Archive for the ‘Book reports’ Category

Fritz Schweiger

 This book is about the history of f-expansions, their theory, their application, and their connection to other parts of mathematics. Sketches of proofs of some of the theorems about f-expansions–particularly theorems from historical sources–are included not to convince the reader of the truth of the theorem but rather as a way to demonstrate why the theorem is true. These sketches should give a clearer and more easily understood description of the working of the theorem than a hand-waving literary flourish.

Publication Date: May 2, 2016

ISBN/EAN13: 1942795939 / 9781942795933

Language: English

Related Categories: Mathematics / History & Philosophy

Information send it by Manfred Kronfellner

Mathematical Association of America’s Convergence is undergoing many changes (as part of a website conversion). Please visit the journal’s homepage:

Below are several short abstracts of recently published articles.


 Diamantopoulos, John; and Woodburn, Cynthia. Maya Geometry in the Classroom. Loci: Convergence (August 2013), 5 pp., electronic only. The authors show how classic Maya people may have used knotted ropes to form desired geometric shapes in art and architecture.


Branson, William B. Solving the Cubic with Cardano. Loci: Convergence (September 2013), 8 pp., electronic only. The author shows how, in order to solve the cubic, Cardano relied on both classical Greek geometric and abbaco traditions, and he illustrates Cardano’s geometric thinking with modern manipulatives.


18th Century

Wardhaugh, Benjamin. Learning Geometry in Georgian England. Loci: Convergence (August 2012), 6 pp., electronic only. A comparison of the geometry found in two 18th century copybooks written with two different purposes, mental acumen and practical application. DOI:10.4169/loci003930

18th and 19th Centuries

Wessman-Enzinger, Nicole M. An Investigation of Subtraction Algorithms from the 18th and 19th Centuries. Loci: Convergence (January 2014), 9 pp., electronic only.  This survey of subtraction algorithms used in North America includes both handwritten “cyphering books” and printed arithmetic books.

19th Century

Del Latto, Anthony J.; and Petrilli, Salvatore J., Jr. Robert Murphy: Mathematician and Physicist. Loci: Convergence (September 2013), 8 pp., electronic only. The authors argue that Murphy (1806-1843) showed “true genius” during his very short life, and they provide a transcription of Murphy’s first published work in 1824.

20th Century

Beery, Janet; and Mead, Carol. Who’s That Mathematician? Images from the Paul R. Halmos Photograph Collection. Loci: Convergence (January 2012 – March 2013), 60 pp., electronic only. For each of 343 photographs taken by functional analyst and mathematical expositor Halmos from 1950 to 1990, the authors identify the subjects and provide biographical information about them. DOI:10.4169/loci003801

Meyer, Walter. External Influences on U.S. Undergraduate Mathematics Curricula: 1950-2000. Loci: Convergence (August 2013), 8 pp., electronic only. An examination of the influence of forces outside of mathematics on such curricular changes as increased emphasis on applications and modeling, introduction of discrete mathematics courses, and calculus reform.


Janet Beery,

Editor, MAA Convergence

 Professor of Mathematics

Department of Mathematics and Computer Science

University of Redlands

1200 E. Colton Ave.

Redlands, CA 92373

Rio de Janeiro: Editora Zahar, 2012.
ISBN 978-85-378-0888-7


This book, in Portuguese, presents a fresh and innovative approach to present the history of mathematics for university lectures, based on recent progress in the methodology of research into the history of mathematics and on subsequent new results and re-assessments.

Gert Schubring

The proceedings from the 6th European Summer University on the History and Epistemology of Mathematics (which was held in Vienna in 2010) is now available from, Holzhausen or via an order form.

This volume contains texts and/or abstracts of all contributions to the scientific programme of the 6th European Summer University (ESU 6) on the History and Epistemology in Mathematics Education, which took place in Vienna, from 19 to 23 July 2010. This was the sixth meeting of this kind since July 1993, when, on the initiative of the French IREMs the first European Summer University on the History and Epistemology in Mathematics Education took place in Montpellier, France. The next ESU took place in Braga, Portugal in 1996, conjointly with the HPM Satellite Meeting of ICME 8), the 3rd in Louvain-la-Neuve and Leuven, Belgium in 1999, the 4th in Uppsala, Sweden in 2004, conjointly with the HPM Satellite meeting of ICME 10 and the 5th in Prague, Czech Republic in 2007.

