Advanced Mathematics: Bachelor's, Master's and Engineering Studies

Von 21.12 Fr /Std

1. Algebra & Linear Algebra
The foundation for success in mathematics. General algebra: Groups, rings, fields, and arithmetic.
Linear algebra: Vector spaces, reduction of endomorphisms (diagonalization, triangularization), duality, and quadratic forms.

2. Topology & Functional Analysis
To move from simple function analysis to the study of space structures.
Metric spaces & Topology: Open and closed sets, compactness, connectivity, and completeness.
Normated Vector Spaces: Convergence of sequences, continuity, and equivalence of norms.
Banach & Hilbert spaces: Study of completeness, orthogonal projections, Riesz theorems, and Fourier series. 3. Numerical Analysis The art of solving mathematical problems through algorithms and high-performance computing.

Solving nonlinear equations: Bisection, Newton-Raphson, and fixed-point methods.
Numerical integration: Trapezoidal rule and Simpson's rule.
Numerical matrix analysis: Solving systems of equations (Gzuss, Lu, Cholesky), eigenvalue calculations, and conditional analysis.

Zusätzliche Informationen

Ort

Online aus Luxemburg

Über mich

Bonjour, je suis Dr. Raouf, titulaire d'un Doctorat en Mathématiques avec une solide expérience dans l'enseignement supérieur et le soutien scolaire personnalisé. J'accompagne les élèves des lycées luxembourgeois (Classique et Général) ainsi que les étudiants universitaires vers l'excellence.

Ma pédagogie repose sur la simplification des concepts abstraits et la maîtrise des méthodes de résolution exigées par le Ministère de l'Éducation nationale du Luxembourg ESC (Classique) et ESG (Général).

1. Enseignement Secondaire (Sections B, C, D, G)
Analyse : Étude approfondie des fonctions (logarithmes, exponentielles), limites, dérivées et calcul intégral.
Algèbre Linéaire : Géométrie analytique dans l'espace, vecteurs, et systèmes d'équations (méthode de Gauss).
Nombres Complexes : Formes algébriques, trigonométriques et résolution dans .
Préparation à l'Examen de Fin d'Études :Travail intensif sur les questionnaires des années précédentes (Annales).

2. Enseignement Supérieur (Université du Luxembourg / CPGE)

Calculus & Analyse réelle : Suites, séries, intégrales généralisées.
Algèbre matricielle : Espaces vectoriels, diagonalisation, valeurs propres.

Ma Méthodologie en Ligne

Outils digitaux : Utilisation d'un tableau blanc interactif et d'une tablette graphique pour une rédaction claire et partagée en temps réel.
Adaptation stricte aux barèmes et aux critères de rédaction du baccalauréat luxembourgeois.
Suivi personnalisé : Envoi d'un résumé de cours et d'exercices d'application après chaque séance.

Bildung

Mastère en mathématiques. PhD en mathématiques appliquées. Chercheur en mathématiques au laboratoire de modélisation de l'école nationale d'ingénieurs de Tunis. Mes champs de compétences en mathématiques s'étendent des bases à acquérir pendant l'enseignement secondaire aux mathématiques supérieures de la licence et du mastere en maths et des classes préparatoires aux études d'ingénieurs. Je maîtrise aussi les programmes d'analyse numérique et d'analyse fonctionnelles enseignés notamment dans les écoles d'ingénieurs.

Erfahrung / Qualifikationen

Une carrière de plus de 20 ans dans une école d'ingénieur en Tunisie dont les programmes de formation sont accrédités EUR-ACE.

Alter

Jugendliche (13-17 Jahre alt)

Erwachsene (18-64 Jahre alt)

Unterrichtsniveau

Anfänger

Mittel

Fortgeschritten

Dauer

60 Minuten

Unterrichtet in

Französisch

Englisch

Arabisch

Fachkenntnisse

Mathematik

Numerische analyse

Algebra

Bewertungen

Verfügbarkeit einer typischen Woche

(GMT -04:00)

New York

Online via Webcam

Mon

Tue

Wed

Thu

Fri

Sat

Sun

00-04

04-08

08-12

12-16

16-20

20-24

Artificial Intelligence in everyday life for seniors to better understand the changes brought about by AI

17.46 Fr /Std

Objective: To understand AI without fear, to use it to simplify one's life and to know how to identify digital traps.

1: Demystifying AI (What exactly is it?)
AI is not a movie robot: Difference between fiction and reality.

How it works (simply): The image of the "giant library": AI has read billions of books and uses them to predict the continuation of a sentence or create an image.

Where is it already present? Spell checkers, Netflix/YouTube suggestions, GPS, and voice assistants (Siri/Alexa).

2: Using AI to make life easier
Conversing with AI (ChatGPT, Claude, Gemini):

Ask him to write an administrative email or a complex letter.

Summarize a long newspaper article or document.

Plan a travel itinerary or find recipe ideas with what's left in the fridge.

AI for creativity and memory:

Generate images to illustrate a birthday card (Midjourney, DALL-E).

Using AI to restore or colorize old family photos.

3: Learning to "talk" to AI (The Art of the Prompt)
The context method: Why "Give me a cake recipe" is less effective than "I am allergic to gluten and I am hosting 4 people, give me a simple chocolate cake recipe".

The expert's role: Learning to tell AI "Act like a travel guide" or "Act like an expert gardener".

4: Precautions and Critical Thinking (The Survival Guide)
"Hallucinations": Understand that AI can make false claims with complete certainty (never take medical or legal advice from AI without verification).

Privacy protection:

Never give sensitive data (social security number, passwords, bank details) to an AI.

Knowing that everything we write to the AI is potentially used to train it.

Spotting "Deepfakes":

How to recognize a doctored image or video (details on the hands, strange reflections, slightly metallic voice).

Verify the information: the golden rule of cross-referencing sources.

5: Ethics and Impacts (To go further)
Copyright: Who owns an image created by AI?

The environmental impact: The water and energy consumption of AI servers.

The future: Will AI replace us or assist us?

Online math courses for Belgian, French, and Swiss high school and university students – Effective and personalized preparation

14.08 Fr /Std

As an experienced mathematics teacher, I offer online private tutoring for high school and university students in Belgium, France, and Switzerland. My courses cover the entire curriculum, from secondary school through the first years of university in science, economics, or engineering.
- For high school students: strengthening of the basics in algebra, geometry and analysis, homework help, preparation for official exams (Higher Secondary Education Certificate, Baccalaureate, specific tests).
- For students: advanced university mathematics with a focus on analysis, linear algebra and numerical methods.
My teaching methods are adapted to the online format, with clear explanations, interactive exercises, and personalized support to ensure progress. The first session is for a precise assessment of your needs.
Key points
- Flexible courses (1 to 2 hours per session) via videoconference using Zoom or Teams.
- Use of digital tools to facilitate understanding (interactive whiteboards, screen sharing).
- Direct application to Belgian programs and requirements of school and university examinations.

Khalil

4.89

(65)

If you’ve ever felt that science and math are difficult, it’s probably because no one showed you how to think like a problem solver.
In my classes, you’ll learn not just formulas or code but how to truly understand concepts, apply them, and build strong logical intuition.

I teach:
• 🔢 Mathematics: From algebra and calculus to applied problem-solving for real-world use.
• 💻 Computer Science: Coding fundamentals (Python, C++), algorithms, and logical thinking for beginners and intermediate learners.
• ⚛️ Physics: Mechanics, thermodynamics, and practical examples that make abstract ideas simple and visual.

As a Software Engineer and Master’s student in Engineering at Nagoya University, I bring both academic knowledge and hands-on experience from real projects. My teaching approach is interactive, visual, and deeply focused on understanding over memorization.

Let’s turn complex problems into clear, step-by-step insights — and make learning something you genuinely enjoy.

Nadine

4.89

(65)

(for English description see below)
Hi there,
I offer tutoring for math and science subjects here.
Regardless of whether it's school, university or work - having to learn to pass a subject is neither fun nor much point, as you'll soon forget most of it.
But how can it be better?
I have experienced several times how much of success depends on the emotions associated with learning. That's why I'll try to create an environment in which you feel free to make mistakes - because mistakes are important for learning! I rely on understanding, patience and curiosity to develop a positive relationship with learning rather than applying pressure.

Following the neurobiologist Gerald Hüther, I see the art in setting just the right big challenges to be exciting but not frightening, so that you automatically develop joy in discovery.
I would be happy to have an introductory meeting in order to take your needs and wishes into account from the outset.
Background information about me:
I am a qualified engineer (mechanical engineering) with 3 years of work experience, as well as a master's degree in bionics (cross-sectional discipline between biology and engineering) and a PhD in environmental protection of mountain regions. I was active as a youth leader at the Alpine Club.
I have been giving tutoring lessons on the side ever since I was at school.
I am pleased to meet you.

