Faculté des Sciences

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Algebra 1 : Mathematical logic , Set theory ,Mappings ,Binary relations , Algebraic structures , Polynomial rings
(Faculty of Sciences, 2025) SACI , Fateh
This course is designed primarily for first-year students in Mathematics and Computer Science under the LMD system. The primary goal is to develop a fundamental understanding and skills necessary for working with mathematical expressions, equations, and functions. This comprehensive course provides a solid foundation in key mathematical concepts, covering logic, set theory, binary relations, mappings, algebraic structures, and rings of polynomials. It starts with Chapter 1: Logic Concepts, where students learn about logical operators, quantifiers, and proof methods. Chapter 2: Sets introduces set theory, including set operations and applications. Chapter 3 : Binary Relations explores reflexive, symmetric, transitive, and equivalence relations. Chapter 4: Mappings delves into injective, surjective, and bijective functions. Chapter 5: Algebraic Structures covers groups, rings, and fields, while Chapter 6: Rings of Polynomials focuses on the structure and applications of polynomial rings, particularly in algebraic geometry. This progression equips students with the foundational knowledge required for advanced mathematical studies.
Analyse Numérique Cours et Exercices
(Faculté des sciences, 2023) Nasri , Nassima
L'analyse numérique a commencé bien avant la conception des ordinateurs et leur utilisation quotidienne que nous connaissons aujourd'hui. Les premières méthodes ont été développées pour essayer de trouver des moyens rapides et efficaces de s'attaquer à des problèmes soit fastidieux à résoudre à cause de leurs grande dimension (systèmes à plusieurs dizaines d'équations par exemple), soit parce qu'il n'existe pas de solutions explicites connues même pour certaines équations assez simples en apparence. Dés que les ordinateurs sont apparus, ce domaine des mathématiques a pris son en vol et continue encore à se développer de façon très soutenu. Les applications extraordinairement nombreuses sont entrées dans notre vie quotidienne. Nous pouvons téléphoner, communiquer par satellite, faire des re- cherches sur internet, regarder des films où plus rien n'est réel sur l'écran, améliorer la sécurité des voitures, des trains, des avions, connaitre le temps qu il fera une semaine à l'avance,...et ce n'est qu'une toute petite partie de ce qu'on peut faire. Le but de ce polycopié est s'initier aux bases de l'analyse numérique et il est destiné aux étudiants de la deuxième année licence en mathématiques en espérant qu'il éveillera leurs intérêts et leurs inspirations.
Analyse Numérique I : Cours et Exercices
(Faculté des Sciences, 2021) KHENNICHE , GHANIA
L'analyse numérique a commencé bien avant la conception des ordinateurs et leur utilisation quotidienne que nous connaissons aujourd'hui. Les premières méthodes ont été développées pour essayer de trouver des moyens rapides et efficaces de s'attaquer à des problèmes soit fastidieux à résoudre à cause de leur grande dimension (systèmes à plusieurs dizaines d'équations par exemple),soit parce qu'il n'existe pas de solutions explicites connues même pour certaines équations assez simples en apparence. Dés que les premiers ordinateurs sont apparus , ce domaine des mathématiques a pris son envol et continue encore à se développer de façon trés soutenue . Les caractéristiques des ordinateurs (rapiditéd , précision,...ect) ont permis d'améliorer plusieurs méthodes numérique connues,et ont facilité la création d'algorithmes relatifs à des problèmes difficile voir impossible à trouver la solution analytique. Ce cours et s'initier aux bases de l'analyse numérique en espérant qu'elles éveilleront de l’intérêt , de la curiosité aux étudiants de2`eme année licence mathématiques. Il a pour objectif de présenter une variété d'outils numériques permettant la résolution d'un certain nombre de problèmes.
