Islamic Geometric Ornaments in Istanbul

Islamic Geometric Ornaments

Islamic Geometric Ornaments

Islamic ornaments are one of the greatest achievements of ancient geometers, artisans and craftsmen in the Middle East, Turkey, India, Spain, and North Africa.  These ornaments are frequently used to decorate sacred, secular and private buildings, books, and furniture. Istanbul, in particular, is a place where such ornaments were, and still are, frequently used.

In this book we will explore selected geometric ornaments from Istanbul. Many of these ornaments can be created by using very precise geometric constructions. We will analyze the structure of these ornaments and show how grids used to draw these ornaments, were constructed. A computer program, The Geometer’s Sketchpad, will be used to construct these grids as well as complete ornaments. In a few examples a computer graphics program will be used to add some finishing touches to our work. Many of the examples presented in this book have a significant cognitive value. While creating them we can learn a number of important topics in geometry, e.g., constructions of regular polygons, constructions of figures circumscribed or inscribed in a circle, division of angles and segments into a given number of parts, transformations of figures, a touch of symmetry groups,  and a number of other topics. (more>>)

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Mathematica for impatient

Cover for the printed version

It has been long time since I finished my last book. In February 2010 I started a new writing project. This is a new book, this time Mathematica tutorial for students and mathematics teachers in Poland. We all know how great is Mathematica, but we also know that all Mathematica books and texts based on Mathematica are rather bulky and we very often we do not have time to go through hundreds of pages with detailed description of Mathematica secrets.  Therefore, we all need a brief Mathematica tutorial book that will show us the most important features of the program and how it can be used for solving and visualizing mathematics problems in high school or at the university.  This is the first objective of my new book – to present major features of Mathematica, those that we desperately need for our maths classes.

For many of us in Poland an additional problem is the language.  Many teachers and students can understand simple English, but how many can understand technical terminology? Therefore, the second objective of this book is to be available for Polish users of Mathematica.

I use for this book so called Mathematica for the Classroom, a product from Wolfram Research that was designed specifically for undergraduate mathematics education – high schools and beginning of university. The text will cover only the most important features of the program to such extend that everybody will be able to start using Mathematica by reading first chapter of the book and then proceed with specific topics reading the remaining chapters. The book will concentrate on mathematical visualization (2D and 3D mathematical graphs, animation), applications of Mathematica to calculus, algebra and some other sections of undergraduate mathematics, an optional chapter will cover programming in Mathematica.

Polish text related to this book as well as link to download page can be found on page
First part of the book (chapters 1, 2, 3 and 4) is available in electronic version (PDF files) at

Polski tekst dotyczący tej książki jak również link do strony z której można pobrać książkę w postaci elektronicznej znajduje się pod adresem
Pierwsza część książki (rozdziały 1, 2, 3 i 4)  jest w postaci elektronicznej (pliki PDF nadające się do drukowania).

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MuPAD for Impatient


MuPAD for Impatient, or in Polish MuPAD dla niecierpliwych, is a Polish book about MuPAD. The book is an outcome of series of MuPAD workshops that I was conducting with Polish maths teachers during one of the MathPAD conferences. After finishing these workshops I revised my notes, updated them, formatted all examples added comments, etc. This work took all my vacations in 2006 and one or two months after vacations.

The book was published by a small private, commercial publisher Omega Press, that is well known for the high quality of their books.  It turned out that Omega Art was very good choice. The book was ready after two weeks. I do not know any other publisher who can do such job in such a short time. The printing was sponsored by Edukacja z TI, Polish distributor of MuPAD at this time.

As I said the book is based on my MuPAD workshops and it can be used for conducting MuPAD workshops for beginners. I cover there the most important basic features of MuPAD that are directly related to high school mathematics. In following years the books served for a number of workshops conducted by my colleagues in Poland. Some of these worskshops took place during MathPAD conferences at the Nicholas Copernicus University.

