The following link points to a series of videos showing chemistry laboratory techniques, such as recrystallization melting point determination, thin-layer-chromatography and titration.

http://ocw.mit.edu/resources/res-5-0001-digital-lab-techniques-manual-spring-2007/videos/

## Friday, 24 May 2013

## Wednesday, 22 May 2013

### A Tally Font

Another short link. At the bottom of this page, there is a TrueType font for tally marks, and a font for calculator buttons.

http://www.subtangent.com/maths/resources.php

Very useful for example worksheets.

http://www.subtangent.com/maths/resources.php

Very useful for example worksheets.

## Saturday, 18 May 2013

### RSA Two-Key Encryption

So
everything in the last seven posts has lead up to this.

The RSA Encryption Algorithm is a mathematical method of generating two encryption keys. You then encrypt a message with one key, and decrypt it using the other key.

This allows you to keep one key private, and publish the other key to the entire world.

Then there are two ways you can use these keys:

The RSA Encryption Algorithm is a mathematical method of generating two encryption keys. You then encrypt a message with one key, and decrypt it using the other key.

This allows you to keep one key private, and publish the other key to the entire world.

Then there are two ways you can use these keys:

- You
look up the public key of your friend, and encrypt a message using
key. You have guaranteed that no-one can read the message**their public**your friend.**except**

- You
encrypt a message using
key. Everyone can read it, but no-one else**your private**could have**but you****sent it.**

__, and__**keep secrets**__Cool.__**prove identity.**### The Euclidean Algorithm and the Extended Euclidean Algorithm

This
is the last trick needed to understand the RSA method. The first
algorithm is a quick(-ish) method to find the greatest common divisor
between two numbers (a and b). The second algorithm also calculates
values of x and y that satisfies the following equation:

$ax
+ by = gcd(a,b)$

### Euler-Fermat Theory and Prime-testing

As
mentioned in the last post, Euler-Fermat's Theory states that for any
element m in a group:

The totient of a number is simply the number of Integers that are smaller, and coprime (i.e. no common factors).

This allows us to come up with a simple (though not foolproof) test for prime numbers.

If n is a prime number p, then the number of smaller Integers that are coprime, are

$m^{\varphi(n)}
= 1 \text{ mod } n$

where $\varphi(n)$ is the totient of n.The totient of a number is simply the number of Integers that are smaller, and coprime (i.e. no common factors).

This allows us to come up with a simple (though not foolproof) test for prime numbers.

If n is a prime number p, then the number of smaller Integers that are coprime, are

__. Thus $\varphi(p) = p-1$ for a prime number, and $m^{(p-1)} = 1 \text{ mod } p$ should be true for all the numbers m, smaller than p.__**all of them**### Lagrange's Theory of Finite Groups and the Euler-Fermat Theorem.

In my Group Theory post, I stated that once a Set of mathematical elements and a
mathematical operation have been proven to satisfy some basic
properties, all theories, proofs and facts from the mathematical
discipline of Group Theory, would automatically apply.

Lagrange's Theory of Finite Groups states that

**any**__can only be divided up into subgroups of the__**group**__.__**same size**
Euler-Fermat's Theorem is an application of this, that says that any
number (coprime to n), rasied to a special power (called the totient
of n) will give 1 mod n.

The coprime and totient properties of the second theory are a
consequence of the structure of the Multiplicative Group of Integers Modulo n.

### Euler's Totient Function

As mentioned in
the last post, when multiplying Integers mod n, there are some
Integers that can't have an inverse. My example was, that it was
impossible to multiply 2 by anything, that once divided by 10, gave
you a remainder of 1. Likewise for 5. And if an element doesn't have
an inverse with respect to some mathematical operation, then that
element can't be a member of a Group.

### The Power of an Example – Modular Mathematics

Recently
I took a class of students on a Physics excursion. On the trip there, I observed some of them working a Maths C assignment on modular multiplication. I knew a
bit of mod mathematics from my programming experience, and was able
to help them on some of the tougher concepts, but something a student
said, instantly cleared up some aspects of Group Theory that I had
been struggling with
for
years.

### Group Theory and the RSA Encryption Algorithm

This is another large group of postings, focusing on the
culmination of three year's private study – I finally understand
the RSA Encryption Algorithm. I'm one of those people that finds
mathematical concepts baffling and confusing unless I understand

Anyway, I will be presenting my understanding of RSA in the following sections:

__aspects of it. If there's any vagueness or ambiguity anywhere, it niggles at my mind and drives me up the wall. No I don't have Aspergers', I'm just very pedantic. :-)__**all**Anyway, I will be presenting my understanding of RSA in the following sections:

### Group Theory

I'm currently reading S. Sternberg's “Group theory and physics”.
I bought it about four years ago. I have notes written in it up to
page 66, but only really understand about ¾ of pages 1-15 and 48-60.
It's hard going, but the book does have the advantage that nearly
everything important about Group Theory seems to be included.

But the basics are:

A mathematical Group consists of:

But the basics are:

A mathematical Group consists of:

- a Set of mathematical elements (numbers, matrices, rotations,
etc.) that, in the abstract, we shall refer to here-on in by
pronumerals (e, a, m ...) and

- an operator (addition, multiplication, matrix multiplication,
etc.) that we shall represent with the $\cdot$ symbol.

__operator. I will be showing an example of each Group property using this group.__**addition**## Wednesday, 15 May 2013

### Manual: GeoGebra 4.2 in a Nutshell - GeoGebraTube

Whoop, just what a math teacher wants, a free manual for the opensource program Geogebra (.org)

I've learnt a few new features just by having a skim through this.

Manual: GeoGebra 4.2 in a Nutshell - GeoGebraTube

I've learnt a few new features just by having a skim through this.

Manual: GeoGebra 4.2 in a Nutshell - GeoGebraTube

## Sunday, 12 May 2013

### Cellcraft - A Cell Organelle Game

The following link is to a wonderful resource for teaching functions of cellular organelles - I consider it to be appropriate for juniors and an intro for seniors.

http://www.carolina.com/teacher-resources/Interactive/online-game-cell-structure-cellcraft-biology/tr11062.tr

http://www.carolina.com/teacher-resources/Interactive/online-game-cell-structure-cellcraft-biology/tr11062.tr

## Friday, 3 May 2013

### Simulating Heat and Energy

Quite recently I've found a lovely little java application on the Internet.

http://energy.concord.org/energy2d/

It's a heat simulator that allows you to investigate conduction, convection and radiation.

http://energy.concord.org/energy2d/

It's a heat simulator that allows you to investigate conduction, convection and radiation.

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