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Semester: 01
Teaching Unit: Fundamental
Subject: Algebra 1
Credits: 5
Coefficient: 3
Teaching Objectives:
The aim of this course is to introduce the basic concepts of algebra and set theory.
Recommended Prerequisites:
Knowledge of classical algebra.
Course Coordinator: Kecies Mohamed
Email: m.kecies@centre-univ-mila.dz
This course is part of the Algebra 1 module for first-year Computer Science students.
Subject: Algebra 1
COURSE SYLLABUS: Algebra I
Chapter 1: Logical Concepts
- Truth tables
- Quantifiers
- Types of reasoning
Chapter 2: Sets and Functions
- Definitions and examples
- Functions: injection, surjection, bijection, direct image, inverse image, restriction, and extension
Chapter 3: Binary Relations on a Set
- Basic definitions: reflexive, symmetric, antisymmetric, and transitive relations
- Order relation: definition, total order, and partial order
- Equivalence relation: equivalence classes
Chapter 4: Algebraic Structures
- Internal composition law: stable subsets and properties
- Groups: definitions, subgroups, examples, group homomorphisms, and isomorphisms; examples of finite groups Z/nZ (n=1,2,3,…) and the permutation group S_3.
- Rings: definition, subrings, computation rules, invertible elements, zero divisors, ring homomorphisms, and ideals
- Fields: definitions, finite fields( Z/pZ where p is prime), IR, and IC.
Chapter 5: Polynomial Rings
- Polynomials and their degree
- Construction of the polynomial ring
- Arithmetic of polynomials: divisibility, Euclidean division, GCD, and LCM of two polynomials; relatively prime polynomials and factorization into irreducibles
- Roots of a polynomial: roots and degree, root multiplicity
Assessment Method:
The evaluation consists of Continuous Assessment and a Final Exam.
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Pondération |
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Final Exam |
60% |
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Continuous Assessment |
40% |
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Attendance and participation |
8=3+3+2 |
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Quizzes (number): |
12 (1) |
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Practical Work (number): |
/ |
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Presentations: |
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Reports: |
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Internship reports: |
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Field trip reports: |
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Other 1/ ………………………………………………. |
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Other 2: ………………………………………………. |
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Other 3 : ………………………………………………. |
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Total |
20 |
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Total |
1 (100%) |
Bibliographic References: Books, Handouts, Websites, etc.
1- Algèbre exercices et problèmes, licence 510/538
2- Algèbre pour la licence3; groupes, anneaux, corps 510/318
3- Théorie des groupes, rappels de cours, exercices et problème corrigés 510/533
4- Cours d'algèbre et exercices corrigés 510/700
5- Ensembles, relation, Applications, Dénombrement – exercices corrigés avec rappel de cours L1 510/523
6- Algèbre 1ere année, cours et exercices avec solutions 510/83
7- Algèbre 1ère année, exercices corrigés 510/85
8- Mathématiques L1, cours complets avec 1000 tests et exercices corrigés 510/468