…for mathematicians

An updated version of the 11 commandments, which seems appropriate at this time of year!

**11 commandments revised**

…for mathematicians

An updated version of the 11 commandments, which seems appropriate at this time of year!

or as a poster: **11 commandments revised**

To quote Angela Lee Duckworth:

“Grit is passion and perseverance for very long-term goals. Grit is having stamina. Grit is sticking with your future, day in, day out, not just for the week, not just for the month, but for years, and working really hard to make that future a reality. Grit is living life like it’s a marathon, not a sprint.”

**Happy New Academic Year **(using **geoGreeting**) (Click on the image).

Many of you will still be enjoying your holidays but holidays are perhaps a good time to make some resolutions for the next academic year.

Firstly, remember the ~~ten~~ eleven commandments!

To elaborate a little more on some of these:

5 – looking it up – there are several excellent resources online for you to **look up definitions** or find **extra examples**. Never rely on just one source if you are finding a topic tricky, it can be helpful to see explanations written by different authors.

6 – **To learn Mathematics you need to do Mathematics**. You can never do enough examples! There are plenty of questions

9 – if you want to practise your arithmetic you could **play some games**! If you enjoy Maths games there are many **excellent free resources** available.

10 – on writing the language of mathematics correctly – see this clear **guide to writing Mathematics**** **from Dr Kevin P Lee** **and from John Kerl some excellent **tips for mathematical handwriting,** many of these tips these apply to students of all ages – do you distinguish carefully between a 1 and a 7 for example? Perhaps it is hard to tell whether you have written a 2 or a z or perhaps your 5s look a bit like a letter s?

Have a look at Peter Alfeld’s guide to **Understanding Mathematics** which he wrote for his students at Utah University.

Are you familiar with all the excellent (free) resources online to help your studies? Have you tried the brilliant **Desmos graphing calculator** for example, or used **WolframAlpha** to check your work?

Some more thoughts for you.

- Are you guilty of making any of the
**classic mistakes**? - How are your problem solving skills? There is plenty of good advice available – see
**this publication**from Arizona State University for example - If you are studying at university then have a look at Kevin Houston’s ‘
**How not to get a good mathematics degree**‘ and ‘**How to get a good mathematics degree**‘. He also has provided a pdf file you can download:**10 Ways to Think Like a Mathematician**. Kevin Houston works at the University of Leeds in the UK.

If you are trying to get organised generally then some of the resources on **this page** might be useful. I recommend Evernote highly (it’s free).

Wishing you all a very happy and productive new academic year!

**Happy 2013 **(using **geoGreeting**) (Click on the image).

Time for some new year resolutions for Mathematics students!

Remember the ~~ten~~ eleven commandments!

To elaborate a little more on some of these:

5 – looking it up – there are several excellent resources online for you to **look up definitions** or find **extra examples**. Never rely on just one source if you are finding a topic tricky, it can be helpful to see explanations written by different authors.

9 – if you want to practise your arithmetic you could **play some games**!

10 – on writing the language of mathematics correctly – see this clear **guide to writing Mathematics**** **from Dr Kevin P Lee** **and from John Kerl some excellent **tips for mathematical handwriting,** many of these tips these apply to students of all ages – do you distinguish carefully between a 1 and a 7 for example? Perhaps it is hard to tell whether you have written a 2 or a z or perhaps your 5s look a bit like a letter s?

Some more thoughts for you.

- Are you guilty of making any of the
**classic mistakes**? - How are your problem solving skills? There is plenty of good advice available – see
**this publication**from Arizona State University for example - If you are studying at university then have a look at Kevin Houston’s ‘
**How not to get a good mathematics degree**‘ and ‘**How to get a good mathematics degree**‘. He also has provided a pdf file you can download:**10 Ways to Think Like a Mathematician**. Kevin Houston works at the University of Leeds in the UK.

If you are trying to get organised generally then some of the resources on **this page** might be useful. I recommend Evernote highly (it’s free).

Wishing you all a very happy and productive new year!

Let’s suppose you are looking for some extra examples. You have probably checked all the usual websites, **BBC Bitesize **for example (also available **on Facebook**).

Some of my students were recently looking at examples like this and wanted some further problems:

Note the thinking behind this:

You should spot that the denominator is the difference of two squares, hence (x+5)(x-5)

If we are to have any hope of simplifying when we factorise the numerator, one of the factors must be (x+5) or (x-5), of those two it must be (x-5) or we would not be able to obtain the -19x term.

Factorise the numerator: (3x-4)(x-5)

A site perhaps not so well known by students is **The Centre for Innovation in Mathematics Teaching.** If you choose the **GCSE course material** and scroll down the page you will see all the pupil textbook chapters. (Also note all the other materials for students from 5 – 18!)

Chapter 10 on equations includes many useful algebra examples and exercises including problems of the type above (see worked example 1 on page 41 and the exercises on page 43). Note that each GCSE section has **answers**.

You should check any factorisation by multiplying out your answer. You could also check answers using WolframAlpha.

Note that you could enter the whole expression and simplify it – WolframAlpha will give you alternate forms; for this type of question you are require to give the simplest single fraction that you can.