Mathematical Computer Science Research Articles

Application of Vedic Mathematics in Computer Science

Application of Vedic Mathematics in Computer Science

Unveiling the Digital Equation Through Innovative Approaches for Teaching Discrete Mathematics to Future Computer Science Educators

Aim/Purpose: This study seeks to present a learning model of discrete mathematics elements, elucidate the content of teaching, and validate the effectiveness of this learning in a digital education context. Background: Teaching discrete mathematics in the realm of digital education poses challenges, particularly in crafting the optimal model, content, tools, and methods tailored for aspiring computer science teachers. The study draws from both a comprehensive review of relevant literature and the synthesis of the authors’ pedagogical experiences. Methodology: The research utilized a system-activity approach and aligned with the State Educational Standard. It further integrated the theory of continuous education as its psychological and pedagogical foundation. Contribution: A unique model for instructing discrete mathematics elements to future computer science educators has been proposed. This model is underpinned by informative, technological, and personal competencies, intertwined with the mathematical bedrock of computer science. Findings: The study revealed the importance of holistic teaching of discrete mathematics elements for computer science teacher aspirants in line with the Informatics educational programs. An elective course, “Elements of Discrete Mathematics in Computer Science”, comprising three modules, was outlined. Practical examples spotlighting elements of mathematical logic and graph theory of discrete mathematics in programming and computer science were showcased. Recommendations for Practitioners: Future computer science educators should deeply integrate discrete mathematics elements in their teaching methodologies, especially when aligning with professional disciplines of the Informatics educational program. Recommendation for Researchers: Further exploration is recommended on the seamless integration of discrete mathematics elements in diverse computer science curricula, optimizing for varied learning outcomes and student profiles. Impact on Society: Enhancing the quality of teaching discrete mathematics to future computer science teachers can lead to better-educated professionals, driving advancements in the tech industry and contributing to societal progress. Future Research: There is scope to explore the wider applications of the discrete mathematics elements model in varied computer science sub-disciplines, and its adaptability across different educational frameworks.

A neural network solves, explains, and generates university math problems by program synthesis and few-shot learning at human level

We demonstrate that a neural network pretrained on text and fine-tuned on code solves mathematics course problems, explains solutions, and generates questions at a human level. We automatically synthesize programs using few-shot learning and OpenAI's Codex transformer and execute them to solve course problems at 81% automatic accuracy. We curate a dataset of questions from Massachusetts Institute of Technology (MIT)'s largest mathematics courses (Single Variable and Multivariable Calculus, Differential Equations, Introduction to Probability and Statistics, Linear Algebra, and Mathematics for Computer Science) and Columbia University's Computational Linear Algebra. We solve questions from a MATH dataset (on Prealgebra, Algebra, Counting and Probability, Intermediate Algebra, Number Theory, and Precalculus), the latest benchmark of advanced mathematics problems designed to assess mathematical reasoning. We randomly sample questions and generate solutions with multiple modalities, including numbers, equations, and plots. The latest GPT-3 language model pretrained on text automatically solves only 18.8% of these university questions using zero-shot learning and 30.8% using few-shot learning and the most recent chain of thought prompting. In contrast, program synthesis with few-shot learning using Codex fine-tuned on code generates programs that automatically solve 81% of these questions. Our approach improves the previous state-of-the-art automatic solution accuracy on the benchmark topics from 8.8 to 81.1%. We perform a survey to evaluate the quality and difficulty of generated questions. This work automatically solves university-level mathematics course questions at a human level and explains and generates university-level mathematics course questions at scale, a milestone for higher education.

Importance of Mathematics in Computer Science, Engineering and Technology (CSET) Education

Students with weak mathematics background are often overwhelmed by the many mathematics courses that they have to take during their undergraduate Computer Science, Engineering and Technology (CSET) programmes; and tend to question the relevance of mathematics to their CSET studies. This paper examined the syllabuses of undergraduate CSET courses being offered in 10 Ghanaian universities and discussed the importance of relevant mathematics courses to them. Furthermore, it proffered recommendations to promote students’ academic success in CSET programmes.