Hello,
I offer tutoring for maths and science subjects.
Whether at school, university or work - learning to pass a subject is neither fun nor makes much sense, as you soon forget most of it.
But how can it be better?
I have learned many times how much success depends on the emotions associated with learning. That's why I try to create an environment in which you feel free to make mistakes - because mistakes are important for learning! I focus on understanding, patience and curiosity in order to develop a positive relationship with learning rather than exerting pressure.

Following the neurobiologist Gerald Hüther, I see the art in setting just the right amount of challenges to be exciting, but not frightening, so that you automatically develop the joy of discovery.
I would be happy to meet with you to discuss your needs and wishes from the outlet.
Background information about me:
I am a graduate engineer (mechanical engineering) with 3 years of work experience, as well as a master's degree in bionics (cross-sectional discipline between biology and engineering) and have a PhD in environmental protection of mountain regions. I was active in the Alpine Club as a youth leader.
I have been tutoring on the side since my own school days.
I look forward to getting to know you.

Armend

4.89

(65)

Bachelor's student in economics and management offers private lessons in mathematics.
I obtained my bachelor's degree with a specialization in mathematics and physics and I have sufficient knowledge in mathematics, physics, chemistry, German, English and French.
In my teaching, I adapt to the learning conditions and the student's life in order to strengthen their self-confidence and ensure that they understand the lessons and progress.

My goal is to create an effective learning environment. I rely on the student's course, which I supplement if necessary with additional information.

Pia

4.89

(65)

You are a university student and have trouble with your math courses? Don't fret, I'm here to help! It doesn't matter whether you are a math student or from a different major, whether you are from an applied background or struggle with pure maths - the lessons will only cover what you need. Mathematics has a lot to do with practice and getting familiar with the way of thinking logically. With my help and guidance, I am sure you will become confident in solving problems and understanding mathematical concepts.

The lessons will be tailored to your needs and their structure depends highly on you: usually it is a mixture of repeating the content, solving exercises together, summarising important concepts and talking about exercises you tried yourself at home. The topics, content, pace and methods of learning will be adjusted to your needs, ensuring that you get the most out of my lessons. Besides the lessons, you will get "homework" to work on to strengthen your skills and independent working.

Topics include, but are not limited to:
-Trigonometry
-Geometry
-Linear Algebra
-Calculus (limits, derivation, Integration, etc.)
-Set Theory and Metrics
-Analysis (functions, Taylor series, etc.)
-Algebra (Group/Ring/Field theory, Galois theory, etc.)
-Number Theory (sequence and series)
-Probability (statistics, stochastic processes, etc.)
-Logic and Proofs
-Numerical Analysis
-(Algebraic) Topology (Homology theory, etc.)

If you have another topic in mind that you really need help with, just send me a message!

Whether you need someone that explains the concepts to you or just someone to practice exercises with - I am sure I can help you. You have an exam soon and want to review the main topics? No problem! You have a very specific problem, question or topic that you need help with? I'm here to answer any questions!

The most important part of my lessons is, however, to ensure a safe and comfortable environment - I have no issue with explaining the same concept over and over again until I am convinced that you have understood it. It is important to me that you feel comfortable in asking any questions - I want to show you, that Math is more than a subject and that it can be fun!

Baia

4.89

(65)

Struggling with school math or aiming for exam excellence? In this class, I make complex topics simple, clear, and even enjoyable. From middle school to university level math, I adapt to every student's level and mindset. Whether it's building strong foundations or mastering advanced concepts, you or your child will walk away feeling confident, capable, and ready to shine.

✨ Personalised approach
📚 Clear explanations + real understanding
🏆 Proven results in IB, OMPT, VWO & more

Let’s turn “I don’t get it” into “I’ve got this!”
Book the first session and see the difference.

Narayan

4.89

(65)

Mathematics course(especially from the entrance exam perspective) taught by an engineering graduate with over 14 years of teaching experience in mathematics up to the undergraduate level. I also have more than 3 years of experience in teaching and guiding standardized tests such as the GRE and SAT. I can help you learn these standardized courses (GRE, SAT, and even TOEFL) more effectively.

I offer mathematics lessons for various levels of students, including Bachelor students, IB (Math SL and Math HL) students, A-level students, European S6 and S7 level students, GCSE students, and IGCSE students.

I also provide science courses in Physics and Chemistry for students up to the European upper secondary level, as well as IB and A-level students. Additionally, I offer Biology lessons for students up to the European Secondary level, GCSE level, and IGCSE level.

