Computations in Mathematics, Mathematical Education, and Science

A special issue of Computation (ISSN 2079-3197).

Deadline for manuscript submissions: closed (31 January 2024) | Viewed by 7675

Special Issue Editor

School of Education and Professional Studies, State University of New York, Potsdam, NY, USA
Interests: mathematics education; differential equations; control theory

Special Issue Information

Dear Colleagues,

Just as advances in mathematics often depend on the methods of computation available, the effectiveness of applications of mathematics to education and science depends on our knowledge and understanding of how computers can support advances in areas that use mathematics. The aim of this Special Issue is to collect scholarly reports on the effective use of computations within the wide range of experiences, grade levels, and topics. Of special interest are submissions that demonstrate the duality of mathematical and computational methods in the sense that whereas computations facilitate access to mathematical knowledge, mathematics itself can be used to improve the efficiency of computations, which, in turn, enable advancements in various applications of mathematics to education and science.

At the pre-college level of mathematics education, the Special Issue seeks to identify successful experiences in using computations to communicate the presence of big ideas within seemingly mundane curricular topics and, by the same token, in enabling the study of traditionally difficult and conceptually rich topics through the use of computations. At the college level of mathematics education, the Special Issue invites articles that demonstrate how experimental approaches to mathematics that draw on the power of software to perform numerical and symbolic computations as well as graphical and geometric constructions make it possible to balance informal and formal learning of mathematical ideas. In applications of mathematics to science, this Special Issue invites submissions demonstrating how the availability of symbolic computations enables transition from results based on informal experiments to formal justifications of the results using methods of formal mathematics. Recommended topics to be considered may center on the following questions:

  • How does the use of computations affect mathematics research?
  • How are computations used in the preparation of PK-12 teachers of mathematics?
  • How does the use of computations enable the revision of undergraduate mathematics curricula?
  • How does the use of computations facilitate the transition from high school mathematics to university mathematics?
  • How does the growth of online degree programs affect the use of digital technology within mathematics courses of such programs?
  • How does the use or computations affect research in science?

Articles are expected to include a theoretical discussion of educational, mathematical, and epistemological issues associated with the use of computations in mathematics and their applications to education and science.

Prof. Dr. Sergei Abramovich
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Computation is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematics
  • education
  • science
  • research
  • digital computation
  • curriculum development
  • online programs
  • teacher preparation

Published Papers (4 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

15 pages, 6176 KiB  
Article
Exploring Polygonal Number Sieves through Computational Triangulation
Computation 2023, 11(12), 251; https://doi.org/10.3390/computation11120251 - 10 Dec 2023
Viewed by 1126
Abstract
The paper deals with the exploration of subsequences of polygonal numbers of different sides derived through step-by-step elimination of terms of the original sequences. Eliminations are based on special rules similarly to how the classic sieve of Eratosthenes was developed through the elimination [...] Read more.
The paper deals with the exploration of subsequences of polygonal numbers of different sides derived through step-by-step elimination of terms of the original sequences. Eliminations are based on special rules similarly to how the classic sieve of Eratosthenes was developed through the elimination of multiples of primes. These elementary number theory activities, appropriate for technology-enhanced secondary mathematics education courses, are supported by a spreadsheet, Wolfram Alpha, Maple, and the Online Encyclopedia of Integer Sequences. General formulas for subsequences of polygonal numbers referred to in the paper as polygonal number sieves of order k, that include base-two exponential functions of k, have been developed. Different problem-solving approaches to the derivation of such and other sieves based on the technology-immune/technology-enabled framework have been used. The accuracy of computations and mathematical reasoning is confirmed through the technique of computational triangulation enabled by using more than one digital tool. A few relevant excerpts from the history of mathematics are briefly featured. Full article
(This article belongs to the Special Issue Computations in Mathematics, Mathematical Education, and Science)
Show Figures

