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Abdulla Eid

 

Assistant Professor of Mathematics

University of Bahrain, College of Science

Welcome to Set Theory course webpage

The official course syllabus can be downloaded from here.

Course Description

This introductory course is an essential course for students in the science field and in particular to mathematics major. It teaches the students the methodology of writing a rigouros proof. In this course, we will learn how to write a proof in the context of sets which appears almost in every field of advanced mathematics. The course is divided into 6 major parts:

  • Part 1: Propositional logic, equvalence, predicates, quantifiers.
  • Part 2: Method of proofs with emphasis on direct proof, indirect proof (proof by contrapositive and by contradiction), and proof by induction.
  • Part 3: Set theory which includes arbitrary union, intersection, and product of sets. Emphasis on the proof techniques in the context of sets which include pick a point method, Venn diagram, and algebraic method.
  • Part 4: Functions, one to one, onto, composition of functions, inverse, inverse image and image of sets.
  • Part 5: Relations, equivalence relation, equivalence classes, well defined functions, partial order relation.
  • Part 6: Advanced topics: countable and uncountable sets, cardinal numbers, ZF axioms, axiom of choice.

Official topics include (from the catalog):
Elementary logic. Methods of proofs. Concepts of sets. Relations and Functions. Denumerable sets and nondenomerable sets. Cardinal numbers and cardinal arithmetic. The axiom of choice and some of its equivalent forms.

Course Information

  • Course code and title: MATHS253: Set Theory
  • Credit hours: 3 credit hours
  • Pre– requisite: MATHS 121: Calculus I
  • Class time and place:
    • Section 1: Sunday, Tuesday, and Thursday 09:00 AM –09:50 AM in S41-1016.
  • Course webpage: http://www.abdullaeid.net/teaching/Fall2018/MATHS253.html

Instructor Information

  • Instructor Name: Dr. Abdulla Eid
  • Office: S41-2098
  • Phone: (+973) 1743–7590
  • Office Hours:
    • Sunday, Tuesday, and Thursday:  8:00AM – 8:50 AM.
  • Email: aeid (at) uob.edu.bh

Textbook

References

  1. Chartrand, Polimeni, and Zhang, Mathematical Proofs: A Transition to Advanced Mathematics, 2014, 3rd Edition, Pearson, ISBN-–13: 9781292040646.
  2. Smith, Eggen, and Andre, A Transition to Advanced Mathematics, 2014, 8th Edition, Cengage Learning, ISBN–-13: 978--1285463261.
  3. Kenneth Rosen, Discrete Mathematics and Its Applications, 2011, 7th Edition, McGraw-Hill Education, ISBN–-13: 978--0073383095.
  4. Robert J. Bond and William Keane, An Introduction to Abstract Mathematics, 2007, 1st Edition, Waveland Press Inc, ISBN–-13: 978--1577665397.
  5. Donaldson and Pantano, An Introduction to Abstract Mathematics. Online textbook, 2015.
  6. Sundstorm, Mathematical Reasoning: Writing and Proof. Online textbook, 2014.

Class Notes

Homework

A set of homework problems will be distributed regularly during the semester (around 18 sets). Your instructor will tell you exactly which problem set to turn back for grading. However, all these problems are required for the tests, so take them seriously.

Assesment

Your final course grade will be based on two mid-term exams, homeworks, final exam. The grade distribution is as follows:

  • Homework: 25%
  • Midterm Exams (2): 35%
  • Final Exam: 40%

You can check your grades by clicking here.

Exam Scedules

Important Dates

  • Sept 16, 2018: First day of the semester (Instruction begins).
  • Sept 27, 2018: Last day to drop courses without a `W` grade.
  • November 4 -- 8 , 2018: Mid semester break.
  • Dec 6, 2018: Last day to withdraw with a `W` grade.
  • January 3, 2019: Last day of instruction.
  • January 9, 2019: Final exam.

Course Policies

Academic Integrity

Cheating and plagiarism are strictly prohibited and will result in serious consequences. In particular, cheating or plagiarism may result in an ”F” for the course and be reported to the dean of students affairs for further action. Using any outside materials, looking at another student’s exam or using cell phones might be considered as a cheating (whether or not you get benefit from it). For more information, please refer to the university regulations handbook (Article 75) and Anti--Plagirism (policy).

The Classroom Decorum

The classroom environment should be conductive to learning by all. please no chit-chat talks during the class. Cell phones and all electronic devices should be turned off and put away during the class.