MATH 144 – Set Theory

Spring 2008

 

 

Professor: Dr. Janet Vassilev
Office: Surge 233 

Office Hours:  MW 10-11 am, F 11-12 pm and by appointment.
Telephone: (951) 827-3020
email: jvassil@ucr.edu

webpage: http://math.ucr.edu/~jvassil

Text :  Set Theory and Related Topics, 2nd Edition, by Seymour Lipschutz.  A word of caution on the text.  It is a study guide and doesn’t have any proper homework problems.  It also doesn’t have any proofs in it.  However, it does have lots of examples to illustrate the theorems and concepts that we will be learning in class.  I will be handing out lecture notes so that you have an additional resource for the proofs.  I will probably not spend much time on examples in class. I will suggest examples in the text as reading homework.

Course Meetings:  The course lectures will be held in Sproul 2340 on Mondays, Wednesdays and Fridays at 8:10-9 am.  Discussion sessions will be held on Thursday (12:10 pm or 6:40 pm) with Tiff Troutman.  You are expected to attend both the lectures and the discussion sessions as per Math Department decree. 

Tips for Success: * Come to class!  It is amazing how much you can learn by being attentive in class.  * Collaborative learning is encouraged but remember only YOU will be taking the quizzes and exams... * Like all mathematics, Set Theory is not a spectator sport; you will learn only by doing!  You will find that a consistent effort will be rewarded. * Be organized.   Have a notebook or binder for Set Theory alone to keep your class notes, homework, quizzes and exams in order.  * No question you have should be left unanswered.  Ask your questions in class, discussion session or take advantage of office hours.

Homework (100 points):  Homework will be assigned weekly and will be collected during the next week’s discussion session.  No late homework will be accepted.  Homework will not be graded unless it is written in order and labeled appropriately.    An answer alone will get 0 points.  Make sure to justify every answer.  Your lowest homework score will be dropped and the remaining homework will be averaged to get a score out of 100.

Quizzes (100 points):  There will be a short quiz given at the beginning of most lectures testing you on the definitions and theory that you learned from last class.  You may use your notes.  Quizzes will only last 5 minutes so make sure that your notes are organized and that you arrive on time for class.  There may also be a quiz at the end of discussion with one problem similar to the homework problems assigned during the previous week.  You may not use your notes for this quiz.  The daily quizzes will be worth 3 points each, the lowest two will be dropped and the remaining will be averaged to obtain a score out of 50 points.   The discussion quizzes will be worth 10 points each, there will be at least 6, and I will keep only the top 5 scores for a total of 50 points. 

Exams (300 points):  I will give one midterm (100 points) and a final (200 points). Please bring your ID to each exam.  There are no make up exams. If a test is missed, notify me as soon as possible on the day of the exam. For the midterms only, if you have a legitimate and documented excuse, your grade will be recalculated without that test.  The Midterm is tentatively scheduled on Friday, May 2.  The Final is on Thursday, June 12, from 7-10 pm.  Use of calculators will not be allowed on exams.

Grades:  General guidelines for letter grades (subject to change; but they won't get any more strict): 90-100% - A; 80-89% - B; 70-79% - C; 60-69% - D; below 60% - F.  In assigning Final Grades for the course, I will compare your grade on all course work (including the Final)  and your grade on the Final Exam.  You will receive the better of the two grades.

Tentative Schedule (for Dr. Vassilev’s Set Theory):

Date

Chapter

Topic

Homework

3/31

 

Sets and Basic Notation

Read 1.1-1.4, Solved Problems 1.1-1.6, 1.41-1.44

4/2

 

Unions and Intersections

Read 1.5 and 1.6 Through Theorem 1.3, Look at Table 1-1 Laws 1-6 and Solved Problems 1.7, 1.45

4/4

 

Complements

Read 1.6 and 1.7 then look at suggested problems 1.7-1.13 and 1.46-1.55

4/7

 

Collections of Sets

Read 1.9 and look at suggested problems 1.27-1.30 and 1.64-1.68

4/9

 

Cartesian Product, Ordered Pairs and Relations

Read 3.1-3.7 and look at suggested problems 3.1-3.15 and 3.41-3.54

4/11

 

Equivalence Relations

Read 3.8-3.9, look at 3.16-3.29, 3.55-3.60

4/14

 

Partial Orderings

Read 3.10, suggested problems 3.30, 3.61 and 3.62 and read 7.2-7.5, 7.7 and 7.10

4/16

 

Functions

Suggested Problems 7.1-7.4, 7.6-7.8, 7.10-7.12, 7.21-7.26, 7.33-7.40

4/18

 

One to one and onto functions

Read 4.2-4.4, Suggested problems 4.1-4.3, 4.8-4.23

4/21

 

Peano Axioms

 

4/23

 

Construction of Natural Numbers

 

4/25

 

Basic Arithmetic

 

4/28

 

Induction

 

4/30

 

Review

 

5/2

 

Midterm

 

5/5

 

Countable Sets

Read 6.2-6.3 Suggested problems 6.4-6.11

5/7

 

Uncountable Sets and Cardinal Numbers

Read 6.4-6.5 Suggested problems 6.1-6.3, 6.12-6.17

5/9

 

Cardinal Numbers form a poset

Read 6.6 Suggested problems 6.18-6.22

5/12

 

Zorn’s Lemma

Read 9.4 Suggested problems 9.5-9.7

5/14

 

Cardinal Arithmetic

 

5/16

 

Well Ordering 

 

5/19

 

Ordinal Numbers 

 

5/21

 

Ordinal Arithmetic

 

5/23

 

Schroeder-Bernstein Theorem

 

5/28

 

Transfinite Induction

 

5/30

 

Axiom of Choice

 

6/2

 

Equivalence of ZL, WO and AC

 

6/4

 

Review

 

6/6

 

Review

 

6/12

 

Final