Workshop and Seminar
A mathematics teacher and his talented student: Athir al-Din Abhari and his pupil Najm al-Din Qazwini Katibi
Lecture: Jan P. Hogendijk
30 April 2016
The famous Islamic philosopher Najm al-Din Qazwini Katibi (died 675H/1276 CE) studied mathematics and astronomy with his master Athir al-Din Abhari. We will analyse the textbook which Abhari wrote for Katibi and which has been preserved in three Arabic manuscripts (Tehran, Majlis 6195, Tehran , Milli 20371 bis). We will analyse the textbook which Abhari wrote for Katibi and which has been preserved in three Arabic manuscripts (Tehran, Majlis 6195, Tehran , Milli 20371 bis). The textbook includes mathematics (trisection of the angle, trigonometry, theorems on the sphere), abstract discussion of astronomical problems, concrete results of astronomical researches, as well as astronomical tables. As we will see, Abhari followed a special didactical approach for his talented student. Abhari explained the theory completely and did not avoid any difficulty, but the explanations were very brief, as compared to the work of authors from the same century such as Nasir al-Din Tusi.
Non-Linear Dimensionality Reduction by Isometric Patch Alignment
Professor Ali Ghodsi, Waterloo University
27 Apr. 2016
Abstract: We propose a novel dimensionality reduction method which has low computational cost. This method is inspired by two key observations: (i) the structure of reasonably large patchesof high-dimensional data can be preserved as a whole, rather than divided into small neighborhoods; and (ii) attaching two neighboring patches will align them such that the overall rank does not increase. In the proposed approach, first the data is clustered, so that it is conceptually reduced to a set of overlapping low-rank clusters. Each cluster is embedded into a low-dimensional patch and then all of the patches are rearranged such that their border points are matched. We show that the rearrangement can be computed by solving a relatively small semide nite program. The embedding computed by this optimization is provably low-rank. The proposed method is stable, fast and scalable; experimental results demonstrate its capability for manifold learning, data visualization, and even complex tasks such as protein structure determination.
Why mathematics is taught to schoolchildren?
Toghyan Angoshtari
23 Apr. 2016
This question is a key; because this well-reasoned and persuasive answer may be useful in teaching children.
In order to provide a definitive answer to this fundamental question, a scientific and documentary unity about three concepts; Children, Education and Mathematics, should be achieved first. After that, it will be possible to agree on the obtained answers.
It will be shown that the education of mathematic, can have very useful and unique role to, in promoting education, development and children awareness. Along with it, updating methods of education mathematics to children will also be revealed.
Simultaneous estimation and Wonders of high Dimensions
Dr. kasra Alishahi
11 Mar. 2015
Series of IMH lectures
26 Jan. 2015
Lecture by Dr. M. Mirzavaziri (Ferdowsi University of Mashhad)
For high school students, 2nd-grade (Pairwise Intersecting figures)
For Teachers (Systematic Table)
Lecture by Dr. O. Naghshine Arjmand (AmirKabir University)
For University Students (From Pythagorean theorem to Fourier series)
Lecture by Mr. M. Hosseini (Math Highschool Teacher)
For Teachers (What are main factors of math phobia and
What are the obstacles of students motivation to solve mathematical problems?)
Data Clustering, A Bayesian View
8 Aug. 2014, 17:30
Clustering refers to estimating a grouping for data. Data grouping is a basis for knowledge extraction from information and therefore a very important problem in any scientific discipline. This talk focuses on explaining why clustering is a challenging issue. We describe how one can formalize clustering as a mathematical problem. Statisticians understand the world through a probabilistic model. Hence, as a statistician, I focus on methodologies that applies this approach.
Handling clustering in Bayesian paradigm is more coherent in terms of combining uncertainties and merging prior knowledge with data information, and I will emphasize on this paradigm throughout the talk. Important challenges and open problems of this context are discussed at the end.
Life Tables
Terry Mills (Australia)
1 Sep. 2014
Honorary Statistician at Bendigo Health
Emeritus Professor at La Trobe University
Abstract: Life tables are mathematical tables that describe death rates at different ages in a society. Thus, the life table contains some essential features of the health of a nation. One can calculate life expectancy of a population from a life table. We will examine life tables from a mathematical point of view. Probability is often regarded as a difficult branch of mathematics. Life tables provide an effective approach to introducing concepts in probability. Difficult concepts such as conditional probability become easy to understand when presented in the context of a life table. Furthermore, the mathematical models that underpin life tables are applications of calculus and more advanced notions in probability. A few books that contain information about life tables are listed below in the references. This paper has been written in collaboration with Dr Mehdi Hassani (University of Zanjan).
