Monthly Archives: March 2010

The Drunken Finn

I just learned that the guy I talked about here, the one who goes randomly left or right, is known as the Drunken Finn. :-)

How Many Good Colorings?

Please comment your solutions, questions and remarks.. Suppose G is a graph in which each vertex has three neighbours, for example: Suppose we have three colors, red green and blue, with which we want to color the edges of the … Continue reading

Nasty Finite Combinatorics

Please comment your solutions, questions and remarks.. I was blamed for having too easy Wednesday problems. So beware! The level is coming up! Suppose that K is a set of n elements, $$n\in\mathbb{N}$$. Suppose that $$K_1,\dots,K_n,K_{n+1}$$ are subsets of K. … Continue reading

Andre’s Reflection Method

I promised to post something about random walks. I learned the content of this post while listening to Vilppu Tarvainen’s bachelor’s degree talk and I consider it is quite cute. Let us consider a one dimensional random walk: formally it … Continue reading

Posted in Combinatorics, Mathematics, Probability, Recreation | 1 Comment

Back To College

Please comment your solutions, questions and remarks.. Show that the following inequality holds for all $$k>0$$ and $$x\in \mathbb{R}$$: $$e^x>kx-k\ln k.$$ Level 1/5

Posted in Calculus, Mathematics, Wednesday Problem | 2 Comments

Even More On BFPT

I wouldn’t mind writing this unless I haven’t already posted two different proofs of Brouwer’s Fixed Point Theorem. Namely a friend of mine and a reader of this blog, exposed me to another way of proving it. This proof has … Continue reading

How Many Are True?

Please comment your solutions, questions and remarks.. At most 1 statement of this post is true. At most 2 statements of this post are true. At most 3 statements of this post are true. At most 4 statements of this … Continue reading

Posted in Logic, Mathematics, Recreation, Wednesday Problem | 1 Comment

walksonmath.net

Now this address redirects here. Also whitemath.org still redirects here.

Solution To The Previous Problem

Exceptionally I will present a solution to the previous Wednesday Problem. Only not shall I present any simplest solution but a cool one. The question was the following. Suppose a function $$f\colon \mathbb{R}\to\mathbb{R}$$ has the property that given any reals … Continue reading

Posted in Calculus, Mathematics | 3 Comments

Walks On Math

We’ve got a new name. The new name attempts to give a better impression of the nature of this blog. The posts mostly concern those mathematical entities that are currently dominating my mind in addition to my main research. Includes … Continue reading

Please comment your solutions, questions and remarks.. A continuous function $$f\colon\mathbb{R}\to\mathbb{R}$$ on the real numbers has the following property: Given any two reals a<b, the function f gets all possible values between f(a) and f(b) on the interval [a,b] (i.e. … Continue reading