Currently, I am teaching a diverse range of students, including:
- GCSE students
- IGCSE students
- IB students
- European School students
- AS/A-level students
- Lycée Vauban students
- Athénée de Luxembourg students

I also provide homework help for school students, and student progress can be assessed through periodic tests as per the requirements of parents or the students themselves.

Note:
Please note that while some of my students may have courses taught in French, German, or Swedish, my primary teaching language is English. As the subject is mathematics, it is generally easy to understand the task at hand, and I explain the answers in English.

Shyam

4.89

(65)

Learn Vedic Math from a Certified Teacher
Unlock the power of fast and efficient math calculations with Vedic Math! I offer courses for learners of all levels, from beginners to advanced, teaching easy-to-master techniques for faster math problem-solving.
Course Topics Include:
•Addition, Subtraction, Multiplication, and Division
•Polynomials
•Linear Equations
•Quadratic Equations
•HCF & LCM
•Squares, Cubes, Square Roots & Cube Roots

Classes are held via Zoom, where you'll learn various tips and tricks to solve math problems quickly and easily.
Key Methods Taught:
•Dot Method
•Vinculum to Normal Numbers
•Normal Numbers to Vinculum Numbers
•Base Method
•Dot and Stick Method
•Right Neighbor Rule
•Left Neighbor Rule
•Nikhilam Method
•Arthur Benjamin Method

What You Can Expect:

• Tailored lessons based on your individual needs and learning style
•Access to unique learning materials and lesson notes
•Continuous support and correspondence between lessons

Kevin

4.89

(65)

For many years, I have successfully supported Swiss students in the fields of statistics, data analytics, machine learning, and artificial intelligence. I have gained extensive experience using R as a statistical programming tool and know exactly what students in Switzerland are required to do. I have numerous sample projects, datasets, and exam questions at my disposal and have prepared many students for their assignments and exams in a targeted, sustainable, and highly successful manner. My focus is on explaining complex statistical procedures, algorithms, and data analyses in an understandable way, demonstrating them in a practical way, and building confidence in the secure handling of data. My goal is not only to improve grades, but also, in the long term, to develop a deep understanding of data-driven questions and modern technologies such as machine learning and AI, which are crucial in later professional life.

► How do I teach?

►I attach great importance to ensuring that my students truly understand statistical concepts, data analytics methods, machine learning, and AI models, rather than just applying them mechanically – this is how we achieve sustainable success in statistics, data analytics, and modern technologies.

►My success is based on my ability to flexibly adapt my teaching style to the individual needs of students in statistics, data analytics, machine learning and AI, including topics such as regression methods, logistic regression and other machine learning algorithms.

►I use practical, lively examples from statistics, data science and AI to clearly explain abstract concepts such as hypothesis testing, analysis of variance, linear and nonlinear models and to anchor them deeply in the memory.

►With patience and clarity, I break down complex statistical analyses, machine learning models, and data processes into their essential components so that no student is overwhelmed and can build a solid foundation in statistics, data analytics, and AI.

►I am convinced that trusting collaboration is crucial to reducing uncertainty in statistics or data science and creating a productive learning atmosphere.

►I offer intensive exam preparation and project support in statistics, data analytics, machine learning and AI, develop strategies to combat exam anxiety with my students and train them on real data sets and complex algorithms.

►As an experienced online tutor for statistics, data analytics, machine learning, and AI, I use modern tools such as interactive whiteboards and live coding sessions in R to make teaching as efficient and practice-oriented as possible.

►Locations: I teach statistics, data analytics, machine learning, and AI at your home, online, or by appointment – flexible, professional, and tailored precisely to your needs.

Álvaro

4.89

(65)

I am a student at the Polytechnic University of Valencia. I have a degree in Aerospace Engineering and am currently pursuing a Master's degree in Aeronautical Engineering. I scored 13.8/14 on the university entrance exams. I am familiar with the exam format and can help students prepare for them. I can also reinforce knowledge from other levels, making high school much easier. I have over five years of experience tutoring students to prepare for the university entrance exams and first-year university subjects. I also help reinforce fundamental concepts in lower grades to ensure students are as prepared as possible for the university entrance exams.

Jihen

4.89

(65)

Mathematics is a key subject in the Baccalaureate exam and requires clear understanding and regular practice.
In this course, I help Bac students master mathematics step by step, following the official program. Lessons are explained in a simple and structured way, with many examples and exam-style exercises.
The course focuses on understanding methods, avoiding common mistakes, and gaining confidence to solve problems independently.
This class is suitable for students who want to improve their level, prepare seriously for the Bac exam, and achieve better results.