ANIMAL PHYSIOLOGY 2nd year Agronomy : The invertebrates & the vertebrates
(Faculty of Sciences, 2023) OUDJANE , Faiza
The first Metazoans developed an external rather than an internal circulation system. the sponges and the Cnidarians don't have neither heart, neither system circulatory differentiated. the Transport of O2 and nutrients takes place from cell to cell by diffusion. It's the middle exterior which serves as a transport medium thanks to a permanent renewal ensured by the activity of ciliated, flagellated or muscular cells. In all other cases, transport is assured by internal fluid movements : blood or hemolymph
Applied statistical hydrology course
(Faculty of Sciences, 2024) Hebal , Aziz
Precipitation includes all meteoric waters that fall on the surface of the earth, both in liquid and solid forms (drizzle, sleet, hail), and deposited or occult precipitations (dew, frost, hoarfrost...) caused by temperature or pressure changes. The most commonly used precipitation measurement devices are: – Pluviometers; – Pluviographs; – Snow gauges; – Radars. Point analysis concerns the series of measurements from a given point, i.e., a single station. From a series of point measurements, two types of graphs can be constructed: the rainfall height curve and the hyetogram.
Biostatistics course : According to the official educational program of third year Agroecology semester 3
(Faculty of Sciences, 2025) BELAIDI : Abdelouahab
The aim of teaching biostatistics is to provide second-year students with essential skills and knowledge to analyze, interpret, and draw conclusions from biological data. The objectives of teaching biostatistics are: - Understanding of fundamental statistical concepts: students should gain a thorough understanding of basic statistical concepts such as probability, distribution, mean, median, standard deviation, etc. - Data collection and analysis: students should learn data collection techniques, including the design of experimental studies, sample selection and collection of relevant data. They should also be able to analyze these data using appropriate statistical methods. - Interpretation of results: Instruction should enable students to correctly interpret statistical results. This includes the ability to draw meaningful conclusions from statistical analyses, assess the validity of results, and recognize study limitations. To achieve these goals, the student must have notions of probability and numerical analysis already seen in the subject Mathematics in the first year.
Cell Biology (Master 1 – Applied Biochemistry)
(Faculty of Sciences, 2025) Bendjazia , Radia
This course manual has been developed to facilitate the assimilation and understanding of key concepts in cell biology, tailored specifically for first-year Master’s students in Applied Biochemistry. It offers a comprehensive overview of the fundamental structures and dynamic processes that govern the life of eukaryotic cells, providing students with a solid foundation for both theoretical and practical applications in modern biomedical and biotechnological research. The content has been carefully organized to reflect the logical progression of cellular complexity. It begins with a detailed examination of the structural and functional organization of the cell, establishing the basis for understanding subcellular compartments and molecular interactions. This is followed by an exploration of the extracellular matrix, which plays a critical role in tissue architecture and intercellular communication. The course then addresses cell differentiation, highlighting how specialized cell types arise and are maintained. Further sections delve into intracellular trafficking, which ensures the precise distribution of molecules within the cell, and the regulation and deregulation of the cell cycle, a key area in understanding cancer biology. We also examine the mechanisms of communication and signal transduction, which coordinate cellular responses to external stimuli. The process of apoptosis, or programmed cell death, is then discussed as a vital mechanism for maintaining cellular homeostasis. Finally, students are introduced to cell imaging techniques, which are essential tools for visualizing cellular structures and functions with high resolution. This course is not only foundational for advanced modules in the Master’s curriculum, but it also serves as a practical resource for students engaging in research projects, including theses and doctoral work. A deep understanding of cellular mechanisms and experimental tools will enable students to confidently design and conduct laboratory studies relevant to their field. The pedagogical approach adopted in this manual emphasizes clarity and accessibility, using straightforward language supported by practical examples. To make the content more engaging and easier to understand, numerous illustrations—including simplified diagrams, photographs, and summary tables—are provided throughout the text. As with any academic endeavor, this document may contain errors or omissions. Feedback, corrections, and suggestions from fellow educators and researchers are therefore welcomed and encouraged, in the spirit of continuous improvement and academic collaboration.
Cours : Chimie Des Produits Naturels A Activité Biologique : Master II , Chimie Organique.
(Faculté des Sciences, 2021) Boudermine , Sihem
La nature et sa biodiversité offre des molécules biologiquement actives. Cette biodiversité très riche va conduire à une diversité chimique et structurale d’autant plus importante. Des substances sont étudiées par les biologistes qui les utilisent dans leurs recherches pour déterminer et certaines de ces substances deviendront même des médicaments. Les substances naturelles offrent des potentialités considérables comme : - Molécules d’intérêt pharmacologique, agronomique et cosmétique. -Marquent l’identité d’une espèce, familles ou genres donc des outils moléculaires pour l’exploration du monde vivant.
