Real and Complex numbers Notes on real and complex numbers
    Dec 13   Review Sample optional exam
    Dec 15  
  • Optional Exam
    • Dec 20  
  • Optional Final Exam
    		• Sample Final