Linear algebra, vector spaces, eigenvalues and eigenvectors, and linear applications.

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From 29 $ /h

List of lessons

1. Vector Spaces & Subspaces
Key concepts: Understanding the definition of vector space and the ten conditions (Vector Space Axioms) to prove that a set with addition and multiplication operations in its standard form a vector space.
Linear Independence & Dependence: Testing whether vectors are linearly independent or dependent on each other.
Span, Basis & Dimension:
Determine the generative span of the space.
Finding the basis and dimension of different spaces (such as vector spaces \mathbb{R}^n, matrices M_{m \times n}, and polynomials P_n).
Subspaces: Subspace conditions, finding the null space, column space, and row space of matrices.
2. Linear Transformations and Applications
Definition and properties: Proving the linearity of applications and determining the Standard Matrix Representation.
Kernel and Range:
Calculate the kernel (Kernel/Null Space) and image (Image/Range) for conversion.
Applying the Rank-Nullity Theorem and calculating rank and nihilism.
Change of Basis: Transition Matrices and how to represent the same linear transformation under different bases and families.
3. Eigenvalues & Eigenvectors
Characteristic Equation: Finding the eigenvalues of \lambda by solving the equation \det(A - \lambda I) = 0.
Eigenvectors and Eigenspaces: Finding the eigenspace associated with each eigenvalue by solving the homogeneous system (A - \lambda I)\vec{v} = \mathbf{0}.
Diagonalization:
Diagonalizability Condition Test.
Formulating the decomposition of diagonal A = PDP^{-1} to facilitate the calculation of matrix powers A^k and the solving of systems of differential equations.
Orthogonal Diagonalization: For symmetric matrices and the application of Spectral Theorem.

Location

Online from Egypt

About Me

I am a university teaching assistant and economic researcher specializing in government research centers. I provide simplified explanations of econometrics, statistics, finance, and economics, emphasizing in-depth understanding and practical application. I help students grasp concepts, complete assignments, and prepare for exams. I also offer training in using EViews, Stata, SPSS, and Excel, as well as data analysis, interpreting statistical results, and writing academic papers. I ensure that sessions are interactive and tailored to each student's needs, with ongoing support until optimal results are achieved.

Education

I am a university lecturer specializing in econometrics, statistics, economics, finance, and business administration. I provide professional educational sessions for students of public universities, private universities, and foreign universities, as well as graduate students and researchers.

Experience / Qualifications

Bachelor of Statistics from the Faculty of Economics and Political Science, Cairo University
Experience in teaching at more than one private Egyptian university, as well as in the research field at governmental and private research centers.

Age

Teenagers (13-17 years old)

Adults (18-64 years old)

Seniors (65+ years old)

Student level

Beginner

Intermediate

Advanced

Duration

60 minutes

The class is taught in

English

Arabic

Skills

Math

Numerical analysis

Algebra

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

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The service includes:
Explanation of topics in microeconomics and macroeconomics.
Solving and analyzing mathematical applications, problems, and exam exercises.
Clarifying and simplifying economic curves and data.
The curriculum is explained in either Arabic or English, depending on the university requirements.
Service features:
Interactive sessions with students via Zoom.
Summaries and worksheets to review key concepts before tests.
Support, interaction, and a space to answer any questions during the study period.

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Descriptive and Inferential Statistics.
Probabilities, statistical distributions, and hypothesis testing (t-test, ANOVA, Chi-Square).
Training in statistical analysis using popular software such as SPSS, Excel, or R.
Review and test preparation:
Intensive reviews before midterm and end-of-term exams.
Solve past exam papers and focus on the most frequently asked questions.
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► Online Mathematics, Physics & Chemistry Tutor from Switzerland
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For older students, I offer support in Mathematics, Physics, Chemistry, Statistics and technical modules. I help students understand difficult theory, work through assignments, prepare for exams and strengthen the analytical skills needed for university-level study.

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As a teaching professional, I have always enjoyed sharing my knowledge. My goal is to provide quality education. I am aware that some topics may seem complex, but often this is simply the result of an inadequate explanation by the teacher. With me, you will discover a real interest in the material!

We strive together to achieve academic excellence, overcoming the shortcomings and difficulties encountered by your child. Studies will become a pleasant experience for him. In addition to the courses, I can also help with school orientation, identifying their preferences and highlighting the advantages and benefits of a fulfilling educational ambition.

The sessions generally take place according to the following stages:

1️⃣ The first sessions are devoted to the assessment of the student's level in order to detect existing gaps.

2️⃣ Next, we create a personalized plan to address these gaps, including the number of hours of work needed, specific areas to focus on, and appropriate training and development exercises.

3️⃣ We stay in constant contact with the student's class teacher, to keep up to date with the latest requirements and ensure a consistent approach.

4️⃣ Subsequently, I provide exams similar to those that are likely to be asked in class, to prepare the student effectively.