Cours de la théorie des semi groupes d'opérateurs linéaires
(Faculté des Sciences, 2023) Leulmi ,Soumya
La plus part des phénomènes dans la nature peuvent être reformulé et modélisé sous forme d'une équation différentielle (ordinaire ou aux dé- rivées partielles, inclus les conditions au bord) ou d'un systèmes d'équations différentielles. Une vaste classe de ces équations peuvent être écrite sous forme d'un problème d'évolution : du(t) dt = Au(t) + f(t); t > 0: u(s) = u0: Dans le cas où f(t) = 0, s = 0 et A est une application Lipchitzienne le théorème de Cauchy-Lipchitz -Picard rend un grand service à résoudre ce problème et la solution sera donnée par la formule : u(t) = eAtu0: Mais dans le cas où A est non borné, alors A est non Lipchitzienne, donc on peut pas appliquer le théorème de Cauchy-Lipchitz-Picard. L'idée serait de définir pour une classe d'opérateurs non nécessairement bornés un objet mathématique qui donne l'existence et l'unicité. La théorie des semi groupes d'opérateurs linéaires trouve dans les espaces de Banach une résolution dans le cas où A est non borné.
Cours Statistiques Expérimentales : 3 année Licence (LMD) , Spécialité amélioration de la production animale
(Faculté des Sciences, 2024) Benatmane , C
Les statistiques expérimentales jouent un rôle essentiel dans la conception et l'analyse des expériences agricoles. Elles permettent de garantir la validité des résultats et d'interpréter les données de manière rigoureuse. Voici les principaux concepts et méthodes associés aux statistiques expérimentales dans le contexte de l'agriculture : - Essais randomisés : Chaque traitement est attribué de manière aléatoire pour éviter les biais. - Blocs randomisés : Les essais sont organisés en blocs pour contrôler les variations non contrôlées (par exemple, la qualité du sol). - Plans factoriels : Étudier plusieurs facteurs simultanément pour observer les interactions entre eux.
Cours sur Espaces vectoriels normés : Pour la 3iéme Année Licence Mathématiques - Semestre 5.
(Faculté des Sciences, 2025) Khelili , Besma
Ce polycopié pédagogique, intitulé " Les espaces vectoriels normés " , est le fruit de plusieurs années d'enseignement des matières Analyse 1-3, Topologie et Algèbre linéaire. Il est destiné aux étudiants de L3 en licence de mathématiques et a été dispensé à l' université 20 août 1955 de Skikda entre 2018 et 2025. Ce cours introduit les concepts fondamentaux des espaces normés et des espaces de Hilbert , qui jouent un rôle clé en analyse fonctionnelle. Ce manuscrit constitue un guide complet visant à aider les étudiants à développer une compréhension approfondie de ces espaces, de leurs propriétés et de leurs applications. L' étude de ce sujet leur fournit une base rigoureuse pour la recherche et les applications mathématiques avancées dans divers domaines scientifiques. Il se décline en trois chapitres, chacun étant suivi d'une série d'exercices. Nous commençons par un rappel des concepts fondamentaux des espaces vectoriels et de leurs sous-espaces, qui forment le cadre général des structures algébriques utilisées en mathématiques. Ensuite, dans le chapitre 1, nous introduisons la notion de norme sur un espace vectoriel, en définissant la norme, la distance et en présentant divers exemples d'espaces vectoriels normés. Il explore l' équivalence des normes et les boules, essentielles pour l' étude de la convergence et de la continuité. Des concepts topologiques fondamentaux, tels que la limite, les ouverts, les fermés, l' adhérence et l' intérieur, sont abordés, ainsi que les ensembles et fonctions bornés. Enfin, la dernière partie traite des espaces de Banach, caractérisés par leur complétude, en introduisant les suites de Cauchy et en illustrant leurs propriétés par des exemples concrets. Le deuxième chapitre étudie les applications linéaires continues et la continuité dans les espaces vectoriels normés. Il traite des formes linéaires, de la dualité topologique et des propriétés des espaces de dimension finie. Des exercices pratiques illustrent ces concepts Le troisième chapitre est consacré aux espaces de Hilbert, qui jouent un rôle central en analyse fonctionnelle en raison de leur structure géométrique riche et de leurs nombreuses applications. Il commence par l' introduction du produit scalaire, qui permet de définir une distance et d' étudier les propriétés géométriques des espaces vectoriels. L'étude se poursuit avec les espaces préhilbertiens complets, où l' on introduit les notions essentielles d orthogonalité et de projection orthogonale. Le théorème de représentation de Riesz est également abordé, illustrant l importance de la dualité dans ces espaces. Une section d' exercices est incluse pour consolider ces concepts fondamentaux. Ensuite, le chapitre se focalise sur les systèmes orthogonaux et les bases hilbertiennes, en introduisant les concepts