Figure 1

16 pages, 938 KiB  
Article
The Accuracy of Computational Results from Wolfram Mathematica in the Context of Summation in Trigonometry
Computation 2023, 11(11), 222; https://doi.org/10.3390/computation11110222 - 06 Nov 2023
Viewed by 1128
Abstract
This article explores the accessibility of symbolic computations, such as using the Wolfram Mathematica environment, in promoting the shift from informal experimentation to formal mathematical justifications. We investigate the accuracy of computational results from mathematical software in the context of a certain summation [...] Read more.
This article explores the accessibility of symbolic computations, such as using the Wolfram Mathematica environment, in promoting the shift from informal experimentation to formal mathematical justifications. We investigate the accuracy of computational results from mathematical software in the context of a certain summation in trigonometry. In particular, the key issue addressed here is the calculated sum n=044tan1+4n°. This paper utilizes Wolfram Mathematica to handle the irrational numbers in the sum more accurately, which it achieves by representing them symbolically rather than using numerical approximations. Can we rely on the calculated result from Wolfram, especially if almost all the addends are irrational, or must the students eventually prove it mathematically? It is clear that the problem can be solved using software; however, the nature of the result raises questions about its correctness, and this inherent informality can encourage a few students to seek viable mathematical proofs. In this way, a balance is reached between formal and informal mathematics. Full article
(This article belongs to the Special Issue Computations in Mathematics, Mathematical Education, and Science)
Show Figures

Figure 1

15 pages, 1902 KiB  
Article
Computational “Accompaniment” of the Introduction of New Mathematical Concepts
Computation 2023, 11(10), 194; https://doi.org/10.3390/computation11100194 - 02 Oct 2023
Viewed by 979
Abstract
The computational capabilities of computer tools expand the student’s search capabilities. Conducting computational experiments in the classroom is no longer an organizational problem. This raises the “black box” problem, when the student perceives the computational module as a magician’s box and loses conceptual [...] Read more.
The computational capabilities of computer tools expand the student’s search capabilities. Conducting computational experiments in the classroom is no longer an organizational problem. This raises the “black box” problem, when the student perceives the computational module as a magician’s box and loses conceptual control over the computational process. This article analyses the use of various computer tools, both existing and specially created for “key” computational experiments, that aim at revealing the essential aspects of the introduced concepts using specific examples. This article deals with a number of topics of algebra and calculus that are transitional from school to university, and it shows how computational experiments in the form of a “transparent” box can be used. Full article
(This article belongs to the Special Issue Computations in Mathematics, Mathematical Education, and Science)
Show Figures

Graphical abstract

28 pages, 416 KiB  
Article
Revealing the Genetic Code Symmetries through Computations Involving Fibonacci-like Sequences and Their Properties
Computation 2023, 11(8), 154; https://doi.org/10.3390/computation11080154 - 07 Aug 2023
Cited by 1 | Viewed by 3419
Abstract
In this work, we present a new way of studying the mathematical structure of the genetic code. This study relies on the use of mathematical computations involving five Fibonacci-like sequences; a few of their “seeds” or “initial conditions” are chosen according to the [...] Read more.
In this work, we present a new way of studying the mathematical structure of the genetic code. This study relies on the use of mathematical computations involving five Fibonacci-like sequences; a few of their “seeds” or “initial conditions” are chosen according to the chemical and physical data of the three amino acids serine, arginine and leucine, playing a prominent role in a recent symmetry classification scheme of the genetic code. It appears that these mathematical sequences, of the same kind as the famous Fibonacci series, apart from their usual recurrence relations, are highly intertwined by many useful linear relationships. Using these sequences and also various sums or linear combinations of them, we derive several physical and chemical quantities of interest, such as the number of total coding codons, 61, obeying various degeneracy patterns, the detailed number of H/CNOS atoms and the integer molecular mass (or nucleon number), in the side chains of the coded amino acids and also in various degeneracy patterns, in agreement with those described in the literature. We also discover, as a by-product, an accurate description of the very chemical structure of the four ribonucleotides uridine monophosphate (UMP), cytidine monophosphate (CMP), adenosine monophosphate (AMP) and guanosine monophosphate (GMP), the building blocks of RNA whose groupings, in three units, constitute the triplet codons. In summary, we find a full mathematical and chemical connection with the “ideal sextet’s classification scheme”, which we alluded to above, as well as with others—notably, the Findley–Findley–McGlynn and Rumer’s symmetrical classifications. Full article
(This article belongs to the Special Issue Computations in Mathematics, Mathematical Education, and Science)
Show Figures

Graphical abstract

Back to TopTop