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Since January 2020
Instructor since January 2020
Math and math for Test prep tutoring - Private Tutor
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From 58 C$ /h
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Hi! I have been a private math and math for test prep tutor for over 12 years, I love to help students quickly build math knowledge and achieve their goals. I have also taught engineering courses at the university level, as well as math at two private schools and a learning center.

I work with all levels of K-12 math including algebra, geometry, trigonometry, precalculus, calculus, AP and IB curriculum, and college math. I also help students prep for math competitions. I especially enjoy working with international students.

I am also experienced with math for test prep for the SAT, ACT, PSAT, SSAT, ASVAB, GRE and any other standardized test . Test prep requires a different approach than regular classroom work and I will work with you on test-taking techniques and strategies I have developed.

I love math, and I hope to support you in your math journey! I look forward to meeting you!
Extra information
Our meeting will be in a very easy to setup online sessions from wherever you are.
You will need your own computer with audio and video capabilities as well as a good internet connection.
Location
location type icon
Online from United States
Age
Children (7-12 years old)
Teenagers (13-17 years old)
Adults (18-64 years old)
Seniors (65+ years old)
Student level
Beginner
Intermediate
Advanced
Duration
30 minutes
45 minutes
60 minutes
90 minutes
120 minutes
The class is taught in
English
Availability of a typical week
(GMT -04:00)
New York
at teacher icon
Online via webcam
Mon
Tue
Wed
Thu
Fri
Sat
Sun
00-04
04-08
08-12
12-16
16-20
20-24
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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.
verified badge
I am a native American English speaking instructor, editor, and journalist from Florida specializing in teaching, instruction, exam prep, and text correction for a wide range of professionals & students across Belgium.

Approaching from a true native's perspective, I instruct and assist with both educational and business English in a multi-faceted nature covering a wide range of areas including comprehension, conversation, grammar, and situational skills, in addition to working on general language skills and accent training.

My past & present clients have included: professionals from all four major EU institutions, the Belgian government, various NGOs, and musicians, journalists, engineers, as well as a variety of other professions in addition to traditional students. As well, I can provide extensive help and training with the EPSO, IELTS, and TOEFL exams.

I have also written, edited or proofread a variety of academic papers, theses, applications, CVs, and other documents for numerous satisfied academic and professional clients.

I have spent my entire childhood and adult life in the United States before completing a master's degree in Political Science and European Politics at KU Leuven. I have an extensive knowledge and experience of English grammar and literature, as well as current and past working experience in journalism (Anti-Competition Law and European Policy at the Policy and Regulatory Report) and both European and American politics.

I also handle correction of text, editing, proofreading and ghostwriting, with weekly and monthly rates possible. My transportation costs are included.
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With over 18 years of experience, I give private lessons in Mathematics - Analysis - Matrices - Statistics - Algebra - Geometry - Physics - Chemistry - Biology, Geology to students in French program brevet, secondary and Terminale or international program in English (Grades 8, 9, 10, 11, 12) or competitions and preparatory classes for medical or first year university either at home or via the internet online using virtual classroom methods.
The online method is easily done via a link that serves as a shared interactive whiteboard for writing, typing, and projection, unlike Zoom or WhatsApp, through which communication is facilitated. This method is very modern, reliable, and guaranteed.
The results of my students and in particular the students of Terminale are superb with successes in mention very good, good and sometimes excellent. I give my students the working technique to get the best grades.
Homework help for CNED students.
For more information, do not hesitate to contact me, guaranteed response in a few minutes up to 10 hours maximum.
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I am a master student in quantitative economics and all of my courses are given in English. My goal is to help the student in solving the exercises and to understand the theory but above all to give an effective working method to make him independent in the pursuit of his studies.
verified badge
I'm a Natural Sciences student at the University of Birmingham looking to tutor science or maths online over the summer. I can tutor any level from KS1 - GCSE for physics, and KS1 - A Level for chemistry, biology, and maths. I aim to give confidence and enjoyment in the subject, working with my student's own interests as well as following a syllabus. I am flexible to work with what you want to achieve.

I have two years tutoring experience, especially with home-educated children, and can provide references if needed. I am DBS checked with GirlGuiding UK.
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I specialize in online physics and maths tutoring for A-Level and GCSE level students. I aim to give fun and engaging tutorial sessions, lifting problems out of the textbook and applying them to the world around us. My tutoring is flexible and I will adapt lessons to the needs of the student.

My background is in engineering and I am currently a PhD researcher in aerospace specializing in spacecraft propulsion and plasma physics. I have also been awarded a NASA Fellowship invitation.
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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.
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I am a Math and Physics tutor with over 10 years of experience, backed by an MIT background and training from top technical schools. My lessons are unmatched, blending charisma, passion, and innovative teaching methods to create a magical learning experience. I focus on highly personalized, one-on-one sessions, understanding each student’s unique mindset to unlock their full potential.

Teaching is my true passion! I genuinely enjoy sharing my knowledge and skills with those in need. My friendly and supportive attitude allows me to establish a connection with every student right from the first lesson. So, if you're feeling demotivated and down, don't worry! I'm here to help you find the motivation you need for both academic and personal success.

If you have any questions, please feel free to contact me anytime here. I will respond to you as soon as possible!
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My name is Fawzi, and I am a French language teacher. Since 2012, I have been giving private lessons online. My objective is to support learners towards success in the DELF (Diploma of Studies in French Language) or the DALF (Advanced Diploma in French Language), as well as the TCF (French Knowledge Test). I have had the pleasure of helping many students of different nationalities through my online courses. For me, helping enthusiasts practice the French language is an enriching experience, because I understand the importance of success in the lives of ambitious people.

I speak Arabic, French, Spanish, a little English and a little Turkish. During my classes, I explain concepts in French, Arabic or Spanish, depending on your preference. At the end of each session, I offer exercises to do as homework, in order to identify your gaps and monitor your progress.

Here are some essential points to know about the DELF and DALF:
- The DELF (Diploma in French Language Studies) and the DALF (Advanced Diploma in French Language) are two high-quality official diplomas. They are aligned with the levels of the Common European Framework of Reference for Languages and cover the following six levels, from the most basic to the most advanced: A1, A2, B1, B2, C1, C2. These diplomas are suitable for all ages and all audiences.
- The DELF B2 and, increasingly, the DALF C1, provide access to French, European or French-speaking universities, as well as certain Grandes Ecoles.

If you plan to take DELF or DALF exams, or if you want to improve your level, do not hesitate to book your sessions with me to start preparation. I am available !
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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).
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Learn Spanish in a fun, easy, and engaging way with a certified teacher, official DELE examiner, and IB-trained educator.

✨ FLUENCY · EXAMS · LIVING IN SPAIN · TRAVEL & BUSINESS ✨

Are you planning to travel, study, work, or live in Spain or another Spanish-speaking country? Are you preparing for the DELE or another official Spanish exam, such as the SIELE, IB, or IGCSE? Are you a complete beginner, or do you already know the grammar but still find it difficult to have a fluent conversation?
You’re in the right place to take that big step!

I’m a certified Spanish teacher and official DELE examiner at the Instituto Cervantes, with:

🎓 PhD candidate in Applied Linguistics for Language Teaching
🎓 Master’s in Spanish as a Foreign Language
🎓 Master’s in International Education and Bilingualism with IB certification

I teach children, teenagers, and adults at all levels, with lessons tailored to your goals:

✅ DELE and exams preparation
✅ Speaking fluency and confidence
✅ Spanish from beginner to advance
✅ Real-life communication skills

Each class includes personalized planning, clear objectives, and close guidance so you can make progress from the very first lessons.

Take the next step in your Spanish journey, let’s start!

My lessons combine:
🗣️ An active communicative approach
📚 Clear and practical grammar explanations
🎯 Real-life language use and confidence-building activities

If you are preparing for exams, I provide:
✅ Structured exam preparation
✅ Practice with all exam sections
✅ Personalized feedback and strategies
✅ Continuous support to help you feel confident on exam day

I teach online from Japan with a flexible schedule, and I am happy to adapt lessons to your availability while helping you achieve solid and measurable progress.

Whether your goal is:
✈️ Traveling
💼 Professional communication
🎓 Academic purposes
📖 Official certification
💬 Improving fluency and confidence

I would be delighted to support you on your Spanish-learning journey.

📩 Contact me, and together we will create your personalized study plan!
And if you enjoy the lessons, I would truly appreciate your review 😊🌟

¡Nos vemos en clase! — See you in class!


I offer individualized programs for all levels of the Common European Framework of Reference (A1-C2), specializing in:

📘 General Spanish (Beginner to Advanced)
Progress from beginner to advanced level with a structured, dynamic, and fully communicative method. Classes are completely personalized to adapt to your goals, learning pace, and learning style, helping you improve steadily and confidently.

🎯 Personalized Classes
Classes tailored to your specific goals: travel, work, studies, interviews, or presentations. Learn the Spanish you actually need with a practical and results-oriented approach from the very first class.

🗣️ Conversation Classes
Personalized training for concrete contexts such as travel, professional settings, academic environments, or presentation preparation. My classes focus on real conversation from the very first minute, always adapting to my students’ interests and goals. Ideal if you understand Spanish but don’t feel confident speaking yet, or if you want to become fluent quickly for real-life situations.


🎨🎲 Spanish Classes for Children (Ages 6*-12)
Dynamic and interactive lessons specially designed for children. We use games, songs, stories, and age-appropriate activities so they can learn Spanish naturally, creatively, and in a motivating environment * Children should already be able to read and write in their native language.

📝 Official Exam Preparation (DELE, SIELE, IB, IGCSE, CCSE)
Maximize your score with the guidance of a certified examiner. You will learn real exam strategies, practice with official materials, and receive continuous personalized support so you can take your exam with confidence and peace of mind.

🎓 Spanish for Admission to Spanish Universities
Linguistic and academic preparation designed to meet entry requirements and help you succeed in a university environment.

Feel free to tell me if you would like to focus on a specific skill or if you prefer a particular teaching style. Every program is carefully designed around your goals, interests, and learning preferences.

I teach online from *Japan* with a very flexible schedule, and I will be happy to adapt classes to your availability while guiding you toward solid and measurable progress.
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*Note: My availability on Apprentus may not be up to date. Please contact me to check my current availability.

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.
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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! :)
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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 3 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
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Many students lose confidence in math over the school year - not from lack of ability, but from pace, gaps, or one bad unit that never got resolved. This summer program (through mid-September) is built to fix that before the new year starts, not just review generally.
I work with middle and high school students, including IB, to close specific gaps not a broad refresher, but targeted work on exactly what's holding a student back. I bring the same structured, evidence-based approach I use with my university-admission students: identify precisely what's missing, build a plan around it, and track real progress, not just hours logged.
Best for students who want a calm, focused reset before the new academic year begins not for open-ended tutoring with no target
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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.
verified badge
I am a native American English speaking instructor, editor, and journalist from Florida specializing in teaching, instruction, exam prep, and text correction for a wide range of professionals & students across Belgium.

Approaching from a true native's perspective, I instruct and assist with both educational and business English in a multi-faceted nature covering a wide range of areas including comprehension, conversation, grammar, and situational skills, in addition to working on general language skills and accent training.

My past & present clients have included: professionals from all four major EU institutions, the Belgian government, various NGOs, and musicians, journalists, engineers, as well as a variety of other professions in addition to traditional students. As well, I can provide extensive help and training with the EPSO, IELTS, and TOEFL exams.

I have also written, edited or proofread a variety of academic papers, theses, applications, CVs, and other documents for numerous satisfied academic and professional clients.

I have spent my entire childhood and adult life in the United States before completing a master's degree in Political Science and European Politics at KU Leuven. I have an extensive knowledge and experience of English grammar and literature, as well as current and past working experience in journalism (Anti-Competition Law and European Policy at the Policy and Regulatory Report) and both European and American politics.

