Mathematics for 11-16

Below are the maths-courses for pupils who are around 11-16 year old, though everyone with the appropriate mathematical background is welcome. There is no particular knowledge requirement to join our initial courses, and last courses are really hard. And in any case we expect students to be diligent!

Mathematics for 11-16

Below are the maths-courses for pupils who are around 11-16 year old, though everyone with the appropriate mathematical background is welcome. There is no particular knowledge requirement to join our initial courses, and last courses are really hard. And in any case we expect students to be diligent!

Junior

Intermediate

Senior

School-maths

Extra-maths

Junior school-maths courses revisit the most fundamental things that have probably been covered in your school in years 4-6. And not only we will revisit them, but also answer all the "why"s and teach how to ask correct questions and properly answer them. I.e we will try to set up mathematical thinking :) Moreover, we will also give a great number of challenging extra-problems for people who find the main content easy.

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SM-0: "Numbers"

Starting from scratch we will revisit students' knowledge about integers and operations on them. Since the content is quite easy there will be extra problems that are harder.

**Schedule:** The course consists of 5 small group lessons + 4 homework sheets. Lesson times: either 10:00-11:00 UTC ("earlier group") or 16:00-17:00 UTC ("later group") on Sep 16, 20, 23, 27, 30.

**Price & payment:** The entire course costs 39 dollars. The payment should be made after your place has been confirmed and before the second lesson (i.e you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

SM-1: "Logic"

Before getting down to harder things, we must briefly talk about claims, negations, proofs, logical implications etc... And that is what we will focus on in this course.

**Schedule: **The course consists of 5 small group lessons + 4 homework sheets. Lesson times: either 08:45-09:45 UTC ("earlier group") or 14:45-15:45 UTC ("later group") on Sep 16, 20, 23, 27, 30.

**Price & payment:** The entire course costs 39 dollars. The payment should be made after your place has been confirmed and before the second lesson (i.e you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

SM-2: "Variables and fractions"

First, starting from scratch we will explain variables and basic equations. Second, we will talk about fractions. In both cases we will provide enough material of different levels of difficulty for practice.

**Schedule: **The course consists of 5 small-group lessons + 4 homework sheets. Lesson times: either 10:00-11:00 UTC ("earlier group") or 16:00-17:00 UTC ("later group") on Sep 16, 20, 23, 27, 30.

**Price & payment:** The entire course costs 39 dollars. The payment should be made after your place has been confirmed and before the second lesson (i.e you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

SM-3: "Expressions, equations, transformations"

This course is dedicated to practising manipulations with numbers, variables and algebraic expressions. Starting from elementary problems we will finish by simplifying complicated expressions and dealing with more involved equations.

**Schedule: **The course consists of 5 small group lessons + 4 homework sheets. Lesson times: either 10:00-11:00 UTC ("earlier group") or 16:00-17:00 UTC ("later group") on Sep 16, 20, 23, 27, 30.

**Price&payment:** The entire courses costs 39 dollars. The payment should be made after your place has been confirmed and before the second lesson (i.e you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

Recap week (junior-school-maths)

This course is designed for you to practice the material covered above. It is important that before moving on to harder maths you feel perfectly comfortable with the fundamentals, i.e content of SM-0, SM-1, SM-2 and SM-3.

So during a week participants will be given 3 problem sheets and there will be 3 discussions of them. No hints nor help apart from the discussions!

**Schedule:** We are not launching this course yet. More information later. But you can still log in our website so that we have your email to contact you just in case.

**Price & payment:** -

So during a week participants will be given 3 problem sheets and there will be 3 discussions of them. No hints nor help apart from the discussions!

Junior extra-maths courses are aimed at those who have no or little experience in logical/olympiad-style problems. We will talk about things like "proofs", "counterexample" and see a number of simple but cool mathematical ideas (most of them are olympiad-style). So whether you plan to focus on maths-olympiads, computer science, or you simply want to try out some non-classroom maths, these courses are for you.

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EM-0: "Extra-maths-try-out"

This is course is designed for pupils who have at least finished primary school and are interested in extra-curricular maths. Participants will try to come up with different sorts of non-obvious constructions, solve logical puzzles and finally see a cool non-trivial mathematical idea.

**Schedule:** The course lasts 6 weeks: there is a small group lesson every Sunday from 9:00 till 10:45 UTC starting September 19th; there are 5 homework sheets and there is an Online Rate Table (see educational process if you do not know what is it).

**Price & payment:** This course is completely free of charge.

To apply scroll down on this page and click on "Log in and apply" button.

**Topics:**

Week 1: Games with stones

Week 2: Constructions

Week 3: Dividings

Week 4: Algorithms

Week 5: Parity

Week 6: Chessboard idea

To apply scroll down on this page and click on "Log in and apply" button.