de systèmes orthogonaux et orthonormaux. Le procédé d'orthonormalisation de Gram-Schmidt est présenté comme un outil essentiel pour construire des bases orthonormées. Les inégalités de Bessel et de Parseval sont étudiées en détail, suivies de l'égalité de Parseval, qui met en évidence le lien entre les séries orthogonales et la structure des espaces de Hilbert. Enfin, une attention particulière est portée aux systèmes orthonormés complets dans des espaces concrets, avec une application directe aux séries de Fourier. La base hilbertienne trigonométrique est introduite, illustrant l' utilité des espaces de Hilbert en analyse de Fourier. La majorité des exemples sont extraits des références [1 - 23]. Pour compléter l 'étude , une série d exercices et de travaux dirigés est proposée, couvrant des sujets variés, pour approfondir la compréhension et maîtriser les outils mathématiques abordés dans ce cours.
Course General Biodiversity Intended for L3 Biology and Ecology of Aquatic Environments students
(Faculty of Sciences, 2025) BOUDEFFA , Khaled
Biodiversity encompasses all living organisms and the ecosystems that host them, as well as the complex interactions that connect them. It is both the result of a long evolutionary process and a key factor in maintaining the ecological balance of our planet. Understanding biodiversity, its components, and the threats it faces is now a major challenge for the conservation of ecosystems and the sustainable management of natural resources. This general biodiversity handbook aims to provide a comprehensive overview of the fundamental concepts related to biological diversity. It explores the different levels of biodiversity (genetic, species, and ecosystem diversity), the evolutionary mechanisms that shape it, and the main anthropogenic pressures contributing to its decline. By highlighting the importance of biodiversity in ecological balance and ecosystem services, this document serves as an educational tool to raise awareness about the necessity of its conservation. Designed for students, researchers, and environmental science enthusiasts, this material provides a foundation for reflection and learning. It is based on recent scientific data and concrete examples to illustrate both the richness and fragility of life on Earth. May this handbook serve as a resource to better understand the complexity of the living world and encourage a more responsible and respectful approach to nature.
Course Handout Acoustic : 3rd year Licence (LMD) Sector Physic Specialty Materials Physic
(Faculty of Sciences, 2025) HADEF , Zakaria
This handout of the acoustics course was written for 3rd year students in the Physics of Materials License who are preparing, as part of the L.M.D. reform, a License in the field of "Material Sciences". It complies with the official program. It was written with the aim of providing a work and reference tool covering the knowledge required of them. The manuscript is composed of five chapters, the first is mainly devoted to reminders on oscillations and resonance. The second chapter is reserved for understanding sound and sound sources. The properties of the acoustic wave are detailed in the third chapter. Medical diagnosis by ultrasound was studied in the fourth chapter. The last chapter is devoted to the presentation of the role of sound waves in prospecting and industry. Although this manuscript has been prepared with the greatest care, it obviously remains improvable. I thank in advance anyone who sends me remarks or comments
Course handout Degradation and conservation of ecosystems (DCE) : Ineeded for master 2 of Applied Microbiology students
(Faculty of Sciences, 2025) BOUCETTA , Sabrine
The structure of ecosystems can be visualized with ecological pyramids, which were first described by the pioneering studies of Charles Elton in the 1920s. Ecological pyramids show the relative amounts of various parameters (such as number of organisms, energy, and biomass) across trophic levels. Pyramids of numbers can be either upright or inverted, depending on the ecosystem. As shown in Figure 7, typical grassland during the summer has a base of many plants and the numbers of organisms decrease at each trophic level. However, during the summer in a temperate forest, the base of the pyramid consists of few trees compared with the number of primary consumers, mostly insects. Because trees are large, they have great photosynthetic capability, and dominate other plants in this ecosystem to obtain sunlight. Even in smaller numbers, primary producers in forests are still capable of supporting other trophic levels. Another way to visualize ecosystem structure is with pyramids of biomass. This pyramid measures the amount of energy converted into living tissue at the different trophic levels. Using the Silver Springs ecosystem example, this data exhibits