28th June is a Perfect Day to enjoy some Mathematics!
Perfect because 28 and 6 are both perfect numbers. You can easily check for properties of any number with Tanya Khovanova’s Number Gossip where we learn that 28 does not only have the rare property of being perfect, it is also composite, even, happy, odious, practical, triangular and Ulam! You can browse all the properties here.
28 is also happy! Happy Numbers – a favourite investigation, Dr Who knows about happy primes!
It’s also National Tau Day! Pi is wrong…..
This video provides a short version of the Tau Manifesto (14 minutes)
Have a look at this Desmos page (or select the image).
Before you take a peek in the Love folder, can you identify the functions used for the various letters?
This came about because of a Twitter conversation. , Admissions Tutor & Senior Lecturer at Loughborough University shared this image. I replied that we should do some dancing too!
And Desmos thanked us both for spreading the love!
For more on Desmos – see this series of pages.
UK Maths Challenges
You can practice for the UK Maths Challenges with these past papers. Questions and full solutions are provided.
You could generate a random quiz, using Mathster’s UKMT Mathematics Challenge Online Quiz. Choose Junior, Intermediate or Senior and one of three difficulty levels; you can also choose the number of questions, a time limit and the order the questions are presented in – random or in order of difficulty.
Nrich have a series of short problems based on the UK Junior and Intermediate Challenges.
Nrich publish new problems every month. Why not try and get a solution published on their website? There is a menu specifically for students. You can sign up for an Nrich student newsletter if you want to be notified of new developments on the site.
If you have not tried Nrich problems before you may find their recommended starter problems good to try. You can search for problems by topic if you wish.
If you have not tried Nrich problems before you may find their recommended starter problems good to try. You can search for problems by topic if you wish
Signing up to Brilliant (including an easy option for sign in for Facebook users) will allow you to join an international community and try numerous.questions at various levels.
For a really clear plotter showing the connection between the Cartesian graph of r=f(θ) and the graph in polar coordinates try this Polar Curves and Cartesian Graphs applet. Watch the display carefully as you move the slider; you can easily see when r is negative for example.
For more on Polar Curves – including notes and the use of Desmos, see this post.
Some books that might be useful for you:
Complete GCSE Maths Revision text from CLCnet. Don’t be put off by the 2007 date – this is still useful. The text includes numerous set of questions for each topic by grade with solutions for all the examples.
Craig Barton’s E-Book of Notes and Examples is a comprehensive set of notes with very clear worked examples; this is extremely useful for students age 11 to 16 and for any older students who need a refresher.
AQA Further Maths Text
For Further Mathematics A Level (age 16-18) AQA have provided a set of three textbooks.
(Scroll down to Resources for students).
AQA-MFP2-TEXTBOOK AQA-MFP3-TEXTBOOK AQA-MFP4-TEXTBOOK
‘Street Fighting Mathematics‘ by Sanjoy Mahajan, with the excellent sub-title ‘The Art of Educated Guessing and Opportunistic Problem Solving’ (note the link on the left to the free Creative Commons edition under Essential Info).
Check Amazon for Kindle books, a small number of which are free or very low cost. Now you don’t have to own a Kindle to read Kindle books as the Kindle app is free to download for any device you may own: PC, phone or tablet. It is possible to search Kindle books by price, so a search on Mathematics books by price from lowest to highest will give all the free entries; there are lots of toddler books and samples there but the odd useful book is available. A very useful search for low cost books is a search on popular Mathematics books, price low to high. which returns popular Mathematics and Science books for as little as 99p.
Try Henry Ernest Dudeney’s – Amusements in Mathematics a puzzle collection (with solutions). The first set of puzzles offers a little History, money – pre-decimal! There are several categories of puzzles available. Or try Edwin Abbott’s Flatand the tale of a two-dimensional world occupied by geometric figures.
Project Gutenberg includes numerous Mathematics books, including classics such as Flatland. (Mark Twain’s comment on “Classic’ – a book which people praise and don’t read.” always amuses me!)
You could even write your own book! If publishing your own Kindle eBook feels a little too much right now – you could try something simpler using Storybird – click the image to see this story on Storybird
..and finally, I must mention John & Betty’s Journey Into Complex Numbers!
Firstly, A little more on why we have a leap year from The Telegraph, and/or watch this video from Numberphile.
Mathisfun – Leap Years
We can also find details on Mathisfun.
The Google Doodle for today celebrates Leap Year
For any Excel users this formula will determine whether or not a year is a leap year:
=IF(OR(MOD(A1,400)=0,AND(MOD(A1,4)=0,MOD(A1,100)<>0)),”Leap Year”, “NOT a Leap Year”)
Click on the image and then on the slider!
Why not send your mathematical friends (or anybody else!) a Desmos Valentine? The wonderful team at Desmos have made their brilliant math-o-grams available earlier this year….and watch out for new designs coming soon.
The math-o-grams are really easy to create; why not give it a try? Just select your design, add your message and share!
John Kerl – Tips for mathematical handwriting
Is your writing legible? Is that a 5 or an s, a 2 or a z? Included on the Study Tips page see John Kerl’s Tips for mathematical handwriting.
Dr Kevin Lee – A Guide to Writing Mathematics
Is your writing clear and well structured? Easy to read and follow?
You will find some excellent examples from Dr Kevin Lee in his Guide to Writing Mathematics.
See also Ten Simple Rules for Mathematical Writing from Dimitri Bertsekas.
These sites are mentioned elsewhere on this site but these all include notes and exercises on Algebra. Answers are included in these resources and of course you can check answers on WolframAlpha.
Note there are resources for older students further down the page.
The following example – note the colours shows how to expand three brackets.
You could check your answers on WolframAlpha and change the query to make up your own examples.
The Maths Teacher (age 11-17)
David Smith’s site, The Maths Teacher has an extensive collection of videos to help you study Mathematics. GCSE (age 14-16, though many of these resources would be helpful for younger students also) and A-Level (age 16-18) lessons are available. For each topic not only is a video available but also a transcript and exercises with worked solutions. This makes the site ideal for revision – you have the choice of perhaps just trying the exercises or if you feel you need more help you can watch the video – whatever is right for you.
Trinity School have very helpful Mathematics resources
– many examples for you to try (answers included) including Algebra
Trinity School Nottingham – numerous questions and answers