Week 1: Games with stones

Week 2: Constructions

Week 3: Dividings

Week 4: Algorithms

Week 5: Parity

Week 6: Chessboard idea

EM-1: "Constructions, proofs and a few nice ideas"

In this course participants will also try to come up with interesting constructions and algorithms. Moreover we will give an introduction to formal proofs, in particular "proof by contradiction". Finally, a few cool maths ideas will also be presented in this course.

**Schedule:** The course lasts 12 weeks: there is a small-group lesson every Sunday from 9:00 till 10:45 UTC starting September 19th; there are 11 homework sheets and there is an Online Rate Table (see educational process if you do not know what is it).

**Price & payment:** The entire course costs 99 dollars, but it is free for those who already have at least bronze certificate in one of extra-maths courses. The payment should be made after your place has been confirmed and before the second lesson. If you really want to join but cannot afford it, you can still apply and make a note of that in your application form.

To apply scroll down on this page and click on "Log in and apply" button.

**Topics:**

Week 1: Working backwards

Week 2: Constructions from blocks

Week 3: Is it possible?

Week 4: Case consideration

Week 5: Logic-I

Week 6: Logic-II

Week 7: Proofs

Week 8: Proof by contradiction

Week 9: Variables

Week 10: Counting combinatorics

Week 11: Counting combinatorics again

Week 12: Pirates & Share-out

To apply scroll down on this page and click on "Log in and apply" button.

Week 1: Working backwards

Week 2: Constructions from blocks

Week 3: Is it possible?

Week 4: Case consideration

Week 5: Logic-I

Week 6: Logic-II

Week 7: Proofs

Week 8: Proof by contradiction

Week 9: Variables

Week 10: Counting combinatorics

Week 11: Counting combinatorics again

Week 12: Pirates & Share-out

EM-1+3/7: "Discovering the ideas"

The aim of this course is to give children a chance to discover ideas that will be discussed in EM-2 and some other future courses with no time-pressure and no hints. The teachers will only ask questions which might help and we will take everything slow. It is thus important that the kid barely has any experience with olympiad-style mathematics for this course to be useful, but EM-0 and EM-1 are the prerequisites!

**Schedule:** The course lasts 12 weeks: there is a small group lesson every Sunday from 9:00 till 10:45 UTC starting September 19th; there are 11 homework sheets and this is the only extra-matrhs course where there will be no Online Rate Table.

**Price & payment:** The entire course costs 99 dollars, but it is free for those who already have at least bronze certificate in one of the extra-maths courses. The payment should be made after your place has been confirmed and before the second lesson. If you really want to join but cannot afford it, you can still apply and make a note of that in your application form.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

EM-2: "Basic olympiad ideas"

This is a continuation of the EM-1 course but with more focus on olympiad-style problems. Participants will meet (hopefully discover themselves with some guidance) a number of basic maths olympiad ideas and practise using them to solve problems of various levels.

**Schedule:** The course lasts 12 weeks: there is a small-group lesson every Sunday from 9:00 till 10:45 UTC starting September 19th; there are 11 homework sheets and there is Online Rate Table (see educational process if you do not know what is it).

**Price & payment:** The entire course costs 99 dollars, but it is free for those who already have at least bronze certificate in one of extra-maths courses. The payment should be made after your place has been confirmed and before the second lesson. If you really want to join but cannot afford it, you can still apply and make a note of that in your application form.

To apply scroll down on this page and click on "Log in and apply" button.

**Topics:**

Week 1: Colourings

Week 2: Extremal principle

Week 3: Parity strikes again

Week 4: Pigeonhole principle

Week 5: Algebra: fractions & simplifying expressions

Week 6: Divisibility, introduction

Week 7: Divisibility and remainders

Week 8: Introduction to graph theory

Week 9: Invariants

Week 10: Monovariants

Week 11: Mathematical games

Week 12: Winning and losing positions

To apply scroll down on this page and click on "Log in and apply" button.

Week 1: Colourings

Week 2: Extremal principle

Week 3: Parity strikes again

Week 4: Pigeonhole principle

Week 5: Algebra: fractions & simplifying expressions

Week 6: Divisibility, introduction

Week 7: Divisibility and remainders

Week 8: Introduction to graph theory

Week 9: Invariants

Week 10: Monovariants

Week 11: Mathematical games

Week 12: Winning and losing positions

Recap week (junior-extra-maths)

There are a lot of important ideas mentioned in courses EM-0, EM-1 and EM-2. And it is vital to be able to see when they are useful without any external help and hints. So this course is designed to help with that. We will test junior school-maths knowledge as well.

So during a week participants will be given 3 problem sheets and there will be 3 discussions of them. No hints nor help apart from the discussions!

**Schedule:** We are not yet launching this course. But you can still log in our website so that we have your email around to contact you just in case.

**Price & payment:** -

So during a week participants will be given 3 problem sheets and there will be 3 discussions of them. No hints nor help apart from the discussions!

