University :Mansoura University |
Faculty :Faculty of Science |
Department :Mathematics Department |
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| 1- 1- Course data :- |
| | Code: | 11318 | | Course title: | جبر مجرد (2) | | Year/Level: | ثالثة رياضيات | | Program Title: | | | Specialization: | | | Teaching Hours: | Theoretical: | 4 | Tutorial: | 2 | Practical: | |
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| 2- 2- Course aims :- |
| - The programme unit aims to introduce quotient structures and their connection with homomorphisms in the context of rings and then again in the context of groups; present further important examples of groups and rings and develop some of their properties with particular emphasis on polynomial rings, factorisation in rings and group actions. As a prerequisite to the advande course of algebra .
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| 3- 3- Course Learning Outcomes :- |
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| 4- 4- Course contents :- |
| | No | Topics | Week No. |
|---|
| 1 | What is a ring and all essential kinds of rings | | | 2 | Integral Domain and its properties | | | 3 | Unites, primes and irreducibles elements | | | 4 | Subrings and ideals. Prime and maximal | | | 5 | Factor rings and homomorphisms theorems. | | | 6 | extention of an integral domain to a field | | | 7 | Euclidean domain and its properties | | | 8 | Polynomials over a ring and oynomialsver a field | | | 9 | Prime and irreducible pol | | | 10 | Gauss theorem and Eisenstein’ criterion | | | 11 | Field Splitting fields extensions, | | | 12 | Finite fields and its properties. | | | 13 | extensions | | | 14 | Classification of extensions | |
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| 5- 5- Teaching and learning methods :- |
| | S | Method |
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| Lecturer with exercise sheets and solution sheets | | Tutorials in groups | | Using Internet facilities |
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| 6- 6- Teaching and learning methods of disables :- |
| - no
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| 7- 7- Student assessment :- |
| - Timing |
| | No | Method | Week No. |
|---|
| 1 | Oral exam | 14 | | 2 | Final exam | 16 |
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| - Degree |
| | No | Method | Degree |
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| 1 | Mid_term examination | 0 | | 2 | Final_term examination | 90 | | 3 | Oral examination | 10 | | 4 | Practical examination | 0 | | 5 | Semester work | 0 | | 6 | Other types of asessment | 0 | | Total | 100% |
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| 8- 8- List of books and references |
| | S | Reference | Type |
|---|
| 1 | Lecture Notes | | | 2 | Elements of Abstract Algebra, by Dean | | | 3 | Algebra, by Serge Lang. | | | 4 | Abstract Algebra by John A. Beachy and William D. Blair | | | 5 | John B. Fraleigh,A first cours in Abstract algebra, Addidon-Wesley | | | 6 | R.B.J.T. Allenby, Rings, Filds and Groups an Introduction to Abstract algebra, Addison-Wesley | | | 7 | http://joshua.smcvt.edu/linearalgebra/ | | | 8 | http://www.math.unl.edu/~tshores1/linalgtext.html | | | 9 | http://www.math.niu.edu/~beachy/aaol/ | |
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| 9- 9- Matrix of knowledge and skills of the course |
| | S | Content | Study week |
|---|
| What is a ring and all essential kinds of rings | | | Integral Domain and its properties | | | Unites, primes and irreducibles elements | | | Subrings and ideals. Prime and maximal | | | Factor rings and homomorphisms theorems. | | | extention of an integral domain to a field | | | Euclidean domain and its properties | | | Polynomials over a ring and oynomialsver a field | | | Prime and irreducible pol | | | Gauss theorem and Eisenstein’ criterion | | | Field Splitting fields extensions, | | | Finite fields and its properties. | | | extensions | | | Classification of extensions | |
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| Course Coordinator(s): - |
| - Magdy Hakim Armanious Bekhet
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| Head of department: - |
| Ahmed Habeb Mohamed Nageb Elbassiony |
