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Text:2- There is an unpublished book by Prof Fitting available in the bookstore or at Fitting Book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 firstname.lastname@example.org Office hours: Tues, Thurs 2:30-4:00 and by appointment
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:
|Jan 29||Introduction|| Read the introduction in
|Feb 3||Counting Numbers -- Axioms|| Read Fitting sec 2.1-1.4
|Feb 5||Addition, and Multiplication sec 2.6, 2.7|| Read sections 2.8,2.9
|Feb 10|| Multiplication and Exponents sec 2.8,2.9
||Read sections 2.10,2.11
||Read sec 2.12, 2.13
|Feb 19||Completion of Well-ordering||
|| Read Sections 3.1,3.2,3.3;
|Feb 26||More on whole numbers and signed numbers|| Read Sections 3.4,3.5,3.8, 3.7;
|Mar 4||Addition and Multiplication of signed numbers|| Read Sections 8.4,8.5
|Mar 9||Read Section 8.7
|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|
||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||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 27||Reading continued fractions off the Farey diagram, real numbers as limits of continued fractions||Exercise 8,9|
Infinite continued fractions 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|
||Sample exam - server has been down until this morning 5/18|