School-maths

Extra-maths

Intermediate school-maths courses cover most of the basic and fundamental secondary-school material. Once you are confident with junior-level material feel free to do courses below one by one.

Back to courses

SM-4: "Geometry, introduction"

This course is dedicated to building up geometrical intuition, solving basic geometrical problems and formalizing our knowledge about Euclidean geometry.

**Schedule:** The course consists of 7 lessons and 6 homework sheets. The lessons take place on Sep 10, 14, 17, 21, 24, 28 and October 1 either from 9:00 to 10:00 UTC ("earlier group") or from 15:00 to 16:00 UTC ("later group")

**Price & payment:** The entire course costs 59 dollars. The payment should be made after your place has been confirmed and before the second lesson (so you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

SM-5: "A bit of combinatorics, probability and statistics"

We will start by doing some counting combinatorics and then we will move on to the beginning of probability. We will finish the course by talking about statistics and their interpretation.

**Schedule:** The course consists of 7 lessons and 6 homework sheets. The lessons take place on Sep 10, 14, 17, 21, 24, 28 and October 1 either from 10:30 to 11:30 UTC ("earlier group") or from 16:30 to 17:00 UTC ("later group")

**Price & payment:** The entire courses costs 59 dollars. The payment should be made after your place has been confirmed and before the second lesson (so you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

SM-6: "Around rational and irrational numbers"

We will revisit our knowledge about numbers and make friends with real numbers. We will also talk about square roots, number lines and weird exponents.

**Schedule:** The course consists of 7 lessons and 6 homework sheets. The lessons take place on Sep 9, 13, 16, 20, 23, 27 and 30 either from 8:45 to 9:45 UTC ("earlier group") or from 14:45 to 15:45 UTC ("later group")

**Price & payment:** The entire course costs 59 dollars. The payment should be made after your place has been confirmed and before the second lesson (so you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

SM-7: "Sets and functions, introduction"

From first principles we will talk about functions, in particular about things like range and domain, graphs and coordinates, inverse functions, etc...

**Schedule:** The course consists of 7 lessons and 6 homework sheets. The lessons take place on Sep 9, 13, 16, 20, 23, 27 and 30 either from 8:45 to 9:45 UTC ("earlier group") or from 14:45 to 15:45 UTC ("later group")

**Price & payment:** The entire course costs 59 dollars. The payment should be made after your place has been confirmed and before the second lesson (so you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

SM-7+3/7: "Cartesian coordinates and graphs"

Even though this course is an off-main stream school-maths courses, it is one of the really important courses for school exams, interviews for universities and physics. In this course we will manipulate graphs, talk about equations of different shapes in cartesian coordinates (e.g ellipses) and their intersections, etc..

**Schedule:** The course consists of 7 lessons and 6 homework sheets. The lessons take place on Sep 9, 13, 16, 20, 23, 27 and 30 either from 8:45 to 9:45 UTC ("earlier group") or from 14:45 to 15:45 UTC ("later group")

**Price & payment:** The entire course costs 59 dollars. The payment should be made after your place has been confirmed and before the second lesson (so you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

SM-8: "Around quadratic function and polynomials"

This course is designed to make you more confident with polynomials (especially quadratic functions) by solving all kind of problems involving them.

**Schedule:** The course consists of 7 lessons and 6 homework sheets. The lessons take place on Sep 9, 13, 16, 20, 23, 27 and 30 either from 8:45 to 9:45 UTC ("earlier group") or from 14:45 to 15:45 UTC ("later group")

**Price & payment:** The entire course costs 59 dollars. The payment should be made after your place has been confirmed and before the second lesson (so you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

SM-8+3/7: "More expressions, equations and transformations"

This course is an off-main stream school-maths courses designed for people who need more practice with manipulating with equations and expressions. To be perfectly honest, the course is not much fun but nonetheless important as you will need to do a lot of such things in algebra. So being guru with this will save you a lot of time later on.

**Schedule:** The course consists of 7 lessons and 6 homework sheets. The lessons take place on Sep 9, 13, 16, 20, 23, 27 and 30 either from 8:45 to 9:45 UTC ("earlier group") or from 14:45 to 15:45 UTC ("later group")

**Price & payment:** The entire course costs 59 dollars. The payment should be made after your place has been confirmed and before the second lesson (so you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

SM-9: "Geometry strikes again"

This time we will talk about similar triangles, cyclic quadrilaterals, area and length. Most focus will be obviously on solving problems as there is not that much theory.

**Schedule:** The course consists of 7 lessons and 6 homework sheets. The lessons take place on Sep 10, 14, 17, 21, 24, 28 and October 1 either from 9:00 to 10:00 UTC ("earlier group") or from 15:00 to 16:00 UTC ("later group")

**Price & payment:** The entire courses costs 59 dollars. The payment should be made after your place has been confirmed and before the second lesson (so you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

Recap week (intermediate-school-maths)

This course is designed for you to practice things covered in intermediate-school-maths. It will be of a slightly higher standard than the usual school exam as we will give more challenging problems that make sure students' understanding is crystal clear.

