Get to know the other participants in the Maths Circle and test your logical thinking skills with the brain teasers and puzzles in the Maths Quiz.

The distance between two points is the length of the straight line connecting these points. But what if you live in a city with a rectangular road network?
Then the "straight line" is a poor measure of the distance travelled.

We are looking for a new concept of distance to describe distances here.

We then learn what the concept of a distance (more precisely a "metric") means mathematically and examine further examples of distance concepts.

After fractions, i.e. rational numbers, you learn about irrational numbers at school, e.g. √2, √3, e or π. Why can't 2 actually be represented as a fraction? - In this meeting, we will learn how to prove that 2 is irrational. We will familiarise ourselves with the proof technique of the proof by contradiction. We will then prove for similar irrational numbers that they are not rational.

What does a mathematician or technomathematician actually do after graduation? Get to know other exciting professional fields for mathematicians and technomathematicians in addition to the classic areas of employment at banks and insurance companies.

In the second part of the meeting, we will visit the Paderborn University campus.

Even if you already know vector spaces from school, you should definitely come to this maths circle meeting! We will introduce vector spaces axiomatically (no prior knowledge is required) and will see that they are much more than the ^Rn usually known from high school. For example, sets of functions can form a vector space, and the real numbers can be provided with a different addition and a different scalar multiplication than usual. We analyse many exotic examples to see whether they are vector spaces or not.

Why is ^2n>n2 for all natural numbers n with n>5, and how do you prove this statement? Why is the sum ^13+23+33+...+n3 the^same as (n(n+1)/2⁾²? -- These and other equations and inequalities that apply to all natural numbers above a certain _n0 can be shown using the principle of complete induction.

We get to know this principle and use it to prove various, sometimes surprising statements.

It explains how the common divisibility rules are related to the decimal system and how new rules can be found (for example for the number 7).

If you learnt about stochastics at school, then you are probably familiar with urn models. But where do the different formulae for drawing from the urn with/without putting back and with/without taking the arrangement into account actually come from? We will prove these and then use them to solve exciting combinatorics problems. Here is an example of such a problem: A pizza delivery service has just received 20 new orders, which it wants to distribute among its three delivery staff. The first and third delivery driver should each receive seven orders and the second only six. How many options are there for distributing the orders among the three suppliers?

In this maths circle session, we will learn about sequences of real numbers and their basic properties: bounded from below or above, (strictly) monotonically decreasing or (strictly) monotonically increasing, as well as the concept of alternating sequences.

Sequences of real numbers and the concept of the limit of such sequences (see next session) are the central basis for the introduction of the derivative and the integral.

In this maths circle meeting, we will learn about the concepts of limit and convergence of a sequence of real numbers, which are central to calculus.

Even if you did not take part in the previous maths circle meeting on "sequences of real numbers", you can still successfully take part in this session. However, it is easier if you already know sequences of real numbers from the previous meeting.

Together we solve two competition tasks from the first round of a previous national maths competition.

In this maths circle meeting, we will look at finite sums and infinite sums (series). Firstly, we will familiarise ourselves with the notation of sums and the associated calculation rules. We will prove these arithmetic rules and use them to calculate the arithmetic sum and the geometric sum. Then we will examine simple series: Why is it not possible to assign a finite value to the infinite sum over 1/k with k∈ℕ, but why does the infinite sum over (1/2^)k with k∈ℕ, on the other hand, have a finite value?

Together we will solve two competition tasks from the first round of a previous national maths competition.

(Of course, the tasks are different from those in the session on 28 June).