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Victor Katz and Constantinos Tzanakis (Eds.)

Recent Developments on Introducing a Historical Dimension in Mathematics Education consists of 24 papers (coming from 13 countries worldwide). The volume aims to constitute an all-embracing outcome of recent activities within the HPM Group (International Study Group on the Relations Between History and Pedagogy of Mathematics). We believe these articles will move the field forward and provide faculty with many new ideas for incorporating the history of mathematics into their teaching at various levels of education.

The book is organized into four parts. The first deals with theoretical ideas for integrating the history of mathematics into mathematics education. The second part contains research studies on the use of the history of mathematics in the teaching of numerous mathematics topics at several levels of education. The third part concentrates on how history can be used with prospective and current teachers of mathematics. We also include a special fourth part containing three purely historical papers based on invited talks at the HPM meeting of 2008. Two of these articles provide an overview of the development of mathematics in the Americas, while the third is a study of the astronomical origins of trigonometry.

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The proceedings from the 6th European Summer University on the History and Epistemology of Mathematics (which was held in Vienna in 2010) is now available from, Holzhausen or via an order form.

(Authors: Paulus Gerdes & Ahmed Djebbar, 924 pages in two volumes; Volume 1: 1986-1999 [ISBN 978-1-105-11807-4, 480 pp.]; Volume 2: 2000-2011 [ISBN 978-1-105-14100-3, 444 pp.]; Distribution by Lulu, Morriville NC, Published October 27, 2011)

The book reproduces the thirty-seven newsletters published by AMUCHMA (African Mathematical Union Commission on the History of Mathematics in Africa) since its birth in 1986. The book celebrates the 25 years of AMUCHMA by giving a vivid picture of the activities that took place, of the studies done, of the queries, of sources, of meetings, of lectures, of dissertations, of publications… At the end of the book are included country and name indices.

The book contains Prefaces written by Professor Saliou Touré (President of the African Mathematical Union), by Professors Craig Fraser and Elena Ausejo (Chair and Secretary of the International Commission for the History of Mathematics), and by Professor Eberhard Knobloch (President of the International Academy of the History of Science). Professors Aderemi Kuku (President [1986-1995] and Honorary President of the African Mathematical Union) and Jean-Pierre Ezin (Commissioner for Human Resources, Sciences and Technology of the African Union) wrote the Afterwords.

(text provided by the publisher)

Cover of Devlin book

The Man of Numbers – Fibonacci’s Arithmetic Revolution
Keith Devlin

The untold story of Leonardo of Pisa, the medieval mathematician who introduced Arabic numbers to the West and helped launch the modern era.

In 1202, a young Italian man published one of the most influential books of all time, introducing modern arithmetic to Western Europe. Leonardo of Pisa (better known today as Fibonacci) had learned the Hindu-Arabic number system when he traveled to North Africa as a teenager to join his father, a customs official for Pisa, then one of the principal mercantile centers of Europe. Devised in India in the first seven centuries of the Current Era and brought to North Africa by Muslim traders, the Hindu-Arabic system (featuring the numerals 0 through 9) offered a much simpler method of calculation than the then-popular finger reckoning and cumbersome Roman numerals.

Though written in scholarly Latin, Fibonacci’s book, Liber abbaci (The Book of Calculation), was the first European text to recognize the power in the 10 numerals, and to aim them at the world of commerce. It spawned generations of popular math texts in colloquial Italian and other accessible languages that allowed a wide range of people to buy and sell goods, convert currencies, and keep accurate records more readily than ever before—helping transform the West into the dominant force in science, technology, and large-scale international commerce.