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Getting Started with MuPAD

cover31My two previous books used the programming approach. Which simply means that the programming concepts were introduced first and then the remaining chapters of the book were using programs. This is nice concept, especially when one wants to produce complex graphics – for example a number of graphical objects interacting together. However, this concept is difficult for beginners and especially for high school students or maths teachers who doesn’t have much time to learn basic of programming. They need a simpler text just introducing basics of CAS and a lot of examples. I needed also such a book for my MuPAD workshops with mathematics teachers.  As a result, one day I decided to write the Getting Started with MuPAD book.

The book is a gentle introduction to MuPAD and CAS concepts. I show there step-by-step various features of MuPAD and how we can use it in various areas of mathematics. A large chapter of the book is devoted to graphical visualization of mathematical concepts, and MuPAD graphics are also used extensively throughout the rest of the book.

Each chapter of the book can be considered as a single workshop for MuPAD beginners. The whole book is a good resource for conducting workshops on using Computer Algebra Systems to explore, experiment with, and visualize mathematical concepts.

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MuPAD Pro Computing Essentials II

MuPAD Pro Computing Essentials II

After publishing my MuPAD Pro Computing Essentials I have been doing a number of projects with MuPAD as well as teaching courses with MuPAD. At this time I have been conducting a number of MuPAD workshops all over East Asia as well as in Poland and Germany. In 2002 I started in Poland the MathPAD Conference that was devoted to applications of MuPAD in teaching mathematics. The conference gathered a number of teachers of mathematics and enthusiasts of CAS. In next years the conference changed slightly its formula and its running every year, usually in June or September, at the Nicholas Copernicus University in Poland.

Sometime later a new concept of graphics was implemented in MuPAD. It was a good time to start thinking about new edition of my MuPAD book. I revised the whole content, I added there a number of topics and examples. This was also the time when Klaus Dresher devloped export of MuPAD graphics to JavaView. I developed a whole web site with interactive MuPAD graphics using JavaView as the online visualization tool.

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MuPAD Pro Computing Essentials I

cover1MuPAD Pro Computing Essentials was my very first book about MuPAD. I discovered MuPAD when I was living in Macau and working for the Inter-University Institute of Macau. In fact, MuPAD was a perfect tool for some of the maths courses that we were teaching at IIUM. This was the starting point of my fascination of this beautiful Computer Algebra System. This was also the time when I started writing this book.

Later, when I moved to Zayed University in UAE, I continued working on this book. This work was giving me a lot of satisfaction and, the most important, a chance of forgetting about hectic atmosphere of this university and very unpleasant politics at the university. I have been doing this work as form of entertainment. At this time writing occupied all my time outside of the university. Later I started using parts of my book for teaching the Discrete Mathematics course for Information Systems students.  I know that a few other universities, mostly in Europe, were using my book for a number of courses. Some of them were programming courses and some other covering CAS topics for mathematics majors.

The web site for my first MuPAD book is here. I updated it as much as I could. You will find on these pages preface written by Prof. Fred Szabo from Concordia University in Canada, author’s introduction, and record from US Congress library. Unfortunately the file with examples for the book is missing here. WordPress accepts uploading only selected media files. Therefore, if you need these examples, you can e-mail me at mirekmajewski(at)

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Transition time

My fascination in MuPAD goes back to the year 2002. This was the time when I learned about MuPAD, I started using it and writing about it. Later I wrote quite a few papers with MuPAD as a main character, a few books about using MuPAD in teaching mathematics and modeling mathematical objects. For a few years I was editing and publishing an online magazine MathPAD Online, devoted to MuPAD, that was a good source of information about the program and had tons of MuPAD examples.

For quite a while the web site for my books was published on the producer of MuPAD, SciFace GmBH, web server as However, in September 2008 I found that MuPAD is no longer an independent product and I have to stop publishing my online magazine related to MuPAD and move the web site for my books somewhere out of the SciFace web server. This was a bit unplesant news and a new challange for me.

In January 2009 I decided to move the web site for my books and redesign it as a WordPress blog. I guess it will take me a few weeks to move and update the whole content. I suppose that some of the things that were working well on the original web site may not work here and some new things that were not available there will be a nice addition here on WordPress. The good thing is that the web site as a blog will make communication with my readers easier and perhaps give me more interaction with them.

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