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Text:2- There is an unpublished book by Prof Fitting available in the bookstore or at Fitting Book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. 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.
 
 
 
 

Class and Homework Assignments:
 
 
 

Date	Class Work	Assignment
Jan 29	Introduction	Read the introduction in Fitting Book
Feb 3	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
Feb 5	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
Feb 10	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
Feb 17	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
Feb 19	Completion of Well-ordering	Exercises all in 2.12 and 2.13.1,2.13.2
Feb 24	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
Feb 26	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
Mar 2	10 minute Quiz on secs 3.3,3,4; Signed Numbers Chapter 8;	Read 8.1,8.2,8.3 Exercises 8.2.1,8.2.2
Mar 4	Addition and Multiplication of signed numbers	Read Sections 8.4,8.5 Exercises 8.3.4,8.3.5,8.4.2,8.4.6,8.4.7
Mar 9	10 minute Quiz on secs 8.2,8.3; Fields and Integral domains	Read Section 8.7 Exercises 8.5.2,8.5.3,8.7.1
Mar 11	Chap 4 Naming Numbers Sec 4.1-4.3	Read Chap 4.1-4.5, Ex 4.2.5, 4.3.1, 4.3.3
Mar 16	Quiz cancelled Secs 4.5,4.6	Ex 4.4.1,4.5.1
Mar 18	10 minute Quiz on Chap 8 .3,8.4,8.5,8.7: Sections 4.7,4.8,4.9	Ex 4.7.1, 4.7.3,4.9.1
Mar 23	Review Bring in questions	Sample Exam
Mar 25	Sec 5.1 - 5.3	Study for exam
Mar 30	Midterm Exam	Exercises 5.2.1,5.3.1,5.3.2
Apr 1	Secs 5.3-5.7	Exercises 5.5.1,5.6.1,5.6.2
Apr 15	Continued Fractions and Geometry: The Farey Diagram	Exercises 1,2 in Exercises on Continued Fractions and Geometry
Apr 20	Fans and Umbrellas	Exercises 3,4,5,6
Apr 22	quiz on Farey Diagrams, Euclidean Algorithm, Fans and Umbrellas: Continued Fractions	Exercise 7
Apr 27	Reading continued fractions off the Farey diagram, real numbers as limits of continued fractions	Exercise 8,9
Apr 29	quiz on continued fractions: Infinite continued fractions and real numbers	Exercise 10,11
May 4	Exam on continued fractions and geometry and real numbers	Sample exam
May 6	Class Cancelled	TBA on complex numbers
May 11	Real and Complex numbers Notes on real and complex numbers	TBA
May 13	Complex numbers	TBA
May 18	Optional Exam	Sample exam - server has been down until this morning 5/18
May 25	Optional Final Exam	Sample Final