References
C.L. Chiang, Introduction to stochastic processes in biostatistics. New York: John Wiley, 1968.
C.L. Chiang, Life table and its applications. Malabar, FL: Robert E. Krieger, 1984.
N. Keyfitz, Applied mathematical demography. New York: Springer-Verlag, 1977.
N. Keyfitz and J. A. Beekman, Demography through problems. New York: Springer-Verlag, 1984.
K. Namboodiri and C. M. Suchindran, Life table techniques and their applications. Orlando: Academic Press, 1987.
J.H. Pollard, Mathematical models for the growth of human populations. Cambridge: Cambridge University Press, 1973.
The founders of mathematics
Akbar Zamani
6 August 2014
In this lecture, we will talk about Babylonian and Egyptian mathematics, and then briefly talk about works of Pythagoreans, Euclid, al-Khwarizmi, Pascal, Descartes, Newton and Neper.
Evolutionary history of number set
Payam Seraji
6 August 2014
In this lecture, we will briefly talk about the evolutionary history of natural numbers and real systems, the theory of infinite sets as well as historical facts about some specific numbers, such as numbers and pi and Neper number.
IMH public lecture Series, 14-19, April 2014
| Prof. Gregor Nickel | History and Philosophy of Mathematics for Teacher’s Education Full Text | 17 – 16, 14 April | |
| Prof. Gregor Nickel | Proof – Aspects of a strange phenomenon between freedom and enforcement Full Text | 17:30, 15 April | |
| Roeland Hiele | Flipping the classroom | 17-19, 19 April | |
Prof. Jan P.Hogendijk | Abu Rayhan Biruni in the 15th/21th century | 17-19, 19 April
| |
| Vincent Karels M.Sc | Research Group in History of Mathematics | A mathematical analysis of the dome of the shrine of Shah Nematollah Vali at Mahan | 17-19, 19 April |
History and Philosophy of Mathematics for Teacher’s Education
The talk will analyse various functions of history and philosophy of mathematics as a tool to improve the quality of teacher’s studies. In the second part these two disciplines will be discussed as a goal in themselves – being an essential part of any mathematical literacy. In a third part I will briefly report some of my concrete experiences from an integration of history and philosophy to teachers’s studies at Siegen University.
Proof – Aspects of a strange phenomenon between freedom and enforcement
Proofs play a major role in the everyday life of any mathematician. Undoubtedly, since the time of the ancient Greeks mathematics deals to a large extent with `proofs’. However, the question for the functioning and the function of mathematical proofs remains open. Working mathematicians agree, that a proof proves, but do not ask, how this really works. The talk will discuss various `non-formal’ aspects of mathematical proof – mostly regarding a proof as a special type of communication. Thereby we also refer to the classical controversy in the philosophy of mathematics which tried to decide whether proof is either synthetic or analytic.
Flipping the classroom
Using specific examples I will show how instruction videos can be used to expand the possibilities in and bring variety and interactivity to classroom teaching. This approach can be called the flipping-the-classroom model. Together with the audience, we will reflect on the following questions: what are the strengths, weaknesses, opportunities and threats of this flipping-the-classroom model? What are the possibilities in class?
A mathematical analysis of the dome of the shrine of Shah Nematollah Vali at Mahan
Using modern computer methods and photos of the entire dome in Mahan, we have analyzed the pattern on the dome and its possible design. According to our analyses, which we will present during the talk, the number 11 had a significant influence at various stages of the design. We will show several approaches but have not yet been able to explain all details in the interesting design. g
Abu Rayhan Biruni in the 15th/21th century
Abu Rayhan Biruni (born 365 H.Q. /973 CE, died ca. 440 H.Q. / 1048 CE), was one of the most important astronomers and mathematicians of the medieval Islamic tradition. He also wrote extensively on chronology, history and Indian culture and astronomy and has received universal praise for his objective approach and his respect for different religions and cultures. The talk will give an overview of Biruni’s extant (and lost) work, listing the number of extant manuscripts, and the published editions and translations into many languages. I will then indicate several (small and large) research projects on him that
can be done, and also some new questions that can be asked about him, using the new technology of the internet age (the 15th/21th century). In connection with this lecture, a special bibliographic website has been created http://www.albiruni.nl .
