Teaching

An Eyewitness account from the NCPC – Part 3/3

An Eyewitness account from the NCPC – Part 3/3

Editors note: Yesterday we left Suprdewd and his teammates sweating over the remaining problems to solve, so lets pop our heads back in and lets see how this ends. Read part 1 and 2

Problem F

My teammates had trouble understanding the description at first, but figured it out after writing it out on a piece of paper (I recommend taking a pen and paper to a competition if you’re allowed to).

Read the whole problem description here. Continue reading →

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An Eyewitness account from the NCPC – Part 2/3

An Eyewitness account from the NCPC – Part 2/3

Editor note: We are coming back from the short break with a lot of exciting students ready to throw them self at 10 exciting problems that needs to be solve in a very short time. So lets get right into it. Read part 1 here

There are 10 problems, uniquely identified with a character from A to J. They are not ordered by difficulty, but in a competition like this you want to finish the easiest problems first.

The problem set is located here, but since the problem descriptions are long, I won’t be posting them here. I recommend you read the problems and try them out for yourself before reading the rest of the story. You need to read the descriptions of problems A, C,  D and F at least, which are the problems I’ll be talking about. Continue reading →

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An Eyewitness account from the NCPC – Part 1/3

An Eyewitness account from the NCPC – Part 1/3

Editors note: The absolute top commenter and a huge help on the blog Suprdewd  has recently participated in the Nordic Collegial Programming Challenge 2011. I was all excited of his participation and convinced him to write about the experience. SuprDewd is a 17 old computer science student from Iceland with 4 years experience programming and a much greater insight in the C# API than I can ever hope to gain. He keeps a nice collection of methods and algorithms at his Github repository which I can recommend you to pay a visit. But enough blabbering from me. Lets hear what he has to say.

I recently took part in the Nordic Collegial Programming Challenge 2011 (NCPC). It was very exciting and I had loads of fun. The problems were tough, but I’m going to walk you through some of them, while trying to share insight about the competition.

Before we get started, let me just give you a run through what NCPC and the international version ICPC is. Continue reading →

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A Mathematicians Anti-rant

A Mathematicians Anti-rant

This is a rant over other people ranting about people’s ignorance towards mathematics. Or rather an anti-rant since two negatives makes a positive (sometimes). Got your attention? Good, now read on.

By now I have seen a fair share of bitter remarks  over the theme that someone presents them self as a mathematician, and the answer they get is a blank stare and a comment in the ball park of “I can’t even balance my own checkbook”. Same theme of rant also cover someone stating that “Oh, mathematics is easy. It is just memorizing the formulas and plug in the numbers!”.

I have seen them and I have laughed hard over the witty retorts and remarks people have come up with. But I had an epiphany when I thought more about it. The person stating those things are not necessarily being rude, but in their world that is what mathematics is. I agree with you that comments like that are narrow minded  but the person who states it doesn’t know that there is a lot more to the wonderful world of maths.

What I realized is that most things can be reduced to a statement of “Oh that’s easy! Just…” So let me give you an example of a hobby of mine: Photography.

Oh Photography! Now that’s easy!

With today’s camera all you need to do is turn it on and press the shutter, and BANG you have a photo.

Photo of MushroomsWell true you have a photo just like aunt Olga’s 225 vacation photos from some boring resort. The photos are bland the composition sucks and she didn’t really know what she wanted to tell with the photos. Indeed it is photos but they are not really interesting. Taking interesting photos takes knowledge, care and planning. A study of technique, composition and not least hours and hours of practice.

The picture on the right is a photo I spent about half an hour to take. It took a lot of experimenting with mixing the natural light with a flash, and not least getting the composition right. I really like the photo though. Most people can probably tell if a photo is good, I can usually tell what makes it good. The difference is that I have years of practice and interest in it.

A colleague of mine came to work really proud with a photo of a cake his wife made for his daughter’s birthday. It was this bright pink cake formed as a dress around a barbie doll. I am sure it was the most beautiful cake a 4 year old girl could imagine.

However, what I immediately saw was how this wall plug was growing out of the back of the barbie which happens when you are not careful with the interaction between foreground and background. He could have avoided that by taking half a step to the left. I also noticed that the white balance was off. Besides that he should have taken the shot closer to the cake and at a lower angle.

I could have made funny remarks and retorts about his knowledge of photography.  But how should he know? He just used all the photography skills he had to get the result – a picture of the cake he could show me.

So where do I want to go with this?

So photo can be reduced to something trivial even if it contains lots of depth and study. However, there is an important difference between photography and mathematics. Photography  is easy to show people. You can whip out the smartphone and show them your 3-5 best shots. So you can meet people in terms they understand and that they can rather easily relate to. Even though they still don’t know all the work and mechanics behind it.

Mathematics is different. Mathematics beyond arithmetic is highly abstract and requires a special way of thinking to get the grasp the workings of it. And it is not something you are exposed to in your everyday life. Well, sure you use lots of things relying on mathematical breakthroughs, but you can’t see that when you use your GPS or smart phone.

So people who state that math is easy are right –  it is easy in their world. They don’t know that there exist more to it than that. If they state that they don’t get math, it is probably because they were introduced to something abstract but stopped there and never got to the level where they can see these abstract things loop back into the real world.