So during a week participants will be given 3 problem sheets and there will be 3 discussions of them. No hints nor help apart from the discussions!

**Schedule:** We are not launching this course yet. However you can still log in the website so that we have your email in case we decide to contact you.

**Price & payment:** -

So during a week participants will be given 3 problem sheets and there will be 3 discussions of them. No hints nor help apart from the discussions!

Intermediate extra-maths courses are aimed at those who have about a year or two of experience in solving non-standard/olympiad-style mathematical problems. Knowing all the theorems/facts/ideas/... from Junior level school & extra maths is a prerequisite.

Back to courses

EM-3: "Intermediate-extra-maths-try-out"

This course is designed for people with about a year of experience in extra-curricular maths problem solving who want to see what's its like to study more advanced topics at Kvanta. Knowing content from courses EM-1 and EM-2 is a prerequisite. Knowledge of the content of all of the school maths courses from SM-0 to SM-3 is a must as well .

**Schedule:** The course lasts 12 weeks: there is a small group lesson every Sunday from 9:00 till 11:15 UTC starting September 19th; there are 11 homework sheets and there is Online Rate Table (see educational process if you do not know what is it).

**Price & payment:** The entire course costs 99 dollars, but it is free for those who already have at least bronze certificate in one of the extra-maths courses. The payment should be made after your place has been confirmed and before the second lesson. If you really want to join but cannot afford it, you can still apply and make a note of that in your application form.

To apply scroll down on this page and click on "Log in and apply" button.

**Topics:**

Week 1: Combinatorics: miscellaneous

Week 2: Number theory: miscellaneous

Week 3: Algebraic manipulations

Week 4: Decimal representation

Week 5: Mathematical games strike again

Week 6: Logical paradoxes

To apply scroll down on this page and click on "Log in and apply" button.

Week 1: Combinatorics: miscellaneous

Week 2: Number theory: miscellaneous

Week 3: Algebraic manipulations

Week 4: Decimal representation

Week 5: Mathematical games strike again

Week 6: Logical paradoxes

EM-4: "Extra-maths helps to become a great programmer. And not only..."

In this course we have collected mathematical topics and ideas that will be extremely important for programming as well as for maths. Among them: graph theory, mathematical induction, binary representation., etc...

**Schedule:** The course lasts 12 weeks: there is a small group lesson every Sunday from 9:00 till 11:15 UTC starting September 19th; there are 11 homework sheets and there is Online Rate Table (see educational process if you do not know what is it).

**Price & payment:** The entire course costs 99 dollars, but it is free for those who already have at least bronze certificate in one of extra-maths courses. The payment should be made after your place has been confirmed and before the second lesson. If you really want to join but cannot afford it, you can still apply and make a note of that in your application form.

To apply scroll down on this page and click on "Log in and apply" button.

**Topics:**

Week 1: Algorithms strike again

Week 2: Graph theory revisited

Week 3: Graph theory: trees

Week 4: Ordering and extremal principle

Week 5: Mathematical induction, introduction

Week 6: Sequences, introduction

Week 7: Around binary representation

Week 8: Counting information

Week 9: Around greatest common divisor

Week 10: About complexity of algorithms

Week 11: Logic

Week 12: Stirling's formula and quick-sort

To apply scroll down on this page and click on "Log in and apply" button.

Week 1: Algorithms strike again

Week 2: Graph theory revisited

Week 3: Graph theory: trees

Week 4: Ordering and extremal principle

Week 5: Mathematical induction, introduction

Week 6: Sequences, introduction

Week 7: Around binary representation

Week 8: Counting information

Week 9: Around greatest common divisor

Week 10: About complexity of algorithms

Week 11: Logic

Week 12: Stirling's formula and quick-sort

EM-5: "Diving into combinatorics and geometry"

This course is packed with olympiad-style problems and theorems from combinatorics and geometry. Apart from knowing material from previous courses, we also want you to have experience in geometry (e.g course "SM-4").

**Schedule:** The course lasts 12 weeks: there is a small-group lesson every Sunday from 9:00 till 11:15 UTC starting September 19th; there are 11 homework sheets and there is Online Rate Table (see educational process if you do not know what is it).

**Price & payment:** The entire course costs 99 dollars, but it is free for those who already have at least bronze certificate in one of extra-maths courses. The payment should be made after your place has been confirmed and before the second lesson. If you really want to join but cannot afford it, you can still apply and make a note of that in your application form.

To apply scroll down on this page and click on "Log in and apply" button.

