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PhiladelphiaUniversity

Faculty of Science

Department of Basic Sciences and Mathematics

Firstsemester 2017/2018

Course Syllabus
Course code:250442 / Course Title:Abstract Algebra 2
Course prerequisite (s) : 250342
Corequisite (s):------ / Course Level:4
Credit hours:3 / Lecture Time:11:00-12:00S-T-T.
Academic Staff Specifics
E-mail Address / Office Hours / Office Number
and Location / Rank / Name
/ 10:00-11:00
(Sun-Tue-Thu)
11:30-12:30
(Mon-Wed) / 1019 / Ass.Prof. / Khaled Alhazaymeh

Prerequisite:

Abstract Algebra 1 (250342)

Course module description:

This module is the second half of the undergraduate Abstract Algebra series, covering topics in rings and fields: integral domains, polynomial rings, field extensions, finite fields, and a brief coverage of Galois theory, time permitting.

Course/module components:

Books (title , author (s), publisher, year of publication)

  • Joseph A. Gallian, Contemporary Abstract Algebra, Ninth Edition 2016, Brooks/Cole.
  • I. N. Herstein, Topics in Algebra, Second Edition 1975, Wiley.
  • John B. Fraleigh, A First Course In Abstarct Algebra, 7th Edition 2003, Greg Tobin.

Lecture Notes

  • Amin Witno, From Groups to Galois. Students are required to download a softcopy of these notes for free from the University website. We will cover Chapters 14 to 26; students who wish to review lessons from group theory are suggested to read the first 13 chapters.

Teaching methods:

Duration: 16 weeks, 48 hours in total

Lectures: 34 hours, 2 per week + two exams (two hours)

Assignments: Homework from every chapter

Learning outcomes:

Knowledge and understanding

Students will have knowledge and understanding of:

  • Definition and examples of rings, integral domains and fields.
  • Subrings, subfields, ideals: how to test them.
  • Principal ideal: examples and counter-examples.
  • Factor rings: how to determine their elements.
  • Isomorphism and homomorphism for rings.
  • Polynomial rings: what their properties are.
  • Irreducible polynomials and divisibility among them.
  • Finite fields and their classification.

Cognitive skills (thinking and analysis).

Students are expected to develop abilities in:

  • Understanding mathematical definitions and demonstrating it by writing them in their own

words.

  • Reading and writing mathematical proofs.
  • Finding examples and counter-examples to a given propositional theorems.

Communication skills (personal and academic).

Students will learn specific skills in:

Expressing mathematical ideas in a logically correct manner.

Good logical writing.

Identifying ambiguities in mathematical statements and how to overcome them.

Making good and acceptable presentation of their works.

Practical and subject specific skills(Transferable Skills).

Students will also experience and gain awareness in:

  • Planning and undertaking project assignments.
  • The high value of meeting deadlines.
  • Working independently and managing time wisely.
  • Using word processor to write their reports legibly.

Expected workload:

On average students need to spend 3 hours of study and preparation for each 50-minute lecture/tutorial.

Attendance policy:

Absence from lectures and/or tutorials shall not exceed 15%. Students who exceed the 15% limit without a medical or emergency excuse acceptable to and approved by the Dean of the relevant college/faculty shall not be allowed to take the final examination and shall receive a mark of zero for the course. If the excuse is approved by the Dean, the student shall be considered to have withdrawn from the course.

Internet Resources:

In addition to the online textbook site, there are other websites which contain relevant

materials pertaining to the course, such as

  • Basic Sciences Department .
  • Amin Witno Website .

Assessment Instruments:

Allocation of Marks
20% / First examination
20% / Second examination
40% / Final examination:
20% / Quizzes, Homework, Class Participation
100% / Total

* Make-up exams will be offered for valid reasons only with consent of the Dean. Make-up exams may be different from regular exams in content and format.

Course/module Academic Calendar:

Week / Basic and Support Materials to be Covered
(1) / Review of Group Theory
(2) / Introduction to rings and subrings, basic properties of rings, the subring test
(3) / Integral domains, zero divisors and unit elements, fields, the subfield test
(4) / Ideal, the ideal test, principal ideal domains
(5) / Factor rings, prime ideals and maximal ideals
(6) / Ring homomorphism, the fundamental homomorphism theorem for rings, the Chinese remainder theorem
(7) / The ring of polynomials over an integral domain
(8) / Divisibility theory in a polynomial ring over a field, the division algorithm, greatest common divisor
(9) / Irreducible polynomials over a field, unique factorization of polynomials in F[x], irreducibility tests over Q
(10) / Minimal polynomials of algebraic elements over a field, field extensions, splitting fields
(11) / The characteristic of a field, classification of finite fields, the subfield lattice
(12) / Introduction to cyclotomic fields, irreducibility of the cyclotomic polynomials over Q
(13) / Degree of a finite extension, algebraic field extensions
(14) / Some applications in classical geometry: geometric constructions, constructable numbers, regular polygons
(15) / Review for Final exam
(16) / Final Exam

Class Rules and Regulations

ClassAttendance:

Attendance is expected of every student.

Being absent is not an excuse for not knowing about any important information that may

have been given in class.

Under the University's regulations, a student whose absence record exceeds 15% of total

class hours will automatically fail the course.

Students who in any way disrupt the class will be expelled from the classroom and will not

be allowed to return until the problem has been resolved.

Project Assignments:

Students are allowed to work together on a project assignment; however, the work that is

turned in by each student must be his own. For instance, a mere copy of another student's

work will not be graded.

Awritten project must be properly presented to receive full credit.

Alate project is penalized one point per day after its due date.

Aproject sent by email will not be accepted.

Late Exams:

Late (make-up) exams will be given only to students who have a valid excuse and are able

to provide a written document for its verification.

The level of difficulty of a late exam is about 50% higher than that of the corresponding

regular exam.

All late exams will be conducted during the last week of the semester.

Each student is allowed only one make-up in a semester, either for the first exam or the

second, but not both.

There is no make-up for a late exam.

Dishonesty:

Any form of dishonesty conduct will be strictly punished.

A student who is caught cheating, or attempting to do so in an exam will be given a zero for

the exam and a report will be written to the Dean for further action.

A student who helps another student or is seen communicating with another student in an

exam will be given the same penalty stated in the previous point.

Students with different exam forms are not exempt from the above rules.

Repeat offenders will be expelled permanently and banned from future courses.