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Discovering Mathematical Objects of Interest – A Study of Mathematical Notations [article]

Andre Greiner-Petter, Moritz Schubotz, Fabian Mueller, Corinna Breitinger, Howard S. Cohl, Akiko Aizawa, Bela Gipp
2020 arXiv   pre-print
In this paper, we present the first in-depth study on the distributions of mathematical notation in two large scientific corpora: the open access arXiv (2.5B mathematical objects) and the mathematical  ...  Mathematical notation, i.e., the writing system used to communicate concepts in mathematics, encodes valuable information for a variety of information search and retrieval systems.  ...  Hereafter, we define these components as Mathematical Objects of Interest (MOIs) [37] . The importance of math objects is a somewhat imprecise description and thus difficult to measure.  ... 
arXiv:2002.02712v1 fatcat:x6ulzyupzbexxk3xha7uolcyme

Page 22 of Mathematics Teacher Vol. 54, Issue 1 [page]

1961 Mathematics Teacher  
Following the study of the Hindu- Arabic notation, the children were led to consideration of notations using bases other than 10.  ...  To enlarge somewhat on one of these topics, the following explanatory state- ment is offered: In an attempt to interpret our decimal notation in a meaningful way, study was begun by analyzing place value  ... 

Enhancing Students' Interest through Mathematics Learning

A Azmidar, D Darhim, J A Dahlan
2017 Journal of Physics, Conference Series  
A number of previous researchers indicated that students' mathematics interest still low because most of them have perceived that mathematics is very difficult, boring, not very practical, and have many  ...  The c onclusion of this literature study is the Concrete-Pictorial-Abstract approach can be used as an alternative to improve students' mathematics interest.  ...  Some aspects of students interest that are, a sense of excitement, interest in learning, show concern when studying and engagement in learning: a) Students with a high mathematics learning interest will  ... 
doi:10.1088/1742-6596/895/1/012072 fatcat:57zk7uejirbbvbpt5srybtt2oe

The Construction of Mathematics, by Klaus Truemper

P. Lynch
2017 Irish Mathematical Society Bulletin  
Mathematical platonism posits that all of mathematics resides in a realm of abstract objects that is separate from the sensible world.  ...  His interests include all areas of mathematics and its history. He writes an occasional mathematics column in The Irish Times and has recently published a book of articles entitled That's Maths.  ... 
doi:10.33232/bims.0079.87.91 fatcat:pwfj7djj35azbh6q6lpksewgyi

A New Kind of Science: Ten Years Later [chapter]

David H. Bailey
2013 Emergence, Complexity and Computation  
A new formula for pi Perhaps one of the most interesting of the recent computer-discovered mathematical facts is what is now known as the "BBP" formula for π = 3.14159 . . .: π = ∞ k=0 1 16 k 4 8k + 1  ...  Wolfram's entry on "History of experimental mathematics" (pg. 899) contains a number of interesting insights on the practice of using computers as exploratory tools in mathematics. 2.  ... 
doi:10.1007/978-3-642-35482-3_6 fatcat:fo7mhvpynjczleq52vs2oukpba

François Viète's revolution in algebra

Jeffrey Oaks
2019 Research Outreach  
Nearly two decades ago he decided to combine his two main interests, Mathematics and History, in the study of Medieval Arabic mathematics.  ...  Physical Sciences -PREMODERN POLYNOMIALS Oaks discovered that algebraists before Viète conceived of the objects of their study, that is monomials, polynomials, and equations, differently than we do today  ... 
doi:10.32907/ro-106-3841 fatcat:da24yxfnnjaanlshqot3knnewm

Trends toward unity in mathematics

Charles Ehresmann
1966 Zenodo  
So the great ideal of Plato and Leibniz, the ideal of Mathematics as the essence of all knowledge, might at last be attained.  ...  Mathematics is the key for the understanding of the whole Universe, unifying all human thinking, from Sciences to Philosophy and Metaphysics.  ...  At present, given this definition of a p-structure as a precise mathematical object,mathematical research, I believe, will be less concerned with the study of a given pstructure or even of a given functor  ... 
doi:10.5281/zenodo.3930890 fatcat:snljdanvqrccpcexdo3mi5lq4q

Page 253 of Mathematical Gazette Vol. 4, Issue 71 [page]

1908 Mathematical Gazette  
During this course they are taught to measure and weigh (incidentally learning to realize the advantages of the decimal notation), to determine the surfaces and volumes of actual objects, to determine  ...  Laboratory work in Mathematics. Many schools now arrange that boys of 13-15 shall take, as part of their mathematics, a course of experi- mental work in the laboratory.  ... 