So now we are getting to my point. When people say something you find derogatory about math they are likely right in their world and not really trying to be provocative. Try to put your self in their shoes and think. Do they know that arithmetic is just a small part of mathematics, or is that all they have ever been taught? Tp be anecdotal again;  another colleague and good friend of mine once told me something wise when I got pissed off by someone. He said “The person with the greater surplus should always try to see things from the other person’s perspective and act based on that”. I still hate him for being so right about that.

If they don’t know better, you have no right whining about it. You have a job to do! You need to explain what the maths, you are working with, is about in a terms they can  relate to. I know it is insanely difficult for some areas, but you need to work on it since you are the one with the knowledge. Personally I have at least five different stories I can tell in a short time about my work depending on what level of understanding people are at, and what I think they find interesting. And trust me people will let you know if they are bored.

So, it was a long rant but the point is: Don’t make retorts and don’t be mad at them, in their world mathematics is equal to arithmetic. If you want them to know otherwise you have to teach them, since there is no way they will discover it for them self.

Image credits

The image was created by Shoutput.com and kindly shared under the creative commons license. So a little shout our for them

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Relatively prime – Stories from the Mathematical Domain

Samuel Hansen has come up with the great proposal of making an 8 part podcast called Relatively prime which he describes as

Relatively Prime will be an 8 episode audio podcast featuring stories from the world of mathematics. Tackling questions like: is it true that you are only 7 seven handshakes from the President, what exactly is a micromort, and how did 39 people commenting on a blog manage to prove a deep theorem. Relatively Prime will feature interviews with leaders of mathematics, as well as the unsung foot soldiers that push the mathematical machine forward. With each episode structured around topics such as: The Shape of Things, Risk, and Calculus Wars, Relatively Prime will illuminate each area by delving into the history, applications, and people that underlie the subject that is the foundation of all science.

Continue reading →

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Khan Academy – a great source of math knowlegde

Khan Academy – a great source of math knowlegde

This post is shameless promotion of what I think is a great site – Khan Academy. If you don’t like shameless promotions, you should stop reading now.  The site features a whole set of instructional videos along with a good amount of exercises. All topics are what I consider to be some basic skills of mathematics. Not basic because they are simple skills, but because they are fundamental for you to build upon. Continue reading →

Posted by Kristian in Math, 3 comments

Proof method: Direct Proof

In my first post on my journey for improving my mathematical rigour I said that I would go through a few different techniques for conducting proofs.

The first one I want to dabble into is direct proofs.  This is the “simplest” method and sometimes it can seem that the proof isn’t there at all.

It will often go something like “if a then b”. So using some definition of a, we can show that b follows as a direct consequence through an unbroken line of logical arguments such that

a -> … -> b

Lets try it out on some sample problems Continue reading →

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Improving my mathematical rigour

I have reached a point in my mathematical journey where I feel the need to learn how to make sound arguments for the validity of a mathematical claim. Or in other words, I want to learn more on how to prove things.

The path I took through the Danish educational system has never dealt much with mathematical proofs, but rather on how to apply the mathematics we have learned. I have developed an intuition for mathematics in some areas. But I lack mathematical rigour, so I often time have to resolve to hand waving instead.

The usual approach to learning proving techniques is through a taught topic where you are presented with some proofs. Through that you will expand your toolbox and learn how to do proofs. However, I would through a series of blog posts dabble into how to prove mathematical things and study different techniques.

Ben Tilly pointed me through his blog – random observations – to a document he wrote on how to do proofs. It has a flow chart which you can also see to the below, which I think is a very thorough way to ensure that you get through the proof. It doesn’t say anything about how to actually make your arguments, but it helps you break down the problem.

Let me spend the rest of this blog post to go through the flow chart and interpret it. Continue reading →

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GeoGebra – a cool geometric tool

GeoGebraAt work I use many fairly advanced tools that can do a lot of things such as Matlab, which in all it’s glory is a very nice tool. However, for things such as Project Euler which does contain small problems, where I try to get a feeling for the problem in a whole other sense than I usually do Matlab is not very good, let alone that I could never afford it for private use.

I have been pointed towards a tool called GeoGebra which is a free tool written in Java, where you can manipulate lots of different geometric objects such as functions, points and lines. You can also use tools such as intersection and getting the slope shown. You can even define your own tools if you like.

I think it has been made as a teaching tool for high school students, but I have been playing around with it for a short while now and I can definitely see some useful things in it when I try to grasp a problem. It wont work on abstract problems, but small geometric problems will be a thrill to work with from now on.

It promotes it self as

GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus in one easy-to-use package. It has received several educational software awards in Europe and the USA.

The best thing about the tool is the readily available material. There are a tutorial and manual right at the GeoGebra help site, there are tons of You tube videos from GeoGebra let alone the ton of user made videos and there is the user forum.

Math and Multimedia has a list of the 10 best tutorials for the tool to get you started. and GeoGebra Applet Central has some applets which shows the use of different parts of GeoGebra and I especially like the applet showing how to approximate Pi by increasing the number of sides in a polygon inscribed in a circle.

I am very impressed so go ahead and take a look at it at GeoGebra. You will definitely see some illustrations from me using this tool in the future, since it is so easy to illustrate the functions and so on.

Posted by Kristian in Math, 7 comments