The Invariant Principle is applicable to algorithms (games, transformations). Some task is repeatedly performed. What stays the same? What remains invariant? Here is a saying easy to remember:

If there is repetition, look for what does not change!

In algorithms there is a starting state S and a sequence of legal steps (moves, transformations).

One looks for answers to the following questions:

1. Can a given end state be reached?

2. Find all reachable end states.

3. Is there convergence to an end state?

4. Find all periods with or without tails, if any.

Problems

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Our courses

Curriculum Mathematics

8+

Curriculum Mathematics

Our goal at this course is to enhance our students’ mathematical intuition by focusing on a deep understanding of mathematical concepts and to enable them to link different concepts and apply their knowledge to solve mathematical problems to help them to improve their performance at Maths exams.

Olympiad Mathematics

8+

Olympiad Mathematics

Olympiad Mathematics is a comprehensive course designed to help students win UKMT competitions. It is suitable for high-achieving mathematics students who are looking to take their skills to the next level.

Introduction to Python with Turtle

9+

Introduction to Python with Turtle

This course guides you through the fundamentals of Python programming using an interactive Python library known as Turtle.

Coding in Python

8+

Coding in Python

Python is a versatile and widely-used programming language that is particularly well-suited for beginners. It is known for its simplicity and readability, making it a great choice for students who are new to coding.

Data Science

16+

Data Science

This course is designed for those with little or no prior programming or data science experience, but who are eager to learn how to use Python to analyze and visualize data.

Chess

7+

Chess

Supercharge your potential by studying chess alongside maths and programming. Boost strategic thinking, problem-solving, and concentration. Unleash your competitive edge and unlock endless possibilities in these fields.

Olympiad Geometry

12+

Olympiad Geometry

This course encompasses a range of Geometry topics such as coordinate and spatial geometry, introductory trigonometry, angles, parallel lines, congruent and similar triangles, polygons, circles, the Pythagorean Theorem, and more. Emphasis will be placed on reinforcing Algebra skills and enhancing critical thinking through problem-solving in both mathematical and real-world contexts.

Where do you hold your classes?

We hold our classes online or on-site on Saturdays at our branch in Pimlico Academy, London.
You can find our timetable here.

What do you need to start learning online?

For lessons you only need a computer or phone with a microphone, camera and Internet access. Wherever you are - in London, Nottingham, New York or Bali - online lessons will be at hand.

When can I take the introductory lesson?

You can get acquainted with the school at any time convenient for you. To do this, just leave a request and sign up for a lesson.

I can't attend class, what should I do?

It is OK, it happens! Students have the opportunity to cancel a lesson up to 8 hours before the scheduled time without loss of payment. So you can reschedule it for a convenient time, and the teacher will have the opportunity to

I don't have much free time, will I have time to study?

Learning can take place at your own pace. We will select a convenient schedule and at any time we will help you change the schedule, take a break or adjust the program.

How long is one lesson?

All classes last 1 hour.

Hear from some of our amazing students who already achieved incredible results with us!

"Olympiad Maths Lessons helped me a lot to get the Gold medal in Junior Maths Challenge"

St. Paul's Student

"Thanks to the 'Data Science' and 'Coding in Python' lessons I got accepted to my dream university."

Data Science Student
Warwick University

"Great courses, which thoroughly explained topics beyond the capability of the GCSE answer sheet. Thanks so much."

Ivan

GCSE Student in Dubai

"Financial Mathematics! Best course to understand Python and Mathematics behind Finance!"

Gleb

VC Investor

"We got silver in PMC! Thanks George!"

Mum of St. Paul's Student

Prepare for the Primary Maths Challenge

"My daughter took a batch of 10 classes with George to understand Python with Turtle. I found George extremely knowledgeable and accessible."

Dad of Latymer School Student

Python with Turtle

We’re hiring!

Meet our team

Our teachers will tell you how to prepare for exams, help you cope with difficult tasks and win the Olympiad
‍
They will tell you about the pitfalls of exams and the most common mistakes, and explain how to avoid them

George Ionitsa

Founder &
Teacher of Maths and Coding