an upright biomass pyramid (Figure 8), whereas the pyramid from the English Channel example is inverted. The plants (primary producers) of the Silver Springs ecosystem make up a large percentage of the biomass found there. However, the phytoplankton in the English Channel example make up less biomass than the primary consumers, the zooplankton. As with inverted pyramids of numbers, this inverted pyramid is not due to a lack of productivity from the primary producers, but results from the high turnover rate of the phytoplankton. The phytoplankton are consumed rapidly by the primary consumers, thus, minimizing their biomass at any particular point in time. However, phytoplankton reproduce quickly, thus they are able to support the rest of the ecosystem. Pyramid ecosystem modeling can also be used to show energy flow through the trophic levels. Notice that these numbers are the same as those used in the energy flow compartment diagram in Figure 8. Pyramids of energy are always upright, and an ecosystem without sufficient primary productivity cannot be supported. All types of ecological pyramids are useful for characterizing ecosystem structure. However, in the study of energy flow through the ecosystem, pyramids of energy are the most consistent and representative models of ecosystem structure (Figure 8).
Course handout Industrial Microbiology : Intended for 3rd year Microbiology students
(Faculty of Sciences, 2025) BOUCETTA , Sabrine
This industrial microbiology handout is intended for 3rd-year Microbiology degree students and is divided into two parts. The first part enables students to acquire a basic knowledge of the subject, th rough the study of the three main players in industrial microbiology: industrial microorganisms, industrial fermenters and industrial culture media. After acquiring the basic notions, the second part of the subject will discuss the various products of industrial fermentation, which are (i): microbial biomass: generally used as a source of proteins of unicellular origin, (ii): the industrial production of certain primary metabolites represented by amino acids, organic acids and biogases, and (iii) the industrial production of certain secondary metabolites represented by antibiotics, polysaccharides and vitamins. The teaching method used in this course is based on the use of simple and basic language, supported by examples. In addition, and in order to make the content more accessible to students, many illustrations in the form of simplified diagrams, photos and summary tables have been used. As a result, it is always encouraging and motivating to receive corrections, advice and recommendations from our teaching and research colleagues.
Course Handout of "Plant Biology 1" Intended for First-Year Engineering Students in Agronomic Sciences
(Faculty of Sciences, 2025) SOUILAH , Nabila
Plant biology is a broad discipline that encompasses all aspects of plant life, both aquatic and terrestrial, including their morphologies, modes of reproduction (sexual and asexual), adaptations to various environments, and the mechanisms enabling sustainable interactions (such as parasitism and symbiosis) (Campell et al., 2008). The living world consists of an immense collection of organisms in constant evolution. It is divided into two biotic groups (prokaryotes and eukaryotes) and six kingdoms: Archaea, Eubacteria, Protists, Fungi, Animals, and Plants (Margulis & Schwartz, 1988; Raven et al., 2013).
Course Handout on Technology of Agri-Food Industries (T.I.A.A. 1 and T.I.A.A. 2) : For the use of third-year undergraduate students in Agri-Food Science and Quality Control
(Faculté des Sciences, 2025) LAIB , Imen
This handout is intended for third-year undergraduate students in Food Science and Quality Control, as part of the TIAA1 and TIAA2 courses. It has been designed to support students in learning the fundamentals of food science and technology, with a focus on dairy products, the sugar industry, fats and oils, beverages, cereal products, fruits and vegetables, as well as meat products. The food industry is a complex and ever-evolving sector where mastering processing techniques, understanding the properties of raw materials, and managing quality are essential challenges. This document aims to provide students with a solid and structured foundation to understand the various food industry sectors, addressing the technological, microbiological, and nutritional aspects of food products. The objectives of this handout are as follows: to convey fundamental knowledge about raw materials and processing techniques, to facilitate the learning of quality control methods, to develop a global perspective on food industry sectors through concrete examples and case studies, and to prepare students for professional challenges by training them to meet the demands of the food industry market.