**Topics:**

Week 1: Counting combinatorics strikes again

Week 2: One-to-one correspondence

Week 3: Probability

Week 4: Double counting

Week 5: Pigeonhole principle

Week 6: Estimate+example on a board

Week 7: Estimate+example not on a board

Week 8: Combinatorics on a grid

Week 9: Picks formula

Week 10: Compass and ruler

Week 11: Geometry: extra points help solving the problem

Week 12: Using pictures to explain things

To apply scroll down on this page and click on "Log in and apply" button.

Week 1: Counting combinatorics strikes again

Week 2: One-to-one correspondence

Week 3: Probability

Week 4: Double counting

Week 5: Pigeonhole principle

Week 6: Estimate+example on a board

Week 7: Estimate+example not on a board

Week 8: Combinatorics on a grid

Week 9: Picks formula

Week 10: Compass and ruler

Week 11: Geometry: extra points help solving the problem

Week 12: Using pictures to explain things

EM-6: "Diving into Number theory and Algebra"

This course is packed with olympiad-style problems and theorems from number theory and algebra. Even though we will talk about many things like gcd, divisibility, factorization etc. from scratch we will give much harder problems than the ones in EM-2 on similar topics.

**Schedule:** The course lasts 12 weeks: there is a small group lesson every Sunday from 9:00 till 11:15 UTC starting September 19th; there are 11 homework sheets and there is Online Rate Table (see educational process if you do not know what is it).

**Price & payment:** The entire course costs 99 dollars, but it is free for those who already have at least bronze certificate in one of extra-maths courses. The payment should be made after your place has been confirmed and before the second lesson. If you really want to join but cannot afford it, you can still apply and make a note of that in your application form.

To apply scroll down on this page and click on "Log in and apply" button.

**Topics:**

Week 1: Miscellaneous Algebra

Week 2: Divisibility & gcd revisited

Week 3: Fundamental theorem of arithmetic

Week 4: Applying FTA and gcd

Week 5: Modulo arithmetic & divisibility criterions

Week 6: Remainders & Fermat's Little Theorem

Week 7: Processes with numbers

Week 8: Mathematical induction again

Week 9: Periodic sequences

Week 10: Binomial theorem

Week 11: Pascal Triangle

Week 12: Rigorous proof of FTA

To apply scroll down on this page and click on "Log in and apply" button.

Week 1: Miscellaneous Algebra

Week 2: Divisibility & gcd revisited

Week 3: Fundamental theorem of arithmetic

Week 4: Applying FTA and gcd

Week 5: Modulo arithmetic & divisibility criterions

Week 6: Remainders & Fermat's Little Theorem

Week 7: Processes with numbers

Week 8: Mathematical induction again

Week 9: Periodic sequences

Week 10: Binomial theorem

Week 11: Pascal Triangle

Week 12: Rigorous proof of FTA

EM-6+3/7: "Cool serious maths: intermediate level"

This course is off the main stream of extra-maths courses and is designed to show some topics from good-university-level maths. But do not worry, the the main prerequisite is being comfortable with previous courses :)

**Schedule:** The course lasts 12 weeks: there is a small group lesson every Sunday from 9:00 till 11:15 UTC starting September 19th; there are 11 homework sheets and there is Online Rate Table (see educational process if you do not know what is it).

**Price & payment:** The entire course costs 99 dollars, but it is free for those who already have at least bronze certificate in one of extra-maths courses. The payment should be made after your place has been confirmed and before the second lesson. If you really want to join but cannot afford it, you can still apply and make a note of that in your application form.

To apply scroll down on this page and click on "Log in and apply" button.

**Topics:**

Week 1: Nim and a bit of game theory

Week 2: Cooperative algorithms

Week 3: Information problems

Week 4: Conditional probability

Week 5: Mathematical expectation

Week 6: Basic set theory

Week 7: Planar graphs and platonic solids

Week 8: 3D problems

Week 9: Discrete continuity

Week 10: Finite memory algorithms

Week 11: Infinite graphs and diamond lemma

Week 12: Paradoxes in probability

To apply scroll down on this page and click on "Log in and apply" button.

Week 1: Nim and a bit of game theory

Week 2: Cooperative algorithms

Week 3: Information problems

Week 4: Conditional probability

Week 5: Mathematical expectation

Week 6: Basic set theory

Week 7: Planar graphs and platonic solids

Week 8: 3D problems

Week 9: Discrete continuity

Week 10: Finite memory algorithms

Week 11: Infinite graphs and diamond lemma

Week 12: Paradoxes in probability

Recap week (intermediate-extra-maths)

There are a lot of important ideas mentioned in courses EM-3, EM-4, EM-5 and EM-6. And it is vital to be able to see when they are useful without any external help and hints. So this course is designed to help with that. We will test intermediate school-maths knowledge as well.

So during a week participants will be given 3 problem sheets and there will be 3 discussions of them. No hints nor help apart from the discussions!

**Schedule:** We are not launching this thing yet. However you can still log in the website so that we have your email in case we decide to contact you.

**Price & payment:** -

So during a week participants will be given 3 problem sheets and there will be 3 discussions of them. No hints nor help apart from the discussions!

