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Exam preparation in advanced mathematics: Bachelor's, Master's and engineering studies

From 22.96 € /h

1. Algebra and linear algebra
The foundation of 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 and Functional Analysis
Metric spaces and topology: open and closed sets, compactness, convexity.
Normed 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 using algorithms and high-performance computing.
Solving nonlinear equations: bisection, Newton-Raphson and fixed-point methods.
Numerical integration: rectangle rule, trapezoidal rule and Simpson's rule.
Numerical matrix analysis: solving systems of equations (Gauss, LU, Cholesky), eigenvalue calculations and conditioning.

Extra information

Location

Online from Luxembourg

About Me

Dr. Raouf holds a PhD in Mathematics and has extensive experience in higher education and personalized academic support. I guide high school students (both academic and general) and university students toward excellence.
My teaching method is based on simplifying abstract concepts and mastering problem-solving methods.
1. Secondary Education
Analysis: In-depth study of functions (logarithms, exponentials), limits, derivatives and integral calculus.
Linear Algebra: Analytic geometry in space, vectors, and systems of equations (Gaussian method).
Complex Numbers: Algebraic, trigonometric forms and resolution in .
Preparation for the Final Examination: Intensive work on past exam papers (Past papers).

2. Higher Education
Calculus & Real Analysis: Sequences, series, generalized integrals.
Matrix algebra: Vector spaces, diagonalization, eigenvalues.

My Online Methodology

Digital tools: A shared Word document is used in real time to explain the lesson and complete exercises. This document is sent to the student as a PDF at the end of the lesson.
Personalized follow-up: Sending a summary of the lesson and application exercises after each session.

Education

Master's degree in Mathematics. PhD in Applied Mathematics. Mathematical researcher at the Modeling Laboratory of the National Engineering School of Tunis. My areas of expertise in mathematics range from the foundational concepts acquired during secondary education to advanced mathematics at the Bachelor's and Master's levels, as well as preparatory classes for engineering studies. I am also proficient in the numerical analysis and functional analysis curricula taught in engineering schools.

Experience / Qualifications

A career spanning more than 20 years in an engineering school in Tunisia whose training programs are EUR-ACE accredited.

Age

Teenagers (13-17 years old)

Adults (18-64 years old)

Student level

Beginner

Intermediate

Advanced

Duration

60 minutes

The class is taught in

French

English

Arabic

Skills

Math

Numerical analysis

Algebra

Reviews

Availability of a typical week

(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 for seniors and the use of basic software

22.96 € /h

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

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

18.98 € /h

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.

Benoit

5.0

(40)

I am a qualified and experienced mathematics tutor. Graduated from the Free University of Brussels in 2011, I started my career by teaching remedial courses in different schools in Brussels. I then specialized in individual academic support by following educational training at the Harvard Graduate School of Education. I have been giving private mathematics lessons daily for over ten years.

The students who follow my private lessons benefit from personalized support. The first session is devoted to an in-depth assessment of the student's mathematical knowledge. The objective is to detect its weak points and understand their origin in order to adapt my courses to its needs. I develop a tailor-made remediation program for each of my students aimed at filling each of their gaps. Over the course of the sessions, the student builds a solid foundation for learning and regains self-confidence. At the same time, I help him acquire a work methodology that allows him to gradually become autonomous in his studies.

I have a thorough knowledge of the mathematics curriculum for middle and high school (from 6th to 12th grade). I am also qualified to support students in preparing for international exams such as the SAT, the OMPT, and the International Baccalaureate (IB) in all its variations: Analysis and Approaches (AA SL/HL) and Applications and Interpretation (AI SL/HL).

Throughout my years of training, I studied and developed numerous techniques that facilitate learning mathematics. The strength of my teaching approach lies in my ability to explain, in simple terms, anything a student finds complicated. I am passionate about this profession because it offers me the opportunity to guide struggling students toward success. It is a true pleasure to see them progress and rediscover their connection with the fascinating world of mathematics.

I offer private tutoring in Paris (at the student's home) or remotely (online). My online lessons take place on an interactive whiteboard. This whiteboard is specifically designed to facilitate student/teacher interaction online. Thanks to this teaching tool, my online lessons are just as effective as in-person lessons. The student only needs an internet connection and a computer, tablet, or smartphone to participate.

