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Knots Unravelled

“This little book is full of big ideas and exudes all the qualities associated with first-rate mathematical exposition. … almost the first half of the book can be understood and enjoyed by anyone with very little mathematical knowledge.”

Book Review, The Mathematical Gazette — March 2014

“The very impressive feat is that this gentle treatment still manages to be quite precise. … After having read this book, it may be my new favourite for introducing knot theory to non-mathematicians.”

Book Review, Mathematical Reviews — January 2013

“Loads of applications for a class even of limited ability … A thoroughly engrossing read and playfully recommended to any person who loves mathematics.”

Book Review, Mathematics in School — May 2012

Knots Unravelled is slim, easy to read, and filled with delightful mathematical ideas. … The discussion is appropriately informal and is interspersed with exercises … A dedicated high school student could enjoyably pass quite a bit of time drawing pictures or playing with string in an effort to solve them. … The organization and writing of the book are superb.”

Scott Taylor, MAA Reviews — April 2012

Knots Unravelled is a beautiful introduction to the world of knots at a basic level. It is addressed to any enquiring reader from around age 12 or 13, so the concepts and ideas are explained in a very intuitive way.”

Book Review, European Mathematical Society — January 2012

“It is a very attractive presentation of elementary knot theory and I shall have no hesitation in recommending it to any beginner wondering how to start thinking about knots.”

Professor Raymond Lickorish, University of Cambridge, UK — December 2011

“I just got your book, thanks very much! It looks very nice — and I'm sure I'll make use of some things in it when I next teach my course.”

Justin Roberts, Associate Professor, University of California, San Diego — November 2011

“What a gorgeous book! In two senses of the word: First, the content (alternating regular chapters with interludes is a beautiful idea). Second, the excellent figures. Congratulations!”

Jeffrey Weeks, Author of The Shape of Space — October 2011

Progress to Advanced Mathematics

“I have found the material on equations of straight lines and equations of curves especially valuable. The typesetting and diagrams are admirably clear, as one would expect from this source.

There is a strong argument that increasing depth of understanding, by learning how to deal with harder questions, is educationally preferable to acceleration. This book provides plenty of material to assist the former, more thoroughly than in any A Level textbook I have seen. It is strongly recommended to all schools and colleges.”

Book Review, The Mathematical Gazette — July 2013

“Preparing for A Level:

Now that you've finished your GCSE Maths, if you are considering taking A Level Mathematics it is a good idea to do some preparation over the summer.

Not only is it easy to forget your Mathematics over the summer break, A Level is much more algebraic than GCSE so you really need to hone those algebra skills to have a good foundation for September.

Also the link between algebra and graphs is a vital tool which needs to be used with ease when solving A level problems and geometry needs to performed without any difficulty.

Some of the skills you need are included in this new book.”

Mathematics Teacher, Manchester, blog Mrs M's Maths Musings — May 2012

“All diagrams are clear and the grading of questions should give every student confidence with the basics … packed with plenty of questions … At least one class set would enhance any department.”

Book Review, Mathematics in School — May 2012

“First glance: it's just what I was after. I like to start a maths lesson with 10 minutes of basic algebra practice — sorely needed by many A-level students. I've struggled in the past to find a comprehensive resource for that, having to dig up a few exercises here, a few questions there, or knock it out myself. I think that with your book, my problems should be over: no waffle, no unnecessary explanation, just plenty of questions on lots of useful topics, with a good range of difficulty.”

Mathematics Tutor, Leeds — August 2011

Progress to Higher Mathematics

“I am absolutely delighted with Progress to Higher Mathematics. It's a book I've been looking for for a long time. You are definitely filling a gap in the market. I will certainly recommend it to my pupils.”

Mathematics Teacher, Highland — September 2011

“Any student who is progressing to A level or, I assume, Scottish Higher, from a minimal base at GCSE or equivalent urgently needs to make time for work of this sort, and this short book is an excellent resource for such students.”

Owen Toller, Book Review, The Mathematical Gazette — March 2009

“The overall presentation of the book is very good …. The graphical diagrams are very clear and precise (most given to the right of the question). Whether this book is used as an essential skills for the Higher course or as part of the Higher course will be dependent on the class (and school), but either way, pupils who persevere through the exercises will most definitely gain mathematically. At £8 per book, this is value for money and each department should have at least one class set.”

Book Review, Mathematics in School — November 2008

“This book offers students the opportunity to do exactly as it says in its title, Progress to Higher Mathematics!”

Karen Byrnie, Book Review, The Scottish Mathematical Council Journal 37 — March 2008

“An ideal resource for those doing Higher Mathematics—in fact an essential buy!”

Jim Reid — March 2007

“This is what teachers have been looking for for years and is exactly what the pupils need.”

Principal Teacher of Mathematics, Renfrewshire — January 2007

“I’ll use this with the Credit course as well as to augment the Higher Course.”

Principal Teacher of Mathematics, Renfrewshire — January 2007

Geometric Origami

“… for someone with a deep interest in mathematics, especially geometry, who has a passing interest in origami, I would recommend this book as an enjoyable and informative read.”

"The book is well laid out, with frequent use of diagrams, which greatly aid understanding."