School-maths

Extra-maths

Senior school-maths courses are mostly aimed to give a high-quality introduction into key high-school/university level topics. Once you are done with these courses, secondary-school exams will be ridiculous. Moreover you will be able to solve more than half of final exam questions.

Back to courses

Starting from first principles we will dive into the world of sine, cosine, and so on. We will solve a great number of problems with them.

**Schedule:** The course consists of 7 lessons and 6 homework sheets. The lessons take place on Sep 10, 14, 17, 21, 24, 28 and October 1 either from 9:00 to 10:00 UTC ("earlier group") or from 15:00 to 16:00 UTC ("later group")

**Price & payment:** The entire course costs 59 dollars. The payment should be made after your place has been confirmed and before the second lesson (so you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

Starting from the very beginning we will talk about vectors, operations on them and their applications.

**Schedule:** The course consists of 7 lessons and 6 homework sheets. The lessons take place on Sep 10, 14, 17, 21, 24, 28 and October 1 either from 9:00 to 10:00 UTC ("earlier group") or from 15:00 to 16:00 UTC ("later group")

**Price & payment:** The entire courses costs 59 dollars. The payment should be made after your place has been confirmed and before the second lesson (so you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

These strange numbers are important for mathematics of all sorts and have some beautiful properties that are explored at university. Using the knowledge of SM-10 and SM-11 we will introduce to the complex world and show a few nice facts about it. Interestingly, complex numbers might be helpful for problems from real-world...

**Schedule:** The course consists of 7 lessons and 6 homework sheets. The lessons take place on Sep 10, 14, 17, 21, 24, 28 and October 1 either from 9:00 to 10:00 UTC ("earlier group") or from 15:00 to 16:00 UTC ("later group")

**Price & payment:** The entire course costs 59 dollars. The payment should be made after your place has been confirmed and before the second lesson (so you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

The concept of limit of a sequence or a function is fundamental concept for later analysis. We will talk about it and give tons of different examples for practice.

**Schedule:** The course consists of 7 lessons and 6 homework sheets. The lessons take place on Sep 10, 14, 17, 21, 24, 28 and October 1 either from 10:30 to 11:30 UTC ("earlier group") or from 16:30 to 17:00 UTC ("later group")

**Price & payment:** The entire course costs 59 dollars. The payment should be made after your place has been confirmed and before the second lesson (so you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

We will give you a bit of an insight into a huge and important university level topic: Linear algebra. But at this stage it will all be at the secondary-school-exam level.

**Schedule:** The course consists of 7 lessons and 6 homework sheets. The lessons take place on Sep 9, 13, 16, 20, 23, 27 and 30 either from 8:45 to 9:45 UTC ("earlier group") or from 14:45 to 15:45 UTC ("later group")

**Price & payment:** The entire courses costs 59 dollars. The payment should be made after your place has been confirmed and before the second lesson (so you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

Once you feel comfortable with limits (i.e SM-12) we can talk about derivatives and even about integrals. Without going into too many boring details, we will work a lot on differentiation.

**Schedule:** The course consists of 7 lessons and 6 homework sheets. The lessons take place on Sep 10, 14, 17, 21, 24, 28 and October 1 either from 10:30 to 11:30 UTC ("earlier group") or from 16:30 to 17:00 UTC ("later group")

**Price & payment:** The entire course costs 59 dollars. The payment should be made after your place has been confirmed and before the second lesson (so you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

Mathematicians can do anything and in particular physics. Using the tools from SM-10, ..., SM-13 we will talk about mechanics from scratch but from a mathematical point of view. Believe it or not it should all start making more sense with the right tools.

**Schedule:** The course consists of 7 lessons and 6 homework sheets. The lessons take place on Sep 10, 14, 17, 21, 24, 28 and October 1 either from 9:00 to 10:00 UTC ("earlier group") or from 15:00 to 16:00 UTC ("later group")

**Price & payment:** The entire course costs 59 dollars. The payment should be made after your place has been confirmed and before the second lesson (so you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

What is the use of all the tools developed above if there is no important application for them? So we will show you one, which is probability and statistics. And there is real money behind this stuff, trust us...

**Schedule:** The course consists of 7 lessons and 6 homework sheets. The lessons take place on Sep 10, 14, 17, 21, 24, 28 and October 1 either from 10:30 to 11:30 UTC ("earlier group") or from 16:30 to 17:00 UTC ("later group")

**Price & payment:** The entire course costs 59 dollars. The payment should be made after your place has been confirmed and before the second lesson (so you can still freely withdraw from the course after the first lesson). If you really want to join but cannot afford it, you can still apply and make a note of that in your application form. We will then contact you later.

To apply scroll down on this page and click on "Log in and apply" button.

To apply scroll down on this page and click on "Log in and apply" button.