I also handle correction of text, editing, proofreading and ghostwriting, with weekly and monthly rates possible. My transportation costs are included.
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With over 18 years of experience, I give private lessons in Mathematics - Analysis - Matrices - Statistics - Algebra - Geometry - Physics - Chemistry - Biology, Geology to students in French program brevet, secondary and Terminale or international program in English (Grades 8, 9, 10, 11, 12) or competitions and preparatory classes for medical or first year university either at home or via the internet online using virtual classroom methods.
The online method is easily done via a link that serves as a shared interactive whiteboard for writing, typing, and projection, unlike Zoom or WhatsApp, through which communication is facilitated. This method is very modern, reliable, and guaranteed.
The results of my students and in particular the students of Terminale are superb with successes in mention very good, good and sometimes excellent. I give my students the working technique to get the best grades.
Homework help for CNED students.
For more information, do not hesitate to contact me, guaranteed response in a few minutes up to 10 hours maximum.
verified badge
I am a master student in quantitative economics and all of my courses are given in English. My goal is to help the student in solving the exercises and to understand the theory but above all to give an effective working method to make him independent in the pursuit of his studies.
verified badge
I'm a Natural Sciences student at the University of Birmingham looking to tutor science or maths online over the summer. I can tutor any level from KS1 - GCSE for physics, and KS1 - A Level for chemistry, biology, and maths. I aim to give confidence and enjoyment in the subject, working with my student's own interests as well as following a syllabus. I am flexible to work with what you want to achieve.

I have two years tutoring experience, especially with home-educated children, and can provide references if needed. I am DBS checked with GirlGuiding UK.
verified badge
I specialize in online physics and maths tutoring for A-Level and GCSE level students. I aim to give fun and engaging tutorial sessions, lifting problems out of the textbook and applying them to the world around us. My tutoring is flexible and I will adapt lessons to the needs of the student.

My background is in engineering and I am currently a PhD researcher in aerospace specializing in spacecraft propulsion and plasma physics. I have also been awarded a NASA Fellowship invitation.
verified badge
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.
verified badge
I am a Math and Physics tutor with over 10 years of experience, backed by an MIT background and training from top technical schools. My lessons are unmatched, blending charisma, passion, and innovative teaching methods to create a magical learning experience. I focus on highly personalized, one-on-one sessions, understanding each student’s unique mindset to unlock their full potential.

Teaching is my true passion! I genuinely enjoy sharing my knowledge and skills with those in need. My friendly and supportive attitude allows me to establish a connection with every student right from the first lesson. So, if you're feeling demotivated and down, don't worry! I'm here to help you find the motivation you need for both academic and personal success.

If you have any questions, please feel free to contact me anytime here. I will respond to you as soon as possible!
verified badge
My name is Fawzi, and I am a French language teacher. Since 2012, I have been giving private lessons online. My objective is to support learners towards success in the DELF (Diploma of Studies in French Language) or the DALF (Advanced Diploma in French Language), as well as the TCF (French Knowledge Test). I have had the pleasure of helping many students of different nationalities through my online courses. For me, helping enthusiasts practice the French language is an enriching experience, because I understand the importance of success in the lives of ambitious people.

I speak Arabic, French, Spanish, a little English and a little Turkish. During my classes, I explain concepts in French, Arabic or Spanish, depending on your preference. At the end of each session, I offer exercises to do as homework, in order to identify your gaps and monitor your progress.

Here are some essential points to know about the DELF and DALF:
- The DELF (Diploma in French Language Studies) and the DALF (Advanced Diploma in French Language) are two high-quality official diplomas. They are aligned with the levels of the Common European Framework of Reference for Languages and cover the following six levels, from the most basic to the most advanced: A1, A2, B1, B2, C1, C2. These diplomas are suitable for all ages and all audiences.
- The DELF B2 and, increasingly, the DALF C1, provide access to French, European or French-speaking universities, as well as certain Grandes Ecoles.

If you plan to take DELF or DALF exams, or if you want to improve your level, do not hesitate to book your sessions with me to start preparation. I am available !
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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).
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Learn Spanish in a fun, easy, and engaging way with a certified teacher, official DELE examiner, and IB-trained educator.

✨ FLUENCY · EXAMS · LIVING IN SPAIN · TRAVEL & BUSINESS ✨

Are you planning to travel, study, work, or live in Spain or another Spanish-speaking country? Are you preparing for the DELE or another official Spanish exam, such as the SIELE, IB, or IGCSE? Are you a complete beginner, or do you already know the grammar but still find it difficult to have a fluent conversation?
You’re in the right place to take that big step!