5️⃣ Upon request, I write a regular report, usually monthly, to keep parents informed of their child's progress throughout their course.

I adapt my methodology according to the specific needs of each student, thus offering them a personalized and adapted work approach.

In addition, I offer crash courses for students preparing for the start of the school year, allowing them to start the year well prepared, with a solid lead on the school curriculum.

If you have any questions, do not hesitate to contact me. I will be happy to help you.

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With over 18 years of experience, I offer private lessons in Mathematics - Analysis - Matrices - Statistics - Algebra - Geometry - Physics - Chemistry - Biology, Geology to students in French or international (English) programs, including Terminale, Bac, 1ère, Seconde, Brevet, competitive exams and university preparatory classes for medical or first-year university students, either at home or online using a virtual classroom method with a shared interactive whiteboard, in addition to Zoom for communication.
Homework help for CNED students.
For more information, do not hesitate to contact me, answer in a few minutes up to 12 hours maximum..

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Do you aspire to master mathematics, physics and engineering at a university level? Do you want to exceed your limits and excel in these demanding fields? Do not search anymore ! Our tailor-made private lessons are there for you.

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Quality Teaching Materials: We provide high-quality learning resources to support your progress.

Who can benefit from our courses?

High school students preparing for their baccalaureate or entrance exams to engineering schools.

University students pursuing a degree in mathematics, physics or engineering.

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Join us today!

Excellence doesn't wait. Contact us now to book your first lesson. Together we will build a bright future based on a solid understanding of mathematics, physics and engineering.

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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.

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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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Passionate & empathetic teacher. I have a Master's in Physics with honors from the University of Leicester (which was featured at the time as a top 5 Physics university in the UK by The Guardian) and a - french - European School diploma in which I achieved 90% in Physics and 85% in Maths.

Helping others understand difficult topics and skills is something that I am very passionate about as an empathetic person. I have 6 years of experience teaching Physics and Maths to kids from unprivileged backgrounds both in a homework schools as well as via private teaching. In private teaching, I have experience tutoring people with learning disabilities (ADHD, Dyslexia, Discalculia and more), younger kids of ages 7-12 and older students preparing for their final baccalaureate exams in advanced maths/physics curriculums.

In my classes, I aim to:

- help students achieve better grades in exams/tests in all branches of Physics & Maths
- clearly explain and break down topics
- give context and or example applications of topics (to improve understanding and memorization)
- help with ADHD & other learning disabilities
- give practical advice for university applications (eg. UCAS in the UK) and discuss the exciting Physics research/work and projects you can work on later in life.

Physics has a plethora of useful and fascinating applications, from the detection of Gravitational Waves and Gamma-Ray Bursts to the development of novel Medical Imaging techniques and Nano-technology (eg: smartphones). It is a subject that I am very passionate about and I hope to make use of my years of experience and extensive knowledge to help you understand and love the subject! My lessons will always be tailored to the individual needs of the student, so please do not hesitate to contact me if you have questions!

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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).

Baia

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I work with two kinds of students: those preparing to meet university math admission requirements (OMPT, CCVX, VWO), and those already enrolled who need solid support in calculus, linear algebra, differential equations, probability & statistics, or discrete math including students at TUM, ETH Zurich, TU Delft, KTH, EPFL, and RWTH Aachen.
Lessons are in English; I can explain in German where it helps.

Narayan

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*Note: My availability on Apprentus may not be up to date. Please contact me to check my current availability.

I am an MSc CIvil Engineering, M.Sc Finance and Economics, and an MBA graduate with over 14 years of experience teaching Mathematics up to the undergraduate level. Over the years, I have worked with a wide range of students and have successfully helped them excel in their studies. In addition to my extensive teaching background, I have more than 8 years of experience guiding students through standardized tests such as the GRE and SAT. My goal is to help you master these tests with effective strategies and a clear understanding of the subject matter.

My Mathematics lessons are tailored for students of all levels, including:
Master and Bachelor Students (subjects like Financial Mathematics, Business Mathematics, Basics of Mathematics for data science students, etc)
Pre-university students
IB (Math SL and Math HL) students
AS/A-level students
European S6 and S7 students
GCSE and IGCSE students
Primary school students

In addition to Mathematics, I also offer tutoring in Physics and Chemistry for students up to the European upper secondary level, as well as IB and A-level students.

For Biology, I provide comprehensive lessons for students up to the European Secondary level, GCSE, and IGCSE levels. My teaching style is flexible and adaptable, ensuring that every student receives personalized guidance based on their learning style and goals.

Currently, I am teaching a diverse group of students from different educational backgrounds.

