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Computer science lessons in Douala

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Trusted teacher: Digital suites courses I - General A numeric sequence is an application from N to R. • Bounded sequence A sequence (Un) is bounded if there exists a real A such that, for all n, Un ≤ A. We say that A is an upper bound of the series. A sequence (Un) is reduced if there exists a real number B such that, for all n, B ≤ one. One says that B is a lower bound of the sequence. A sequence is said to be bounded if it is both increased and reduced, that is to say if it exists M such that | Un | ≤ M for all n. • Convergent suite The sequence (Un) is convergent towards l ∈ R if: ∀ε> 0 ∃n0 ∈ N ∀n ≥ n0 | un − l | ≤ ε. A sequence which is not convergent is said to be divergent. When it exists, the limit of a sequence is unique. The deletion of a finite number of terms does not modify the nature of the sequence, nor its possible limit. Any convergent sequence is bounded. An unbounded sequence cannot therefore be convergent. • Infinite limits We say that the following (un) diverges Towards + ∞ if: ∀A> 0 ∃n0∈N ∀n ≥ n0 Un≥A Towards −∞ if: ∀A> 0 ∃n0∈N ∀n≤ n0 Un≤A. • Known limitations For k> 1, α> 0, β> 0 II Operations on suites • Algebraic operations If (un) and (vn) converge towards l and l ', then the sequences (un + vn), (λun) and (unvn) respectively converge towards l + l', ll and ll '. If (un) tends to 0 and if (vn) is bounded, then the sequence (unvn) tends to 0. • Order relation If (un) and (vn) are convergent sequences such that we have a ≤ vn for n≥n0, then we have: Attention, no analogous theorem for strict inequalities. • Framing theorem If, from a certain rank, un ≤xn≤ vn and if (un) and (vn) converge towards the same limit l, then the sequence (xn) is convergent towards l. III monotonous suites • Definitions The sequence (un) is increasing if un + 1≥un for all n; decreasing if un + 1≤un for all n; stationary if un + 1 = one for all n. • Convergence Any sequence of increasing and increasing reals converges. Any decreasing and underestimating sequence of reals converges. If a sequence is increasing and not bounded, it diverges towards + ∞. • Adjacent suites The sequences (un) and (vn) are adjacent if: (a) is increasing; (vn) is decreasing; If two sequences are adjacent, they converge and have the same limit. If (un) increasing, (vn) decreasing and un≤vn for all n, then they converge to l1 and l2. It remains to show that l1 = l2 so that they are adjacent. IV Extracted suites • Definition and properties - The sequence (vn) is said to be extracted from the sequence (un) if there exists a map φ of N in N, strictly increasing, such that vn = uφ (n). We also say that (vn) is a subsequence of (un). - If (un) converges to l, any subsequence also converges to l. If sequences extracted from (un) all converge to the same limit l, we can conclude that (un) converges to l if all un is a term of one of the extracted sequences studied. For example, if (u2n) and (u2n + 1) converge to l, then (un) converges to l. • Bolzano-Weierstrass theorem From any bounded sequence of reals, we can extract a convergent subsequence. V Suites de Cauchy • Definition A sequence (un) is Cauchy if, for any positive ε, there exists a natural integer n0 for which, whatever the integers p and q greater than or equal to n0, we have | up − uq | <ε. Be careful, p and q are not related. • Property A sequence of real numbers, or of complexes, converges if, and only if, it is Cauchy SPECIAL SUITES I Arithmetic and geometric sequences • Arithmetic sequences A sequence (un) is arithmetic of reason r if: ∀ n∈N un + 1 = un + r General term: un = u0 + nr. Sum of the first n terms: • Geometric sequences A sequence (un) is geometric of reason q ≠ 0 if: ∀ n∈N un + 1 = qun. General term: un = u0qn Sum of the first n terms: II Recurring suites • Linear recurrent sequences of order 2: - Such a sequence is determined by a relation of the type: (1) ∀ n∈N aUn + 2 + bUn + 1 + cUn = 0 with a ≠ 0 and c ≠ 0 and knowledge of the first two terms u0 and u1. The set of real sequences which satisfy the relation (1) is a vector space of dimension 2. We seek a basis by solving the characteristic equation: ar2 + br + c = 0 (E) - Complex cases a, b, c If ∆ ≠ 0, (E) has two distinct roots r1 and r2. Any sequence satisfying (1) is then like : where K1 and K2 are constants which we then express as a function of u0 and u1. If ∆ = 0, (E) has a double root r0 = (- b) / 2a. Any sequence satisfying (1) is then type: - Case a, b, c real If ∆> 0 or ∆ = 0, the form of the solutions is not modified. If ∆ <0, (E) has two conjugate complex roots r1 = α + iβ and r2 = α − iβ that we write in trigonometric form r1 = ρeiθ and r2 = ρe-iθ Any sequence satisfying (1) is then of the type: • Recurrent sequences un + 1 = f (un) - To study such a sequence, we first determine an interval I containing all the following values. - Possible limit If (un) converges to l and if f is continuous to l, then f (l) = l. - Increasing case f If f is increasing over I, then the sequence (un) is monotonic. The comparison of u0 and u1 makes it possible to know if it is increasing or decreasing. - Decreasing case f If f is decreasing over I, then the sequences (u2n) and (u2n + 1) are monotonic and of contrary Made by LEON
Math · Physics · Computer science
