Course Outline - Mat 604 - Spring 2003

Course meetings, Tues -Thurs 4:30-5:45 pm  Room Gillet 305

Text:1- Modern Mathematics by Wheeler and Wheeler   11th Edition. This is a good reference book but I will not follow it section by section.
Text:2- 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Text:3- There is an unpublished book by Prof Fitting available at Fitting Book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. 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.

Dates for the exams will be announced on this page well in advance.
 
 
 
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Class and Homework Assignments:
 
 
 
Date  Class Work Assignment
Sep 2  Introduction  Read the introduction in
  • Fitting Book
    		•
    Sep 4  Counting Numbers  Read Fitting sec 2.5 to discuss next time
  • Do Exercises Fitting 2.3.2,2.3.3,2.4.2,2.4.2,2,6.2,2.6.3
    		•
    Sep 9  Addition, Multiplication and Exponents  10 minute Quiz on Thursday on exercises from 9/4 and 9/9
  • Do Exercises Fitting 2.7.1,2.7.2,2.8.3,2.8.4,2.8.5,2.9.1,2.9.2
    		•
    Sep 16  Multiplication, Exponents and order  
  • Do Exercises Fitting 2.8.3,2.8.4,2.8.5,2.9.1,2.9.2,2.10.4,2.10.5,2.10.6
    • Sep 18  Multiplication, Exponents and Order   10 minute Quiz on Thursday on exercises from 9/9 and 9/16
  • Do Exercises Fitting 2.11.1,2.11.3,2.11.4,2.12.1,2.12.4,2.12.6
    		•
    Sep 23  Order  
  • Do Exercises Fitting 2.12.1,2.12.4,2.12.6
    		•
    Sep 25  Well Ordering   10 minute Quiz on Thursday on exercises from 9/18 and 9/23
  • Do Exercises Fitting 2.13.1,2.13.2,2.13.3
    		•
    Sep 30  The Whole Numbers: Zero and Order and Basic Properties  
  • Do Exercises Fitting 3.3.1,3.3.2,3.3.3
    		•
    Oct 2   No Quiz this week. Topic: Zero and Order and Basic Properties  
  • Do Exercises Fitting 3.4.1,3.4.2,3.4.3,3.5.2,3.5.4,3.5.6,3.5.8
    		•
    Oct 7  No Class - Monday classes will be held
  • No Assignment
    • Oct 9   Quiz on Section 3.1-3.5. Topic: Subtraction   Will whoever took the quizzes last week please bring them in today. Thanks
  • Do Exercises Fitting 3.6.1,3.6.2,3.6.3
    		•
    Oct 14   Topic: Archimedian order, division  
  • Do Exercises Fitting 3.71-7, 3.8.1,3.10.2
    		•
    Oct 16   Quiz on Section 3.7 Topic: Finish Chap 3 and review  
  • Study for Midterm
    		•
    Oct 21   Midterm Exam, cumulative.
  • sample exam
    • Oct 23   Topic: Naming Numbers  
  • Fitting Chap 4 - 4.1-4.5 Ex 4.5.1/3, 4.5.2
    • Oct 28   Topic: Addition and Subtraction  
  • Exercises 4.6.2, 4.6.4/3 4.6.7/3,4.6.9
    		•
    Oct 30   Topic: Multiplication  
  • Quiz on place names; 4.9.1.1,4.9.7, optional 4.9.8/1.4.9.9
    		•
    Nov 4   Topic: Fractions and rationals  
  • Ex 5.3.1, 5.4.1,5.4.2, 5.2.3,5.2.4
    • Nov 6   Topic: Properties of Rational numbers No Quiz  
  • 5.6.1,5.8.2,5.10.4
    • Nov 11   CLASS CANCELLED  
    • Nov 13   Quiz on sec 5.1-5.10 Topic: Order for rational numbers  
  • 5.13.3,5.13.4
    • Nov 18   Euclidean Algorithms and Farey Numbers : handout  
  • Use the Eucl. Algo. to find d=gcd(302,129); find s,t so that 302s+129t=d; do the same for d=gcd(453,198), find s,t
    • Nov 20   Farey numbers and continued fractions  
  • Find the continued fractions for 37/11, 5/24 and 13/21
    • Nov 25   More continued fractions  
  • Use the Farey diagram to find the cont'd frac for 45/7,21/34,4/29
    • Dec 2   Real numbers as limits of decimals or cont'd fracs  
  • sample exam
    • Dec 4   Optional Exam  
    • Dec 6   Complex numbers and Review  
  • sample exam
    • Dec 11   FINAL EXAM