Self similarity for Penrose and Isfahan patterns
Professor Jost –Hinrich Eschenburg
13 March 2014
Abstact :
Planar patterns can express the idea of infinity in two different ways: By repetition (periodicity) or by self-similarity, where the same details appear on different scales. Self Similarity is less obvious than periodicity; therefore it does not occur too often in arts. One of the sites it occurs is Isfahan, at Darb-i-Imam Shrine, at one of the Iwans of Friday Mosque and some other places. These 300 years old patterns have much in common with the aperidic patterns discovered only 40 years ago by the mathematician Roger Penrose; in fact there is a large coincidence between the two patterns. Both have in common the idea of self-similarity and the local pentagonal symmetry. However, there are differences: The Isfahan pattern has a global dekagonal (10-gon) symmetry which is not shared by the Penrose patterns. However, the coincidence of both patterns sheds some light on the Penrose patterns, too. It uncovers a new Penrose pattern with a hidden approximate 10-gon-symmetry. The new pattern does not arise by the common construction which uses a projection of part of the 5-dimensional periodic grid onto some plane in 5-space (“projection method”). Thus a 300 year old Iranian art work has some influence on todays mathematics.
Virtual Education
University Utrecht, Holland
3 Mar. 2014
Clockwork gearing in ancient Greece and Medieval Islam
Dr. J.L.Berggren
Isfahan Mathematics House
1 March 2014
In its general lectures on mathematics, IMH is organizing a lecture on Clockwork gearing in ancient Greece and Medieval Islam. This Lecture is delivered by Dr. J.L. Berggren professor of Simon Fraser University, Canada om 1 March 2014.
Publications by J.L. Berggren
Abstract :
The chance discovery in 1900 of an ancient shipwreck off the Greek island of Antikythera led to the recovery of some corroded fragments of what turned out to be the earliest known example of precision gearing. Our illustrated talk will tell a fascinating story of how the combined efforts of archaeologists, historians of science and the latest imaging technology have led to the reconstruction of an ancient Greek geared calendar-computer and a complete revision of our views of Greek technology. From this mechanism we will follow the history of precision gearing through the Islamic medieval period, including the geared astrolabes of al-Biruni and Muhammad ibn Abi Bakr of Isfahan, which contain many features similar to those in the Antikythera mechanism.
Dr. Len Berggren is Emeritus Professor of Mathematics at Simon Fraser University in British Columbia, Canada, He was introduced to the Antikythera mechanism by Prof. Derek Price, who did the first study of that instrument using imaging technology, during a visiting year at Yale University in 1972. Prof. Berggren has lectured at major universities around the world and is known internationally as an authority on the history of mathematics and astronomy in ancient Greece and medieval Islam. Among his publications are translations of Greek scientific works by Euclid, Claudius Ptolemy and Geminus, as well as Episodes in the Mathematics of Medieval Islam, which has been translated into German and Farsi.
In its general lectures on mathematics, IMH is organizing a lecture on the current mathematics education in France. This Lecture is delivered by Prof. Martin Andler, Professor of Mathematics, Université de Versailles Saint-Quentin (UVSQ), on Monday 1st December 2008
“The lecture will start with a brief overview of the organizations of education at junior High School and High School level in France, and the ongoing changes. The second topic will be the evolution of the mathematics curriculum between the 1960’s and now, including the controversies around the introduction of “New math” in the 70’s, and the present state of affairs. I will then discuss the role of extracurricular math activities in France, and what is done to develop them.
Teaching Students to Think Mathematically, Prof. Kaye Christine Stacey
Prof. Kaye Christine Stacey from University of Melbourne (Melbourne, Australia) delivered a lecture at Isfahan Mathematics House on Sunday Aug 9. In her talk Prof. Kaye Stacey whose research interests are: Curriculum studies: mathematics education; Educational technology and media; Teacher education; Mathematical thinking and problem-solving addressed the issue of problem solving strategies.
“I will discuss a mathematical problem which can be used to teach students to think mathematically and to solve mathematical problems that are unfamiliar and new to them. The processes of looking at special cases, generalizing, conjecturing and convincing will be highlighted through these examples; these are key processes in thinking mathematically”
The Gems of Combinatorial Geometry, Professor Paul Vaderlind
On Saturday May 14 a lecture on Combinatorial geometry was delivered at Isfahan Mathematics House (IMH) by Professor Paul Vaderlind, the professor of Stockholm University and the Stockholm IMO leader.