Raef

5.0

(40)

Graduated and experienced teacher with results from ALL of my students with honors, I give private or group lessons in Mathematics - Analysis - Matrices - Statistics - Algebra - Geometry - Physics - Mechanics - Electricity - Chemistry - Organic Chemistry - Biology, Geology to students from primary to Terminale, 1st year and 2nd year of university for online courses by a PROFESSIONAL method on a special education platform through a link that serves as a table that includes spaces, dozens of pages, equipped with tools (pens of different colors, ruler, geometric tools, eraser, etc.) and the possibility of saving, writing and projecting the work on this board.
This course is also intended for students of Lycée, CNED and those of the English program (IB Interntaional School or European section in english)
Special reduced rate offer for the group of 4 students only in virtual class The hourly rate will be shared by the 4 students.
The conversation is carried out by Skype or Zoom.
Do not hesitate to write to me for more information.

Bibek

5.0

(40)

Hi! Welcome! I am a Ph.D. researcher in Physics at the University of Cologne, Germany. Recently, I graduated from the University of Groningen in the Netherlands with a Master's degree in Nanoscience (w/ cum Laude). I offer private tutoring (for high school and/or university-level students) so you can understand the fundamental concepts and excel in your studies. I have teaching experience of 5+ years in Physics and Mathematics to both high school and university-level students.

This class aims to provide an overview of calculus and linear algebra and focuses on the fundamental mathematical tools and concepts, such as limits, differentiation, and integration. Building on these basic concepts, we will review methods for solving problems related to optimization, linear differential equations, and matrix algebra.

Outline of the course:
1. Calculus:
1.1 Limits of functions
1.2 Continuity, types of discontinuities, intermediate value theorem
1.3 Differentiation (or derivative), slope, secant, tangent
1.4 Rules and theorems for differentiation, power rule, product rule, chain rule
1.5 Derivatives of exp, log, and trigonometric functions
1.6 Implicit differentiation and derivative of inverse functions
1.7 Rolle's theorem, mean value theorem, critical point, maximum/minimum of a function
1.8 First and second derivative tests, inflection points
1.9 Anti-derivative, indefinite integral, integration by substitution, integration by parts
1.10 Definite integral and its application (area between curves, application in physics)\
1.11 Optimization and linear differential equations

2. Linear Algebra:
2.1 Vectors and scalars in Euclidean space, vector arithmetic, scalar product, cross product
2.2 Equations for lines and planes, vector spaces, linear independence, span, basis, dimension
2.3 Linear transformations, coordinates, and representation of linear transformations by matrices
2.4 Matrix operations: matrix multiplication, transpose, determinant, inverse, and Hermitian conjugate
2.5 Systems of linear equations, Gaussian elimination
2.6 Eigenvalues and eigenvectors
2.7 Range, kernel, and rank-nullity theorem

and many more...

*Note that the sessions will be held online (via Discord/Zoom/Microsoft Teams).

Mohamed

5.0

(40)

As a high school teacher with a Master's degree in mathematics and 11 years of experience in face-to-face and online teaching, I offer qualified and competent private lessons for all levels, ranging from high school TC-SC 1Bac Sc-SM to Bac PC-SM, through middle school and classes of 2nd and 1st general Terminale specialty of the French system, as well as for levels 5th, 4th and 3rd of middle school, and preparation for the baccalaureate and competitions .

I emphasize the method, with a rigorous, personalized approach adapted to the rhythm of each student in order to help him progress while regaining confidence in himself. My job is to identify each student's shortcomings, organize their time and manage their priorities.

I obtained a success rate of 100% for my final year baccalaureate students, 75% of whom obtained a good or very good mention. Some of them have joined the biggest business and engineering schools, as well as prestigious preparatory courses.

I offer online or face-to-face lessons.

Baia

5.0

(40)

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.

Rania

5.0

(40)

The SAT exam is one of the major steps you need to go through in your life; it's a step that is going to determine your college, your university, and your future as a whole. As with a lot of things in life, it can be a hard step, and there is no shame in asking for help. Here comes my role: I will help you overcome your problems and your difficulties. My job here is to help you achieve your desired results and unlock your potential. Simply put, we will go through every lesson, every unit, and every chapter. We will understand the concept of each lesson, with clear examples to follow. After each one, you will be tested, and after finishing your program, you will be tested on it. That's my plan for my students, so if you are interested, you can easily contact me.

Reza

5.0

(40)

I hold a PhD in Mechanical Engineering and currently work as a post-doctoral researcher in the Aerospace Engineering Faculty at TU Delft (Delft University of Technology).
Key topics that I teach for this course include:
• Calculus: Differentiation & integration, Multivariable calculus
• Linear Algebra: Matrices, vectors, systems of equations, Eigenvalues and eigenvectors
• Differential Equations: First- and second-order ODEs, Laplace transforms
• Complex Numbers: Polar form, Euler’s formula
• Vector Calculus: Gradient, divergence, curl, Line and surface integrals
• Series & Transforms: Taylor series, Fourier series

I understand that not all teachers excel in teaching Engineering and Mathematics courses and explaining their importance to students. Courses with strong mathematical backgrounds may become boring for students who lack a solid mathematical basis. To address this, I take a student-centered approach, starting from the basics to actively engage all students, including those with weaker mathematical backgrounds. I also provide practical examples to demonstrate the real-world significance of what they are learning, inspiring and fostering their interest in the subject matter.