The ethnomethodological foundations of mathematics

Martin H Krieger
1987 Advances in Mathematics  
A mathematician is often surprised by the fruitfulness and unity of the mathematical world. One designs objects and spaces and worlds and then discovers that they are just like predecessor objects.  ...  What is needed is a close study of what mathematicians do.  ... 
doi:10.1016/0001-8708(87)90012-0 fatcat:lkjvz37fz5b3lboeb2lyj4myuu

International study group for the relationship between the history and pedagogy of mathematics (HPM)

George Booker
1986 Historia Mathematica  
One such example presented in the second session was devoted to Arabic mathematics as it was developed from Greek geometry into a theoretical discipline with its own methods and precise objects of study  ...  or mathematical interest. ' Distinguishing between content and form provides a third way in which the history of mathematics can be utilized in teaching.  ... 
doi:10.1016/0315-0860(86)90041-8 fatcat:5y4kph24ind6rai7z4afeassau

Context-Aware Adaptation: A Case Study On Mathematical Notations

Christine Müller, Michael Kohlhase
2009 Information systems management  
Cristian Calude, University of Auckland, NZ, she is conducting a case study on the mathematical community and their practices with an emphasis on proof explanations.  ...  We present a comprehensive framework for adaptive notation management and evaluate it on the proof-of-concept prototype panta rhei .  ...  of basic mathematical objects and allows machines to distinguish the meaning of included mathematical objects.  ... 
doi:10.1080/10580530903017583 fatcat:r5dck2jn5fdxtj3t76gxbmphf4

Byerly's Fourier's Series and Spherical, Cylindrical, and Ellipsoidal Harmonics

R. S. Woodward
1893 Annals of Mathematics  
Thirdly, between these two extremes there is a smaller class now commonly called mathematical physicists. Their object, like that of the second class, is the interpretation of natural phenomena.  ...  Such being the diversity of aims and tastes amongst the workers in mathematical science, it is not often that a new book is of special interest to more than one of the classes named.  ... 
doi:10.2307/1967958 fatcat:tu5wufdv7zdzhcu4mgps2iw7rq

Page 4 of Mathematics Teacher Vol. 31, Issue 1 [page]

1938 Mathematics Teacher  
The class will be interested to hear some- thing of Pythagoras when studying his famous theorem concerning the sides of a right angled triangle.  ...  4 THE MATHEMATICS TEACHER many centuries before the introduction of the Hindu-Arabic notation.  ... 

The Enrichment of the Mathematics Course

H. E. Riter, William David Reeve
1938 Mathematics Teacher  
and interest that will lead to voluntary investigation and study.  ...  text book material or prescribed courses of study.  ...  The class will be interested to hear some- thing of Pythagoras when studying his famous theorem concerning the sides of a right angled triangle.  ... 
doi:10.5951/mt.31.1.0003 fatcat:zwwsf6xhjrd2ncg3ca7pp7tx34

Envisioning Transformations—The Practice of Topology [chapter]

Silvia De Toffoli, Valeria Giardino
2016 Trends in the History of Science  
Acknowledgments We want to thank in particular Brendan Larvor for the organization of the cycle of conferences on Mathematical Cultures.  ...  A previous version of this paper was presented at the first meeting in 2010. We thank the participants for useful feedback. Thanks to John M. Sullivan for his comments.  ...  Moving from one notation to another for the same mathematical content is indeed a good strategy to discover new relations.  ... 
doi:10.1007/978-3-319-28582-5_3 fatcat:iomncxhefrfyjkuqsscdkqkki4
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