Trusted teacher: Online Course: Basic Concepts of Algorithms and Data Structures Duration : - 60 minutes: condensed format to introduce fundamental concepts with targeted exercises. - 90 minutes: extended format to explore concepts in depth, solve complex problems, and include an interactive question-and-answer session. --- General description This course is designed for students and professionals who are new to computer science, as well as those who want to solidify their foundation in algorithms and data structures. It provides a clear and practical introduction to the essential tools for solving problems effectively, by learning how to design and analyze algorithms. Whether you are preparing for an exam, a technical interview, or want to improve your programming skills, this course will guide you in understanding theoretical concepts and their practical application. --- Educational objectives At the end of the course, participants will be able to: 1. Understand the fundamental concepts of algorithms: sorting, searching, time complexity. 2. Master key data structures: arrays, lists, stacks, queues, trees, and graphs. 3. Solve problems by choosing appropriate data structures and algorithms. 4. Analyze and optimize the performance of algorithms. --- Course syllabus 1. Introduction (5-10 min) - Presentation of the objectives and concepts covered. - Importance of algorithms and data structures in computer science. 2. Fundamental concepts (20-30 min) - Definitions and roles of algorithms and data structures. - Temporal and spatial complexity: basic notions (Big O). - Basic data structures: arrays, lists, and dictionaries. 3. Practical application and examples (30-40 min) - Simple sorting implementation (insertion sort, bubble sort). - Search example (linear search, binary search). - Manipulation of stacks and queues through practical exercises. - Bonus for the 90 min format: Exploration of trees and graphs (simple example of a route). 4. Q&A and conclusion (5-10 min) - Review of the concepts covered. - Tips for continuing to practice and progress. - Suggestions for personal projects to apply the knowledge acquired. --- Teaching methodology - Interactive learning: a combination of theoretical explanations and practical applications. - Concrete examples: each concept is illustrated by practical cases and guided exercises. - Adaptation to needs: the courses are adjusted to the level and objectives of each participant, with a focus on the most relevant aspects. --- Target audience This course is aimed at: - Computer science students wishing to strengthen their mastery of the basics before exams or projects. - Programming beginners who want to understand the essential mechanisms behind problem solving. - Professionals preparing for technical interviews or seeking to improve their understanding of algorithms. --- Benefits of this online course - Personalized support from an experienced trainer. - Educational materials and practical exercises accessible after the session. - Flexible hours to fit your schedule. - Progressive approach to facilitate learning, even for beginners. Develop your skills in algorithms and data structures today to efficiently solve the complex problems of tomorrow! ---
Tutoring · Computer science · Algorithms
Trusted teacher: Vous êtes impliqué dans les finances, la gestion, la planification, la gestion de projet, les ressources humaines, ou peut-être même un étudiant ambitieux désireux de perfectionner ses compétences en matière de tableau de bord professionnel. Si vous recherchez une solution qui va au-delà des limitations d'Excel et de PowerPoint, alors vous êtes au bon endroit : permettez moi de vous présenter Power BI. Avec Power BI, je vous propose bien plus qu'un simple outil. C'est une passerelle vers des rapports interactifs, une gestion efficace des données et une analyse avancée. Voici ce que je peux vous offrir : - Création et gestion experte de rapports interactifs. - Transformation et nettoyage minutieux des données pour une précision maximale. - Utilisation des puissantes formules DAX pour une analyse de données avancée. - Création de visualisations personnalisées et de tableaux de bord percutants. - Partage sécurisé et publication de vos rapports pour une collaboration sans heurts. -Automatisation des tâches répétitives avec Power BI & Power Query. Peu importe vos besoins spécifiques - qu'il s'agisse de projets professionnels, d'études ou d'aspirations personnelles - je suis là pour vous offrir une solution sur mesure. Ensemble, nous créerons un programme adapté à vos objectifs, vous guidant à chaque étape de votre parcours d'apprentissage. Que vous soyez un novice cherchant à maîtriser les bases ou un expert désireux d'approfondir vos connaissances en analyse de données, je suis là pour vous fournir l'expertise et le soutien nécessaires pour réussir.
Computer science · Microsoft excel
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Only reviews of students are published and they are guaranteed by Apprentus. Rated 4.8 out of 5 based on 58 reviews.

Support courses in mathematics intended for high school students, adapted to different sectors: Science Maths, Science Exp, Letters (Lyon)
Azzedine
Azzedine truly stands out as a remarkable instructor! Despite the short notice, he displayed remarkable consideration for our hectic timetable, ensuring to carve out time to equip me with Excel and Power BI skills for the assessment. A heartfelt thank you, Azzedine, for your exceptional teaching methods. I highly endorse Azzedine as your go-to teacher!
Review by IMANE
Tutor for Math, Physics, and Mechanical/Material Engineering courses (The Hague)
Reza
Extremely professional and knowledgeable with any problem that I have had. Reza is always polite, friendly and always shows great patience, which I believe is of the highest importance when learning difficult subjects. I highly recommend him as a teacher!
Review by EDEN
Oracle Certified Tutor/Trainer For Java, Python and Web with 300+ Reviews (New York)
Aniket
Probably the best instructor on the subject here on the Apprentus site and approved subject knowledge.
Review by SHANT