My current students are from the following schools:

National:
1. St Georges International School, Luxembourg, Edexcel (Pearson) Curriculum (10 students)
2. International School of Luxembourg, Luxembourg, IB Curriculum (6 Students)
3. Lycée Athénée de Luxembourg, Luxembourg, IB Curriculum (4 Students)
4. Lycée - International School Michel Lucius, Luxembourg, Cambridge Curriculum (6 Students)
5. European School Kirchberg, Luxembourg, European Curriculum (4 students)
6. Lycée Aline Mayrisch, Luxembourg, Luxembourgish curriculum (1 student)
7. Lënster Lycée International School, Luxembourg, European Curriculum (2 Students)

International:
8. International School of the Hague, Netherlands, IB Curriculum (1 student)
9. International School Of Nice, France, IB Curriculum (2 students)
10. Merchiston Castle School, Edinburgh, Scotland, Edexcel (Pearson)/Cambridge (1 students)
11. Silverline Private School, Limassol, Cyprus, UK national Curriculum (1 Student)
12. North Broward Preparatory School, Florida, USA, IB Curriculum (1 Student)
13. King Solomon School, Israel, IB Curriculum (1 student)
14. The European School of Bergen, The Netherlands, European Curriculum (1 student)

Additionally, I offer homework assistance and track each student's progress through periodic assessments, which can be scheduled based on the requirements of both students and parents.

Note: While some of my students follow curriculums in French, German, or Swedish, my primary language of instruction is English. Given that Mathematics is a universal language, it’s easy to understand the tasks, and I explain solutions clearly in English, ensuring a seamless learning experience for all.

Let’s embark on this learning journey together and achieve your academic goals with confidence!

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Welcome to my Maths, Physics and Science tutoring class, crafted especially for young minds preparing for IB MYP, IGCSE, and GCSE exams. As a passionate learner and dedicated tutor, I am committed to helping students not only comprehend but also develop a love for these captivating subjects. Here's what you can anticipate from my tutoring sessions

Personalised Learning: Every learner is unique, and I believe in tailoring my teaching methods to suit each student's individual needs. I don't judge; instead, I concentrate on understanding their strengths and areas for improvement to create a supportive and encouraging learning environment.

Concept Breakdown: I dissect complex topics into simpler, more manageable parts, making it easier for students to grasp challenging concepts and build a strong foundation in Physics and Science.

Student-Centred Approach: I enjoy teaching students and continually strive to ignite their curiosity and passion for learning. I aim to make each lesson engaging and enjoyable, helping students recognise the real-world applications of what they learn.

Shared Strategies: As a student who has successfully qualified for the Engineering Entrance exam test and is currently studying abroad on a fully funded scholarship, I bring my own learning strategies and study techniques to the table. These proven methods will help students achieve their academic goals.

Continuous Improvement: I am always learning and growing, just like my students. This continuous improvement mindset, which I actively promote, inspires and motivates students to strive for their best. It enables me to stay updated with the latest educational trends and techniques, ensuring that my students receive the best possible guidance.

Supportive Environment: I encourage students to ask questions, no matter how trivial they might seem. By creating a friendly and comfortable atmosphere, I ensure that students feel comfortable and open to express their doubts and curiosities, leading to a deeper understanding of the subjects.

Reza

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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! :)

Fisnik

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RELIABLE TUTOR — Solvay graduate (Cum Laude), 7+ years of private tutoring, former teaching assistant (Maths/Stats).

I help students regain confidence: we clarify concepts, use concrete examples, then practice assessment-style questions. No rote learning: we reason, test, and master.

What we work on
• Chapters of your choice: equations, functions, trigonometry, geometry, derivatives, probability, statistics.
• Step-by-step method, concrete examples, and a short summary sheet each session.
• Practice on common assessment questions with feedback.

Formats & languages
• 1-to-1 or Duo/Trio (same level) · EN/FR · online (Zoom/Teams) or in person in Brussels.

Packs (year-round)
• Sprint 6 h (3 × 2 h): quick refresher and targeted practice.
• Pack 10 h: full review, study plan, and short follow-up.
• Limited WhatsApp support included with packs.

Wendy

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Welcome to my fun and friendly English and Mathematics class for beginners! Whether you want to improve your English communication skills or make Mathematics easier to understand, you’re in the right place!

📚 In my class, you will:

🗣️ Practice speaking English through fun conversations and activities
✏️ Learn useful vocabulary, grammar, and everyday English
🔢 Understand basic Mathematics step-by-step
🎯 Practice solving problems with easy-to-follow explanations
🎮 Enjoy interactive activities, games, and engaging lessons
💪 Build confidence while learning at your own pace

Don’t worry if you’re a beginner! Mistakes are part of learning. I will patiently guide you, explain lessons clearly, and make sure you understand before moving forward.

✨ Come and learn with me! Let’s make English and Math simple, enjoyable, and exciting. Book a class today, and let’s take the first step toward becoming a more confident learner! 🌈

Suvindu

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(5)

I am very patient with my students and it is important to me that we take our time to understand concepts rather than rushing through them. Once my students feel comfortable with the underlying concepts of a certain topic, then I like to move forward with exam related questions. :)