## An Interactive Animation Visualising a Group Isomorphism

An interactive animation programmed in JavaScript illustrating the isomorphism from the quotient of the additive groups of reals by intergers $Latex formula$ to the unit circle on the complex plane $Latex formula$ defined by the formula:

## How to Tackle the Difficulty to Start

The difficulty to start may be one of the biggest setbacks in achieving almost anything in life. You sit down to write the first chapter of your book. You are bothered by some items on your desk, so you clean that first. Then you put some music on. No, but you can’t concentrate with this music, so you change the music. You adjust the brightness of your screen and then you check social media just in case. Then you think that maybe you should do something else instead, because writing a book may not pay off. You decide to stick to your plan, however, and write, but then you check how much time has passed and realise that you are actually thirsty….

Does this sound familiar? In my case it sometimes gets even worse. I used to start feeling guilt about Read more

## More on my Algebra teaching

What tricks do you use in your teaching or have found useful while studying? Comment below!

A couple of months ago I wrote about my eccentric first algebra lecture. I am lecturing Algebra I in this semester which is in fact split into two parts. The teaching methodology this course is being taught in (and has been taught a couple years before me) is already of interest to people outside of our department. I have additionally experimented with some extra stuff such as magic tricks and YouTube videos and below I summarise all that.

## The Kick-ass Value of Expert Advice

New: Don’t have time to read? Scroll down to watch a 1-minute summarising video instead.

Last Tuesday I was, as regularly, practising acrobatics in Sirkus Huima’s free exercise shift. Osmo Tammisalo who is, among other things, an expert acrobat happened to be there and he came to watch my back flip. He started giving me some advice and in the first ten minutes my back flip improved more than in the previous two months. After these ten minutes he said “perhaps it will help if you learn flic-flac first”. I was horrified. Flic-flac? I always thought it was extremely difficult, and considered it much more difficult and scarier than the back flip. But he insisted that I try to jump backwards… even if landing on my head (don’t worry, into a sea of pillows). And so I did. After 15 minutes of practice under his supervision, this was the result (video):

## Algebra Lectures and Motivation

This semester I am lecturing an introductory course to abstract algebra at the University of Helsinki where I work. For me this is an exercise in mathematics education and public speaking. This is the biggest audience I have ever had in a course: a little short of 200 students. In order to give an exciting first impression of the lectures and maximise future attendance I decided to give a somewhat flashy first lecture. I dressed up in a white suit a hat and a bright red scarf. I dedicated the first lecture to “intuition pumps” which were: