BASICS MATHEMATICS OF CALCULUS , TRIGONOMETRY AND GEOMETRY

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).

Are you a school or university student struggling with math or aiming to improve your skills? I’m here to guide you! With my personalized approach, I simplify complex concepts and help you master topics such as: ✔️ Algebra, Geometry, Calculus, and Statistics ✔️ University-level courses: Analysis, Abstract Algebra, Differential Equations ✔️ Exam preparation: SAT, OMPT-A, VWO Math A & B, and university entrance exams (ETH Zurich, University of Zurich, etc.) What You Get with My Lessons: ✅ Tailored Learning: Every student is unique—I adapt my teaching to your needs. ✅ Exam Success: Focused training to help you pass and excel. ✅ Online Convenience: Learn from anywhere via Google Meet. ✅ Multilingual Support: While I teach in English, I can clarify concepts in French or German if needed. 🚀 Book your lesson today and take the first step toward math confidence!

As a highly qualified maths teacher, a graduate of the college of teachers and with 11 years of teaching experience in public high schools, I am happy to offer tutoring lessons in mathematics at home for students from level T and Common Core Sciences, TC Technological, 1st Baccalaureate Experimental Sciences and final of all the sectors (SVT-PC-SC.Math-L), as well as for the classes of 2nd and 1st general, Terminale specialty of the French system, as well than the 5th, 4th and 3rd levels of college. My primary objective is to help students improve their level, deepen their knowledge, assimilate their lessons, fill their gaps and improve their skills in the discipline of mathematics. In addition, I am perfectly able to support them in the preparation of their exams and competitions for access to the Grandes Ecoles, and to provide them with homework help so that they can succeed in this subject. With my advanced math skills and knowledge, I am confident that I can provide my students with effective tools and techniques to help them progress. My goal is to give them confidence and help them develop a passion for mathematics, a subject that can seem daunting at first, but can be exciting and rewarding if taught in an interesting and fun way. By choosing my tutoring courses in mathematics, students can expect to receive individual attention and personalized help to overcome their difficulties and achieve their goals. My teaching approach is interactive and student-centered, which allows for a deeper understanding of mathematical concepts and a more practical application of acquired knowledge. In summary, I am confident in my skills as a math teacher to help students of all levels progress and succeed in this demanding subject. I am convinced that my dynamic and stimulating teaching methods will help my students achieve their math goals and build a confidence that will follow them throughout their lives.

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: -Linear Algebra -Calculus -Trigonometry -Geometry -Set Theory and Metrics -Analysis -Algebra -Numerical Analysis -Number Theory -Probability -Logic and Proofs -Galois Theory 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!

I am a specialized and certified AS and A-Levels tutor with extensive experience in teaching Sequences and Series, along with a strong emphasis on Calculus. My tutoring sessions are designed to provide in-depth knowledge and understanding of these crucial mathematical topics, helping students to master the material and excel in their exams. Focus Areas in Sequences and Series Binomial Expansion: I guide students through the principles of binomial expansion, helping them understand how to expand expressions of the form (a+b)n . We explore the Binomial Theorem in detail, ensuring that students can apply it effectively in problem-solving scenarios. By the end of our sessions, students will be able to expand binomials with confidence and accuracy. Arithmetic Progressions (AP): Understanding arithmetic progressions is fundamental in mathematics. I provide comprehensive instruction on identifying and working with sequences where each term is derived by adding a constant. Students learn how to find the nth term, the sum of the first n terms, and how to apply these concepts to solve real-world problems. Geometric Progressions (GP): I also specialize in geometric progressions, where each term is obtained by multiplying the previous term by a constant. My approach includes explaining key concepts such as the nth term and the sum of a geometric series, both finite and infinite. We tackle a variety of problems to ensure a deep understanding of the subject. Further Sequences and Series: Beyond the basics, I explore further topics in sequences and series, including convergence and divergence. This advanced understanding prepares students for higher-level mathematics and the challenges they may face in university studies. Mastering Calculus In addition to Sequences and Series, I offer expert guidance in Calculus, which is essential for success in AS and A-Levels. My focus here includes: Differentiation: I help students understand the principles of differentiation, teaching them how to find derivatives and apply them to various functions. We work on techniques, such as the product and quotient rules, and explore applications of derivatives in real-world contexts. Integration: Students learn the fundamentals of integration, including definite and indefinite integrals. I emphasize techniques such as substitution and integration by parts, ensuring that students can tackle a wide range of problems. Application of Calculus: We explore how calculus is used in practical scenarios, including motion problems and areas under curves, to provide a holistic understanding of the subject. Proven Approach to Learning My proven approach focuses on solving past examination questions, which is crucial for familiarizing students with the exam format and types of questions they will encounter. I emphasize understanding core principles rather than rote memorization. This methodology not only boosts confidence but also ensures that students can apply their knowledge effectively in exams. I believe that personalized feedback is vital for growth. Throughout our sessions, I provide constructive feedback and support, allowing students to identify their strengths and areas for improvement. This continuous feedback loop fosters a growth mindset, empowering students to embrace challenges and develop resilience. Book Your Classes If you’re ready to elevate your understanding of Sequences, Series, and Calculus, I invite you to book your classes now. Experience the difference that comes with learning from an experienced tutor dedicated to your success. Let me guide you through an exciting and transformative learning journey that sets you on the path to achieving the highest grades possible. Together, we can unlock your full potential and ensure you are well-prepared for your AS and A-Level examinations. Your success is my priority, and I look forward to helping you reach your academic goals!

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I love math because it's a subject that, while intimidating to some, is also incredibly logical and rewarding. Understanding math is like solving puzzles—every problem has a solution, and every step is a small challenge to overcome. This mathematics course is designed to support primary and secondary school students (up to grade 9) in the French system. It covers all the essential concepts of the curriculum: numeration, calculation, geometry, problem solving, statistics and probability, algebra, and preparation for the Brevet (Brevet). The goal is to strengthen the foundations, clarify gray areas, and give the student confidence and autonomy. Each session is personalized according to the student's level, pace, and needs. Fun methods are used for younger students, while discipline and strategy are used for older students.

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