Recap week (senior-school-maths)

This course is designed for you to practice things covered above. It is like exam-preparation but harder as the problems will be harder and we also want you to understand things. Things like GCSE are ridiculously easy compared to this.

So over a week participants will be given 3 problem sheets and there will be 3 discussions of them. No hints nor help apart from the discussions!

**Schedule:** We are not launching this course yet. However you can still log in the website so that we have your email in case we decide to contact you.

**Price & payment:** -

So over a week participants will be given 3 problem sheets and there will be 3 discussions of them. No hints nor help apart from the discussions!

Senior extra-maths courses are for experienced maths-problem-solvers and they last 12 weeks. So apply only if you are prepared to work hard :) The courses are no longer themed; instead they mimic olympiad-training programs given in many countries. Each contains a lot of advanced problems and a number of non-obvious theorems. The courses are most suitable for those who would like to take part in olympiads of serious level or explore hard maths. It is a prerequisite to feel comfortable with all things covered in Junior & Intermediate school & extra courses.

Back to courses

EM-7: "Olympiad style maths for seniors, part 1"

Many of the topics here are an extension of those in previous courses. Among other topics: introduction to polynomials, similar triangles, cyclic quadrilaterals, Diophantine equations. Problems are of hard olympiad level. In the end we will discuss infinity and infinite series.

**Schedule:** The course lasts 6 weeks: there is a small group lesson every Sunday from 9:00 till 12:00 UTC starting September 19th; there are 11 homework sheets and there is an Online Rate Table (see educational process if you do not know what is it).

**Price & payment:** The course is completely free of charge. However please note that this course is not easy and you need to make sure that you can manage it and that you can work hard. If it turns out that it is not the case we will propose you to move to another group.

To apply scroll down on this page and click on "Log in and apply" button.

**Topics:**

Week 1: Cell combinatorics

Week 2: Geometry: revision

Week 3: Divisibility and GCD revision

Week 4: Diophantine equations

Week 5: Tournaments

Week 6: Similar triangles

Week 7: Arbitrarily large pigeons in infinite holes

Week 8: Polynomials: intro

Week 9: Polynomials: Vietas theorem

Week 10: Cyclic quadrilaterals

Week 11: Problems on a grid

Week 12: Around infinite series

To apply scroll down on this page and click on "Log in and apply" button.

Week 1: Cell combinatorics

Week 2: Geometry: revision

Week 3: Divisibility and GCD revision

Week 4: Diophantine equations

Week 5: Tournaments

Week 6: Similar triangles

Week 7: Arbitrarily large pigeons in infinite holes

Week 8: Polynomials: intro

Week 9: Polynomials: Vietas theorem

Week 10: Cyclic quadrilaterals

Week 11: Problems on a grid

Week 12: Around infinite series

EM-8: "Olympiad style maths for seniors, part 2"

Topics covered: geometry around points I, O, H, radical axes, area-arguments, Chinese remainder theorem, the AM-GM inequality, smoothing, orders and Euler's function. We end with a lecture on cryptography and number theory.

**Schedule:** The course lasts 12 weeks: there is a small group lesson every Sunday from 9:00 till 12:00 UTC starting September 19th; there are 11 homework sheets and there is Online Rate Table (see educational process if you do not know what is it).

**Price & payment:** The course is completely free of charge. However please note that this course is not easy and you need to make sure that you can manage it and that you can work hard. If it turns out that it is not the case we will propose you to move to another group.

To apply scroll down on this page and click on "Log in and apply" button.

**Topics:**

Week 1: Around H and O

Week 2: Around I and external circles

Week 3: Even more extremal principle

Week 4: Chinese remainder theorem

Week 5: AM-GM

Week 6: Smoothing method for inequalities

Week 7: Recurrences in combinatorics

Week 8: Power of a point, radical axes

Week 9: Using area to solve problems

Week 10: Number-theoretical functions

Week 11: Orders and Euler's theorem

Week 12: Cryptography

To apply scroll down on this page and click on "Log in and apply" button.

Week 1: Around H and O

Week 2: Around I and external circles

Week 3: Even more extremal principle

Week 4: Chinese remainder theorem

Week 5: AM-GM

Week 6: Smoothing method for inequalities

Week 7: Recurrences in combinatorics

Week 8: Power of a point, radical axes

Week 9: Using area to solve problems

Week 10: Number-theoretical functions

Week 11: Orders and Euler's theorem

Week 12: Cryptography

EM-8+3/7: "Bashing geometry, part I"

With the help of trigonometry and vectors the very big percentage of geometry can be "calculated". So using the knowledge from school-maths courses SM-10 and SM-11 and things we know about some geometrical constructions we will show you how to kill a great number of geometry problems. This course is off the main stream of extra-maths since this powerful tool is not necessary to become a great geometer. (In fact it might obscure the beauty of geometry...)

