I am a second year student in *Oxford* doing Mathematics and a former top-class *Olympiad competitor in Maths*. I've got many medals from international competitions, including a __slilver medal__ at the LIV __International Mathematical Olympiad__ in 2013.

What I can offer you is a *new, fresh approach* to high school mathematics from the *perspective of my Olympiad and university studies*. My main strength is to prove that not everything is as difficult as it seems and to develop my students' interest in maths.

Since 2014, I've been *lecturing on Olympiad level* to Bulgarian high school students (14+). Apart from that, for the past year I've been giving tutorials to all sorts of Bulgarian students on both Olympiad and high school mathematics.

I've got *excellent mastery of all sorts of high school material*, as well as *Olympiad algebra, number theory and geometry*. I've got some more specific knowledge in combinatorics as well.

I am a second year student in *Oxford* doing Mathematics and a former top-class *Olympiad competitor in Maths*. I've got many medals from international competitions, including a __slilver medal__ at the LIV __International Mathematical Olympiad__ in 2013.

What I can offer you is a *new, fresh approach* to high school mathematics from the *perspective of my Olympiad and university studies*. My main strength is to prove that not everything is as difficult as it seems and to develop my students' interest in maths.

Since 2014, I've been *lecturing on Olympiad level* to Bulgarian high school students (14+). Apart from that, for the past year I've been giving tutorials to all sorts of Bulgarian students on both Olympiad and high school mathematics.

I've got *excellent mastery of all sorts of high school material*, as well as *Olympiad algebra, number theory and geometry*. I've got some more specific knowledge in combinatorics as well.

No DBS Check

A function is a notion somewhat abstract to the non-experienced reader, but can be explained as follows:

You have a domain - that is a set, e.g. the set of all yellow birds. You also have a magic box with no bottom - that is your function. On putting a yellow bird in the box, exactly one thing comes from the bottom of the box; that could be an airplane, or a number, so imagine the box being very, very big. In most cases in the function, which we'll call "f" for convenience, we put only real numbers, say 12.1345. The result that the function gives us is f(12.1345), which as we saw above can easily be an Airbus, or a Concorde, but for the purposes of high school mathematics, f(12.1345) would be a real number. E.g. f(12.1345) = pi (which is approximately 3.1416).

We can denote functions as f(x)=x+1 for all real values of x, or we can denote them in a more general manner as:

f is such that:

1) f(x) = x if x is positive

2) f(0) = 12

3) f(x) = x^2 if x is negative.

Note that in this example for any real value of x we can determine f(x), so that our domain is the set of all real numbers.

The first example (f(x)=x+1 for all real values of x) is an example of a polynomial function, whereas the second example is not a polynomial, but rather three polynomials stitched together:

1) x, the identity polynomial;

2) 12, a constant polynomial;

3) x^2, a second degree polynomial;

Any polynomial is a function, and the main difference between polynomials and functions is that polynomials are very well-behaved. That is if you take p to be a polynomial, then p(12) and p(12.00000001) would most likely be two very close numbers. Also, polynomials p(x) can be written as linear expressions of 1, x, x^2, x^3,... (that is, multiply some of these by constants and add them); e.g. p(x)=3+14x-135x^3+x^2005.

On the other hand, there is a function f for which f(12) is a black hole, and f(12.00000001) is a mice - two not very close objects; a more high school - acceptable example is f(12)=1000 and f(12.00000001)=0, where f(x) could be "defined" (could exist) for x=12 and x=12.00000001 only (it is a matter of choice, really).

A function is a notion somewhat abstract to the non-experienced reader, but can be explained as follows:

You have a domain - that is a set, e.g. the set of all yellow birds. You also have a magic box with no bottom - that is your function. On putting a yellow bird in the box, exactly one thing comes from the bottom of the box; that could be an airplane, or a number, so imagine the box being very, very big. In most cases in the function, which we'll call "f" for convenience, we put only real numbers, say 12.1345. The result that the function gives us is f(12.1345), which as we saw above can easily be an Airbus, or a Concorde, but for the purposes of high school mathematics, f(12.1345) would be a real number. E.g. f(12.1345) = pi (which is approximately 3.1416).

We can denote functions as f(x)=x+1 for all real values of x, or we can denote them in a more general manner as:

f is such that:

1) f(x) = x if x is positive

2) f(0) = 12

3) f(x) = x^2 if x is negative.

Note that in this example for any real value of x we can determine f(x), so that our domain is the set of all real numbers.

The first example (f(x)=x+1 for all real values of x) is an example of a polynomial function, whereas the second example is not a polynomial, but rather three polynomials stitched together:

1) x, the identity polynomial;

2) 12, a constant polynomial;

3) x^2, a second degree polynomial;

Any polynomial is a function, and the main difference between polynomials and functions is that polynomials are very well-behaved. That is if you take p to be a polynomial, then p(12) and p(12.00000001) would most likely be two very close numbers. Also, polynomials p(x) can be written as linear expressions of 1, x, x^2, x^3,... (that is, multiply some of these by constants and add them); e.g. p(x)=3+14x-135x^3+x^2005.

On the other hand, there is a function f for which f(12) is a black hole, and f(12.00000001) is a mice - two not very close objects; a more high school - acceptable example is f(12)=1000 and f(12.00000001)=0, where f(x) could be "defined" (could exist) for x=12 and x=12.00000001 only (it is a matter of choice, really).