If you have any additional questions before starting a class, please feel free to ask me. I am here to assist! :)

Eugene

5.0

(40)

I am a 2021 IGCSE graduate and a 2023 IB graduate, now studying Veterinary Medicine at the University of Edinburgh. Having recently completed these programmes myself, I understand the challenges students face and how to overcome them effectively.

With 2 years of experience teaching the IGCSE and IB syllabus, I specialize in helping students master subject content, strengthen exam techniques, and build confidence. My lessons are tailored to each learner’s pace and goals, ensuring steady progress and measurable results.

What I offer:
- IB & IGCSE syllabus coverage across core and extended levels
- Exam preparation with past paper practice and detailed feedback
- Structured guidance for Internal Assessments (IA), Extended Essays (EE), and coursework
- Study and time-management strategies designed to reduce stress and boost performance
- A supportive, relatable learning environment from someone who has recently been through the same exams successfully

Zeinab

5.0

(40)

With a doctorate in mathematics and experience as a university lecturer, I have dedicated several years to teaching students in France and internationally. I support students of varying levels, emphasizing a clear, progressive, and comprehension-focused approach.

Maham

5.0

(40)

My lessons are designed to help students understand Maths and Science in a simple, step-by-step way. I explain topics clearly and adapt my teaching to each student’s level and learning pace.

I can help with:
Homework support
Exam preparation
Understanding difficult topics
Building strong foundations in Maths and Science

Subjects covered include Maths and Science depending on the level.

My teaching method focuses on:
Clear explanations with real-life examples
Practice exercises to reinforce learning
Identifying and improving weak points
Building confidence for exams and tests

Lessons are interactive and are adapted to the student’s needs so they can progress effectively and feel more confident in their abilities.

Alessandro

5.0

(40)

I offer personalized tutoring and support in Mathematics, Physics, Chemistry, and Science for middle school, high school, and early university students.

My goal is to make scientific subjects accessible and engaging. Rather than just memorizing formulas, my approach focuses on understanding the core concepts so that problem-solving becomes logical and intuitive.

Whether you need to catch up, build your confidence, or deepen your understanding of the material, I am here to help you reach your academic goals in a relaxed and supportive environment.

Antonio

5.0

(40)

Algebra 1 is a fundamental component of math used in many higher level courses and jobs. It mainly helps students with learning how variables function and how patterns and different factors applied to a variable equation impact it. Concepts of the x and y axis, slope, and the quadratic formula are mainly taught here. There are also real world applications to algebra that are taught in Algebra 1.

Alessandra

5.0

(40)

I am an experienced science teacher currently working at an international school in Switzerland. I offer support in Biology, Chemistry and Mathematics for secondary school, IGCSE and A-Level students.

My lessons are tailored to each student’s needs and focus on building confidence, improving understanding and developing effective study methods. I explain concepts in a clear and structured way and provide support with homework, exam preparation and revision.

I have experience working with students from different educational backgrounds and levels of ability. My goal is to create a supportive and motivating learning environment where students can improve steadily and achieve their academic goals.

Lessons can be held online or in person depending on location and availability.

Joshua

5.0

(40)

Making Mathematics Make Sense — For Every Kind of Learner

Do you struggle with maths, or simply want to get better? You're in the right place.

My name is Mr. Joshua, a qualified Mathematics teacher with experience teaching students across all ages and levels — from basic arithmetic to advanced calculus, algebra, and trigonometry.

Every student learns differently, so I tailor each session around *you* — your pace, your gaps, your goals.

What you can expect:
- A patient, encouraging environment where no question is too basic
- Clear explanations tailored to your pace
- Real-life examples that make concepts click
- Exam preparation when needed
- Flexible sessions that adapt as you grow

Whether you're a complete beginner or preparing for an important exam — I'm here to help you build real confidence in mathematics.

Let's turn your biggest maths challenge into your strongest subject.

Eleni

5.0

(40)

“I support children with special educational needs through personalized teaching methods, patience, and encouragement. My goal is to help every student build confidence, improve skills, and enjoy learning. I believe that every child learns differently, and I adapt my approach to meet each student’s unique strengths and needs while creating a safe and positive learning environment.”