Course in Numerical methods For Engineers and scientists
(Faculty of sciences, 2024) SELMANI , WISSAME
The course on numerical methods in mathematics for engineers is a fundamental aspect of engineering education, designed to equip students with tools to solve complex mathematical problems using computational techniques . This course bridges the gap between theoretical concepts and real-world applications by teaching algorithms and strategies to approximate solutions for mathematical models that are otherwise challenging or impossible to solve analytically. Throughout the course, students delve into numerical techniques such as root finding, interpolation , numerical integration, differential equations, and matrix computations.They learn how to apply these methods using programming languages like Maple, MATLAB,Python,or others, gaining hands-onexperience in implementing algorithms and analyzing the accuracy and efficiency of their solutions Understanding numerical methods iscrucial for engineers as it enables them to simulate, model, and solve problems encountered in various engineering disciplines.It empowers them to tackle real-world challenges where analytical solutions may be impractical or unavailable,allow- for accurate predictions,design optimizations,and informed decision-making in engineeringing projects. This course aims to expose the different digital methods for level technicians L2 university. This document contains six(06)chapters and the objectives collectively aim to equipeng ineering students with a robust foundation in numerical methods, preparing them to tackle intricate engineering problems using computational tools and mathematical techniques
Course of : MATHEMATICS 3
(Faculty of sciences, 2024) BENDIB , EL OUAHMA
The aim of this course is to provide general training in numerical series and integral calculus for second-year science and technology students, and to know a new mathematical tools. This course provides the fundamental concept of numerical series, multiple integrals, improper integrals, differential equation and how to use Fourier transform and Laplace transform for solving some differential equations
DYNAMICAL SYSTEMS 1 First semester : For first-year Master’s degree students
(Faculty of Sciences, 2025) Boulfoul , Amel
This course book serves as an introduction to dynamical systems, focusing on ordinary differential equations (ODEs), their stability, periodic solutions, and bifurcations. It is aimed at students in mathematics, particularly those in the first year of their Master’s degree. The book is structured into five main chapters, each addressing important aspects of dynamical systems. The first chapter, Preliminaries of Ordinary Differential Equations, begins with a review of differential systems, followed by their classification, and linear differential systems, including homogeneous and nonhomogeneous cases. The second chapter, General Theory of ODEs, introduces the fundamental aspects of ordinary differential equations, initial value problems, and solutions. It includes key existence and uniqueness theorems, different proof methods, and examples. Additionally, the continuation of solutions and maximal intervals of existence are discussed in detail. The third chapter, Stability in Linear and Nonlinear Systems, explores the concept of stability, starting with linear systems and extending to nonlinear systems. It covers important tools such as Lyapunov’s method and the analysis of conservative and dissipative systems, which are fundamental for understanding system behavior over time. In the fourth chapter, Periodic Solutions and Their Stability, we delve into the nature of periodic solutions, limit cycles, and their stability. Concepts such as Poincar´e maps, Bendixson’s and Dulac’s criteria, and the Poincar´e-Bendixson theorem are explored, offering a deep understanding of the behavior of dynamical systems in the long term. Finally, the fifth chapter, Introduction to Local Bifurcations, introduces the v concept of bifurcation, focusing on one-dimensional and two-dimensional systems. Key bifurcations, including saddle-node, pitchfork, transcritical, and Hopf bifurcations, are explored, laying the foundation for further study and applications in complex systems. In this book, my objective was to collect the most important definitions, information, and tools from the most significant references such as [[12], [14], [15], [10], [5]], and the references therein, to help students focus on the essential notions of dynamical systems. Throughout the book, a formal and clear approach is taken, with numerous examples and illustrations. The topics covered are foundational for the study of dynamical systems and provide the necessary tools to tackle more advanced subjects in mathematical modeling, control theory, and applied mathematics. It is my hope that this book serves as a learning resource for students and a reference for those seeking to deepen their understanding of dynamical systems

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