I’m a certified Spanish teacher and official DELE examiner at the Instituto Cervantes, with:

🎓 PhD candidate in Applied Linguistics for Language Teaching
🎓 Master’s in Spanish as a Foreign Language
🎓 Master’s in International Education and Bilingualism with IB certification

I teach children, teenagers, and adults at all levels, with lessons tailored to your goals:

✅ DELE and exams preparation
✅ Speaking fluency and confidence
✅ Spanish from beginner to advance
✅ Real-life communication skills

Each class includes personalized planning, clear objectives, and close guidance so you can make progress from the very first lessons.

Take the next step in your Spanish journey, let’s start!

My lessons combine:
🗣️ An active communicative approach
📚 Clear and practical grammar explanations
🎯 Real-life language use and confidence-building activities

If you are preparing for exams, I provide:
✅ Structured exam preparation
✅ Practice with all exam sections
✅ Personalized feedback and strategies
✅ Continuous support to help you feel confident on exam day

I teach online from Japan with a flexible schedule, and I am happy to adapt lessons to your availability while helping you achieve solid and measurable progress.

Whether your goal is:
✈️ Traveling
💼 Professional communication
🎓 Academic purposes
📖 Official certification
💬 Improving fluency and confidence

I would be delighted to support you on your Spanish-learning journey.

📩 Contact me, and together we will create your personalized study plan!
And if you enjoy the lessons, I would truly appreciate your review 😊🌟

¡Nos vemos en clase! — See you in class!


I offer individualized programs for all levels of the Common European Framework of Reference (A1-C2), specializing in:

📘 General Spanish (Beginner to Advanced)
Progress from beginner to advanced level with a structured, dynamic, and fully communicative method. Classes are completely personalized to adapt to your goals, learning pace, and learning style, helping you improve steadily and confidently.

🎯 Personalized Classes
Classes tailored to your specific goals: travel, work, studies, interviews, or presentations. Learn the Spanish you actually need with a practical and results-oriented approach from the very first class.

🗣️ Conversation Classes
Personalized training for concrete contexts such as travel, professional settings, academic environments, or presentation preparation. My classes focus on real conversation from the very first minute, always adapting to my students’ interests and goals. Ideal if you understand Spanish but don’t feel confident speaking yet, or if you want to become fluent quickly for real-life situations.


🎨🎲 Spanish Classes for Children (Ages 6*-12)
Dynamic and interactive lessons specially designed for children. We use games, songs, stories, and age-appropriate activities so they can learn Spanish naturally, creatively, and in a motivating environment * Children should already be able to read and write in their native language.

📝 Official Exam Preparation (DELE, SIELE, IB, IGCSE, CCSE)
Maximize your score with the guidance of a certified examiner. You will learn real exam strategies, practice with official materials, and receive continuous personalized support so you can take your exam with confidence and peace of mind.

🎓 Spanish for Admission to Spanish Universities
Linguistic and academic preparation designed to meet entry requirements and help you succeed in a university environment.

Feel free to tell me if you would like to focus on a specific skill or if you prefer a particular teaching style. Every program is carefully designed around your goals, interests, and learning preferences.

I teach online from *Japan* with a very flexible schedule, and I will be happy to adapt classes to your availability while guiding you toward solid and measurable progress.
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*Note: My availability on Apprentus may not be up to date. Please contact me to check my current availability.

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.
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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! :)
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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 3 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
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Many students lose confidence in math over the school year - not from lack of ability, but from pace, gaps, or one bad unit that never got resolved. This summer program (through mid-September) is built to fix that before the new year starts, not just review generally.
I work with middle and high school students, including IB, to close specific gaps not a broad refresher, but targeted work on exactly what's holding a student back. I bring the same structured, evidence-based approach I use with my university-admission students: identify precisely what's missing, build a plan around it, and track real progress, not just hours logged.
Best for students who want a calm, focused reset before the new academic year begins not for open-ended tutoring with no target
Good-fit Instructor Guarantee
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