Mary Fortune, Book Review, The Mathematical Gazette — March 2010

“This is a book which yields wonderful nuggets, regardless whether it is read carefully from beginning to end, or whether it is skimmed superficially.”

“It will be of value to a wide range of audiences; newcomers to the field of mathematical paper-folding will find, easily accessible, all the tools they need, while experts will enjoy a well-written, beautifully illustrated reference work.”

Georg Gunther, Book Review, Crux Mathematicorum — October 2009

“Are you looking for some hands on tasks to do in your upper division geometry or abstract algebra class? If so you should check out Geometric Origami by Robert Geretschläger. This book connects the art of paper folding to geometry and algebra.”

"Rigorous proofs appear mostly in the first section of the text, and could be used as nice examples for students learning to read and write proofs."

Suzanne Caulk, Book Review, MAA Online — September 2009

“… the book is really for a mathematics enthusiast who will see the challenge of constructing a regular heptagon or a trisected angle as an end in its own right. And good for them! The world needs more origami-inclined mathematicians."

David Raynor, Book Review, British Origami 19 — February 2009

The Beauty of Mathematics poster collection

“We recently ordered 4 sets of your posters which are now displayed in our Maths block and generating lots of interest from students and staff.”

Leader of Mathematics, Essex — November 2010

“Many thanks for the poster sets which we received recently from you. We like them so much that we would like to order some more.”

Head of Mathematics, London — June 2008

“I have just received the posters you produced – all were enthusiastically put up by my department, they really are good!”

Head of Mathematics, Sheffield — July 2005

“I bought three sets of Curves from Circles, but have lost the accompanying notes. The kids are desperate to see them – could you send me another copy?

Will shortly put in an order for the Tilings and Polyhedra too – really fabulous posters.”

Head of Mathematics, Kent — March 2005

“Thanks again for an excellent collection of posters.”

Head of Mathematics, Canterbury — February 2005

“These interesting designs use great graphics skills and colours which are pleasing to the eye. My favourite design is the Lemniscate of Bernoulli ... because it looks complex, making a very striking pattern.”

Amy, aged 14 — June 2004

“What a delight to have good quality material to display and to use to initiate class discussion.”

Head of Department, Glasgow — June 2004

ClubMaths™ activities

“I used the material today with a group of talented year 7, 8 and 9 pupils who appeared to enjoy it very much. Thank you.

Head of Mathematics, Surrey — June 2009

“I have just downloaded the first 2 ClubMaths activities, thanks.

Having looked through the first one I am sure our students are going to love these (I did, to the extent that I haven't done any other work yet this morning!). I shall probably buy some more in due course.

I am currently thinking how to dissect a square into an equilateral triangle.”

Head of Mathematics, Beijing — April 2008

“Just to let you know that I really enjoyed this ClubMaths, especially working out the winning strategies for boxes! I do still love that game!”

Head of Mathematics, London — February 2007

“Many thanks for your help, and for producing excellent materials.”

Mathematics Teacher, Oxfordshire — December 2006

“The materials proved very stimulating last year. Keep up the good work!”

Head of Mathematics, Buckinghamshire — October 2006

“Some Y8 students … enjoyed making the models and found the cube straightforward. It then led to an interesting debate about the volume of a tetrahedron and I will certainly use that again.

The second model was much harder to fit together and students found it much more challenging. They were clearly impressed when one student managed to do it before me!”

Mathematics Teacher, London — May 2006

“Many thanks for such superb materials.”

Mathematics Teacher, Warwick — February 2006

“Whenever I use the ClubMaths materials in class I have a very good response – they are accessible to all initially and lead to lots of good discussion.”

Mathematics Teacher, Winchester — February 2006

“I’ve used a few of the monthly activities within my lessons – generally high ability sets. However, I used the Octagrams activity with middle and lowish sets with great effects. I’ve also used Octagrams and the Trapezium/Parallelogram activities with Year 7 to Year 11 – again the activity was easily adapted to each group.

The main problem, as ever, is time to properly think through the material and, in particular, to share the ideas across the department. So, whereas I've had great value from the material, the rest of the department has not used it very much.

I hope to fix this issue this year by presenting each monthly activity at a department meeting. And yes, I still hope to start a Maths Club…energy levels permitting!”

Mathematics Teacher, Berkshire — September 2005

“I've just been doing the Polyhedron activity and it is rather lovely!”

Mathematics Teacher, Winchester — May 2005

“I like these a lot, and I will definitely be using them in my Inter Tutor Group Challenge.

They are accessible to all levels of ability, and can be either practical – with real matchsticks, or done by drawing, which is great.”

Coordinator: Numeracy Across the Curriculum, Chelmsford — February 2005

“This sparked the interest of the whole class and it was great to see (without exception) all students totally engrossed.”

Head of Mathematics, West Yorkshire — December 2004

“I genuinely can't find anything that I would like to criticise – a superb activity with excellent notes for teachers.”

Head of Mathematics, West Yorkshire — November 2004

Enterprising Mathematics Resources

“We are hosting a maths day for 80 students from our own school, a neighbouring high school and the feeder middle schools … and I [hope] to use some of the activities then.”

Mathematics Teacher, Tyne and Wear — November 2005

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