**Schedule:** The course lasts 6 weeks: there is a small-group lesson every Sunday from 9:00 till 12:00 UTC starting September 19th; there are 5 homework sheets and there is an Online Rate Table (see educational process if you do not know what is it).

**Price & payment:** The course is completely free of charge. However please note that this course is not easy and you need to make sure that you can manage it and that you can work hard. If it turns out that this is not the case we will propose you move to another group.

To apply scroll down on this page and click on "Log in and apply" button.

**Topics:**

Week 1: Vector bash

Week 2: Trigonometry bash 1

Week 3: Trigonometry bash 2

Week 4: Cartesian coordinate bash

Week 5: Moving points linearly

Week 6: Bash-practise

To apply scroll down on this page and click on "Log in and apply" button.

Week 1: Vector bash

Week 2: Trigonometry bash 1

Week 3: Trigonometry bash 2

Week 4: Cartesian coordinate bash

Week 5: Moving points linearly

Week 6: Bash-practise

EM-9: "Olympiad style maths for seniors, part 3"

Among the topics covered: Bipartite graphs, LTE, factorization in polynomials, symmedians, homotethy, spiral symmetry and movements on the plane as the last lecture.

**Schedule:** The course lasts 12 weeks: there is a small group lesson every Sunday from 9:00 till 12:00 UTC starting September 19th; there are 11 homework sheets and there is an Online Rate Table (see educational process if you do not know what is it).

**Price & payment:** The course is completely free of charge. However please note that this course is not easy and you need to make sure that you can manage it and that you can work hard. If it turns out that this is not the case we will propose you move to another group.

To apply scroll down on this page and click on "Log in and apply" button.

**Topics:**

Week 1: LTE lemma + Diophantine equations

Week 2: Bipartite graphs

Week 3: Factorization and irreducibility of polynomials

Week 4: Movements on the plane

Week 5: Number theoretical constructions

Week 6: Bijections, injections, surjections

Week 7: Combinatorial geometry strikes again

Week 8: Cycles in graphs

Week 9: Geometric inequalities

Week 10: Around symmedians

Week 11: Asymptotic behaviour

Week 12:

To apply scroll down on this page and click on "Log in and apply" button.

Week 1: LTE lemma + Diophantine equations

Week 2: Bipartite graphs

Week 3: Factorization and irreducibility of polynomials

Week 4: Movements on the plane

Week 5: Number theoretical constructions

Week 6: Bijections, injections, surjections

Week 7: Combinatorial geometry strikes again

Week 8: Cycles in graphs

Week 9: Geometric inequalities

Week 10: Around symmedians

Week 11: Asymptotic behaviour

Week 12:

This course differs in content from the main stream of extra-maths courses and is designed to introduce accessible and interesting topics from university maths. To do this course, students must be on top of the material in previous courses. This is because there are some advanced mathematical topics like Quadratic Residues, Ramsey theory, conics and intuitive topology. And they are quite hard.

**Schedule:** The course lasts 12 weeks: there is a small group lesson every Sunday from 9:00 till 12:00 UTC starting September 19th; there are 11 homework sheets and there is an Online Rate Table (see educational process if you do not know what is it).

**Price & payment:** The course is completely free of charge. However please note that this course is not easy and you need to make sure that you can manage it and that you can work hard. If it turns out that this is not the case we will propose you move to another group.

To apply scroll down on this page and click on "Log in and apply" button.

**Topics:**

Week 1: Permutations

Week 2: Analysis: sequences

Week 3: Analysis: continuity and applications

Week 4: Functional Equations

Week 5: Helly's theorem

Week 6: Countability, uncountability

Week 7: Probabilistic Method to solve problems

Week 8: Ramsey theory

Week 9: Quadratic Residues

Week 10: Intuitive Topology

Week 11: Geometrical properties of conics

Week 12: Using physics to solve maths problems

To apply scroll down on this page and click on "Log in and apply" button.

Week 1: Permutations

Week 2: Analysis: sequences

Week 3: Analysis: continuity and applications

Week 4: Functional Equations

Week 5: Helly's theorem

Week 6: Countability, uncountability

Week 7: Probabilistic Method to solve problems

Week 8: Ramsey theory

Week 9: Quadratic Residues

Week 10: Intuitive Topology

Week 11: Geometrical properties of conics

Week 12: Using physics to solve maths problems

Recap week (senior-extra-maths)

There are a lot of important ideas mentioned in courses EM-7, EM-8 and EM-9. And it is vital to be able to see when they are useful without any external help and hints. So this course is designed to help with that. We will test senior school maths knowledge as well.

So during a week participants will be given 3 problem sheets and there will be 3 discussions of them. No hints nor help apart from the discussions!

**Schedule:** We are not launching this course yet. However you can still log in our website so that we have your email in case we decide to contact you.

**Price & payment:** -

So during a week participants will be given 3 problem sheets and there will be 3 discussions of them. No hints nor help apart from the discussions!

Calendar