Liber abbaci and Leonardo’s other books made him the greatest mathematician of the Middle Ages, earning him a personal audience with the greatest monarch of the era, the Holy Roman Emperor Frederick II, for whom he solved complex mathematical puzzles. Yet despite the significance and spread of his discoveries, Leonardo of Pisa has largely slipped from the pages of history. His name is best known today for the “Fibonacci sequence” of numbers he revealed, which appears with great regularity in biological structures throughout nature, and which some claim can predict the rise and fall of financial markets. Recreating the life and times, and the enduring legacy, of an overlooked genius, linking his achievements to our own time, Keith Devlin makes clear how central numbers and mathematics are to our daily lives.

Keith Devlin is a Senior Researcher and Executive Director at Stanford’s H-STAR institute, which he co-founded. He is also a co-founder of the Stanford Media X research network. Known to millions as NPR’s “Math Guy,” he is the author of more than twenty-eight books, including the highly successful The Math Gene. He lives in Palo Alto, California.

(Text from the publisher.)

Robert Stein: Math for teachers. An Exploratory Approach.
KendallHunt 2009

Bob Stein’s textbook for prospective K-8 (kids age 5-14) mathematics teachers, which appeared in its second edition in 2009, is interesting to the HPM community because it includes the historical dimension. In this review, I will therefore almost entirely be interested in the way it includes history.

In this book, history of mathematics is included in four ways. First, there are about 70 historical footnotes giving additional information on the topics treated in the text. They range from a sentence on who first used the equality sign to mini-biographies on mathematicians such as Blaise Pascal. The second way of including history of mathematics is to include it in the main text. For instance, the text on multiplication includes some historical algorithms. The third way is to give exercises explicitly based on the history. For instance, there are exercises on historical proofs of Pythagoras’ theorem. The fourth way is to base the treatment of the mathematical topic on the historical background in an implicit way, such as giving a geometrical way of solving quadratic equations without noting the history of such methods. The combination of these four strategies means that the historical dimension becomes an important part of the book, without competing with “an exploratory approach” as the main approach.

Students reading this book will have access to a significant amount of historical information, and may well be inspired to look for more elsewhere (for instance in the books noted in “Selected References with Annotations” in the back of the book). However, they are not given any help as to how they could themselves include history of mathematics in their own teaching. There is no discussion of different ways of including history of mathematics, drawing on the discussions in the ICMI Study (Fauvel & Van Maanen, 2000) and discussions in HPM conferences, for instance. Thus, the students are mostly left to figure these things out on their own or to ask their professor for help, or to look at the Historical Modules (Katz & Michalowicz, 2005) which are mentioned in the references. It could be said, of course, that the book sets an example on how history of mathematics can be included in teaching. It would be helpful, though, if this was explicitly commented upon to make students aware of this.

Moreover, because the author tends to give information about who did what first, the readers will mostly be shown how mathematics has developed through history, not how it has been used in different cultures. They will see that mathematics is a field of knowledge developed by human beings, but the role that mathematics has played in different societies and cultures throughout history will not be so visible.

Continuing in a critical vein, I will note that the history of mathematics is unevenly distributed. For instance, the part on “counting and probability” has few historical components. In my experience, the history of probability is highly suitable for work with students.

The history of mathematics is such a rich resource that every person can have his own favorites, and not everything fits into a textbook of less than 800 pages, covering so many subjects. This is a textbook which gives the students a taste of what history of mathematics can be and a possibility for understanding a little about how mathematics has evolved. That is in itself valuable for prospective mathematics teachers.

Bjørn Smestad, Norway

Fauvel, J., & Van Maanen, J. (2000). History in mathematics education: An ICMI Study. Dordrecht: Kluwer Academic Publishers.
Katz, V. J., & Michalowicz, K. D. (Eds.). (2005). Historical Modules for the Teaching and Learning of Mathematics: Mathematical Association of America.

The May 2010 issue of Mathematics in School was devoted to history of mathematics, edited by Leo Rogers. It contained a rich collection of articles, specifically chosen to help teachers widen “students’ horizons and linking mathematics with other aspects of their life”. The list of authors includes Elisabeth Boag, Jackie Fairchild, David Kaye, Eileen Magnello, Sue Pope, Chris Pritchard, Jenny Ramsden, Peter Ransom, Leo Rogers, Madeleine Shiers and Chris Weeks, many of whom are frequent contributors to the HPM conferences as well.

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