Second year

So this summer I decided to return a few weeks earlier and use the opportunity to work on Alumni Events. This was different from term times in Cambridge; I had time to visit many museums and galleries. Unfortunately, there are almost no concerts outside of term, and student theaters are obviously closed.

Second year is quite different from the first. The pace is faster, which is natural because we are used to working hard now. The lectures are not much harder, but completing work for supervisions takes me much more time now. On the other hand, they are more inspiring than before. Mathematics consists to a large extent of understanding its language. That is why there are so many definitions and why they cannot be omitted. This language (or system of definitions) forms the way in which we think.

For example, I was told that teachers in the USA define the angle bisector as the line through a vertex of a triangle which divides the opposite side in the ratio of lengths of the adjacent sides. This is equivalent to saying that it halves the angle, which is the next property proved. In contrast, Czech teachers define it as the line bisecting the angle and the prove the property called the bisector theorem. This changes how we approach the object. The first definition makes you think about it as an algebraic object, whereas the second shows it as geometrical object.

In higher mathematics, it is similar. You may build the theory of, let's say, Markov chains on either of the concepts of probability or linear algebra. Both approaches give you the same results, and the proofs are often similar, just proved using different languages. And the results are the same, since it describes the same theory.

This happens a lot. For example, the independent discovery of calculus by Newton and Leibniz, or the creation of non¬Euclidean geometry by Gauss, Lobachevsky and Bolyai.

If you have read down to here, you are probably pretty interested in studying abroad. If this is the case, please don't hesitate to contact me.