Jasmin

4.89

(65)

Do you want to improve your math skills? Whether for school, exam preparation, or simply as a leisure activity.

I've been teaching math for about 15 years. Over the years, I've met a wide variety of people, including students of all ages and from all over the DACH region (Germany, Austria, Switzerland), as well as students from German schools abroad. My youngest student was 4 years old and my oldest was 56!

During the final stages of my studies, I increasingly focused on teaching until I started working full-time as a tutor about four years ago. Now I tutor students of all ages in Math, Biology, German, and English.

I want my students to enjoy learning. Accordingly, my teaching style is very relaxed. No two lessons are the same, as each one is tailored to the individual student. What I've learned over the years is that every student thinks and learns differently.

I haven't obtained a formal certification in dyscalculia, but I have occasionally tutored children with mild dyscalculia. Depending on the severity of the dyscalculia, I would prefer to refer you to a specialist.

Carmen

4.89

(65)

Diplomierte Lehrer bietet individuelle Lehrmethoden, Hilfe bei der Vorbereitung von Prüfungen und/oder Arbeiten. Mein Ziel ist es, dem Schüler zu helfen, Fortschritte zu machen, ohne ihn zu überlasten. Ich gebe nach jeder Unterrichtsstunde Aufgaben und erstelle regelmäßige Fortschrittsberichte.

Partha

4.89

(65)

Mastering the Universe: Mathematics & Physics Excellence

Unlocking potential from foundational basics to advanced problem-solving.

Overview
Welcome to a learning environment where numbers and the laws of nature come to life. Whether your child is just starting their journey with arithmetic or navigating the complexities of quantum mechanics and calculus, these classes are designed to bridge the gap between "knowing" and "understanding."

Philosophy
I believe that Mathematics and Physics are not just subjects to be memorized, but languages to be spoken. By focusing on conceptual clarity, logical reasoning, and real-world application, we transform academic challenges into confidence-building milestones.
Tailored Approaches by Level
1. Primary Level: Building the Foundation (Grades 1-5)

At this stage, curiosity is our greatest tool. I focus on making abstract concepts tangible through interactive learning.

Mathematics: Developing "number sense," mastering mental math, and understanding geometry through shapes and space.

Physics (Integrated Science): Exploring how the world works—why things fall, how light moves, and the basics of energy and force.

Goal: To eliminate "math anxiety" early and foster a lifelong love for inquiry and logic.

2. Secondary Level: Mastery & Application (Grades 6-12)

As the curriculum intensifies, we shift toward analytical thinking and exam readiness.

Mathematics: Comprehensive coverage of Algebra, Trigonometry, Calculus, and Statistics. We focus on the "why" behind the formulas to ensure long-term retention.

Physics: Deep dives into Mechanics, Thermodynamics, Electromagnetism, and Optics. We break down complex problems into manageable, logical steps.

Goal: To equip students with the problem-solving skills needed for top-tier board exams and competitive entrance tests.

Why Join This Class?

Conceptual Clarity: I move beyond rote learning to ensure every student understands the underlying principles.

Interactive Problem Solving: Students are encouraged to ask "why" and "how" until the concept clicks.

Personalized Pace: Small group sizes allow for individual attention, ensuring no student is left behind and high-flyers remain challenged.

Regular Assessments: Consistent feedback through mock tests and progress reports to keep students on track for their academic goals.

"Mathematics is the music of reason; Physics is the poetry of the universe. Let’s learn to compose them together."

Mohamed

4.89

(65)

This course is aimed at students who need support in mathematics. The goal is to clearly explain fundamental mathematical concepts and systematically close knowledge gaps.

During the lessons, I adapt to each learner’s individual level and needs. Complex topics are explained step by step to ensure they are easy to understand. I place strong emphasis on ensuring that students not only understand the solutions, but are also able to apply the methods independently.

The course is suitable both for improving grades and for targeted preparation for tests and exams. Additionally, I focus on strengthening students’ confidence in dealing with mathematics and teaching a structured approach to problem-solving.

Vivienne

4.89

(65)

Hi! I'm Vivienne, a Business Administration student at the University of Zurich. I offer personalized one-on-one lessons in Spanish, English, Math and Business Administration for students up to high school/canton school level. I adapt my teaching style to your individual goals and pace so you feel comfortable and make real progress. I'm patient, reliable and genuinely motivated to help you succeed!