“Combinatorial geometry is one of those few branches of mathematics that offer almost an immediate access to a variety of open problems.
In this talk several such problems will be presented. Although many of them are quite natural and have been formulated some time ago, the final answers are still not known and the problems offer some
excellent topics for the research. Except for the basic knowledge of geometry, no other prior knowledge of combinatorial geometry is needed.”
Professor Jan Hogendijk’s Lecture on “History of Mathematics” in Isfahan On Saturday, Dec 29, 2007, Professor Jan Hogendijk, from Utrecht and Leiden Universities in the Netherlands delivered a lecture in Isfahan. This lecture was focused on the history of mathematics in the Netherlands during 16th and 17th centuries and its relationships and similarities with the history of Islamic –Iranian mathematics during 4th – 5th of Hijrah.
In his talk, professor Hogendijk affirmed that according to historical documents, the Islamic mathematical tradition was dominant in the world between the 3rd and 9th centuries of Hijra, and in the 4th century of Hijra the center of gravity was in the east of the Islamic world especially the Greater Iran. In 16th and early 17th century, Holland was the most important in the world of mathematics. The Dutch mathematical tradition especially in the northern Netherlands was important between 1550 and approximately 1660.
Professor Hogendijk mentioned that the main transmission of Islamic mathematics from the Islamic world to Europe started in 11th and 12th centuries which took place in Spain and Sicily and then to Europe; therefore most of the results in mathematics in the Netherlands in 16th and 17th centuries were taken from European resources, and not directly from the Islamic sources.
Comparing the two traditions, he stated that around 1600, mathematics in Holland was almost on the same level as mathematics in Iran in 14th -15th centuries. The Dutch mathematicians were working independently on the same problems which interested Iranian mathematicians two centuries earlier. One example is the discovery of the decimal fractions which happened independently by the Iranian mathematician Kashi and by the west mathematician Simon Stephen. Also the most particular example is the computation of the number π.
Referring to the Dutch translation of the “Elements” (1695), which is preserved in the library of Leiden University, professor Hogendijk confirmed that in this book there are references to Iranian mathematicians, Ali Abul Hasan Nasawi, Nasir Al-Din Tusi and Abu Sahl Kuhi.
In the end, professor Hogendijk clarified some advantages of studying history of mathematics in the development of mathematical sciences, in particular in the improvement of mathematics education.
Before his lecture, professor Hogendijk thanked Isfahan Mathematics House for inviting him and his students and pointed out that since its establishment, Isfahan Mathematics House and the two universities of Leiden and Utrecht have had many cooperation projects and in recent years this cooperation has remarkably increased.
Teaching Mathematics as a Constructive and Creative Activity
On Thursday, September 6, 2006, Professor John Mason, Professor of London Open University delivered a lecture at Isfahan Mathematics House. This lecture was on: Teaching Mathematics as a Constructive and Creative Activity
“I will invite participants to engage in some mathematical tasks which call upon the learner to construct mathematical objects, and offer the conjecture that this not only engages learners actively, but calls on their natural powers to make sense of mathematics and to make sense mathematically. Using construction tasks in teaching, not only displays mathematics as a constructive activity, but engages the teacher in constructive and creative activity as well”.
The CD of this lecture is available at Isfahan Mathematics House library.
Psycho Acoustic, Applications of Statistics in Biology, by Dr. Gazor
Dr.Saeed Gazor, the professor of Queen’s University of Canada visited Isfahan Mathematics House on April 23, 2006 and delivered a lecture for the members of Isfahan Mathematics House.
In his lecture, Dr. Gazor first gave some explanations on the human auditory system and then noted some applications of statistics in biology and technology with respect to this system.
In continuation, he mentioned that statistics helps physicians and researchers in artificial making of the inner members of ears, and it also helps engineers to omit or replace sounds in an optimized way through the recorded tapes.
He pointed out that recently scientists have discovered that the human ear makes sounds all by itself; it means, the sounds produced- as guessed by psychologists, relate to the different mental states of human. He, along with a team of psychologists, are studying the case and continuing to research in this field.
If you are interested in following up this topic, you may receive the CD of his speech at the Library of Isfahan Mathematics House.
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lecture on Iranian qanats and Roman aqueducts
Wilke Schram M.Sc, 7 may, 18:30