Application of Mathematics in Computer Science

No one escape the learning of mathematics in one way or other, ranging from our kitchen to our journey from earth to Moon or Mars. Mathematics persists everywhere around us. It can be perceived in our garden or park from symmetry of leaves, flowers, fruits etc. and by so many examples of Geometry and symmetry can be seen in nature. God used mathematics in creation of the universe in one form or the other. Likewise, Mathematics is the queen of all sciences. Scientists and researchers can not perfectly accomplish their work without including mathematics. Mathematics is the foundation of Computer Science. If one is eager to learn any arena of Computer Science, first he/she has to imbibe a love of Mathematics that will be supportive for progressive learning of the said subject. Mathematics is friendly for analytical skills needed in Computer Science. Concepts of binary number system, Boolean algebra, Calculus, Discrete mathematics, linear algebra, number theory, and graph theory are the most applicable to the subject of computer science with the emergence of new concepts like machine learning, artificial intelligence, virtual reality and augmented reality.

RECENT RESULTS ON CARDINALITY ESTIMATION AND INFORMATION THEORETIC INEQUALITIES

I would like to dedicate this little exposition to Prof. Phan Dinh Dieu, one of the giants and pioneers of Mathematics in Computer Science in Vietnam. In the past 15 years or so, new and exciting connections between fundamental problems in database theory and information theory have emerged. There are several angles one can take to describe this connection. This paper takes one such angle, influenced by the author's own bias and research results. In particular, we will describe how the cardinality estimation problem -- a corner-stone problem for query optimizers -- is deeply connected to information theoretic inequalities. Furthermore, we explain how inequalities can also be used to derive a couple of classic geometric inequalities such as the Loomis-Whitney inequality. A purpose of the article is to introduce the reader to these new connections, where theory and practice meet in a wonderful way. Another objective is to point the reader to a research area with many new open questions.

The Beauty of Mathematics in Computer Science

The Beauty of Mathematics in Computer Science

Improving Students’ Perception Towards Learning Mathematics: Impact of Teaching Application of Mathematics

Numerous decisions in our daily lives require the ability to calculate, solve problems, and employ concepts and skills in mathematics. However, students always have bad perceptions in mathematics as this subject is often challenging for students to master. Reports on issues about students’ mathematical education have been raised by many mathematics educators. Among of the issues are about difficulties in understanding mathematical concepts, attitudes towards mathematics, low achievement in mathematics and many more. Hence, the aim of this study is to explore students’ perceptions and attitudes towards mathematics by analyzing the impact of teaching application of mathematics to the students. The data were collected from Computer Science students where each participant was assigned to complete self-reported and close ended questionnaire. In this study, examination on attitudes of student include engagement, confidence and importance of mathematics. Data were analyzed by measuring the difference of individual statements on percentage of agreeing in pre – Smart for mathematics and post – Smart for mathematics. The findings show that when students learned and exposed to the application of mathematics, their engagement, confidence and importance of mathematics increases. It can concluded that by exposing students the purpose of learning mathematics in computer science, students’ positive attitude towards mathematics can be developed and hence improve their interests in learning mathematics

Eulogy for Professor Mirka Miller (1949–2016)

The CIMPA Research School on Mathematical Models for Security Applications was dedicated to the memory of Emeritus Professor Mirka Miller, who suggested that it be held in Havana. Mirka Miller, member of the editorial board of Mathematics in Computer Science, devoted her research to Graph Theory and Data Security, fields where she made important and beautiful contributions.

Kinematics and dynamics motion planning by polar piecewise interpolation and geometric considerations

The importance of numerical methods in science and engineering [Chapra, S.C., and R.P. Canale, “Numerical Methods for Engineers,” McGraw-Hill, 6th Ed., 2010] was long recognised and considered a fundamental factor in improving productivity and reducing production costs. The ability to model flexible systems and describe their trajectories [Gasparetto A., Boscariol P., Lanzutti A., Vidoni R., Trajectory planning in Robotics, Mathematics in Computer Science 6 (2012), pp. 269–279] involves usually the study of nonlinear coupled partial differential equations. Since their exact solutions are not normally feasible in practice, computational methods [V. Kumar, M. Zefran, J.P. Ostrowski, Motion Planning and Control of Robots, Handbook of Industrial Robotics, 2nd Edition, J. Wiley and Sons (2007), pp. 295–315] can be considered.

Existence of fixed points for $$\mathcal {J}$$ J - $$\psi $$ ψ -fuzzy contractions in fuzzy metric spaces endowed with graph

Graph plays the role of partial ordering in fuzzy metric spaces. Also, the language of graph in a fuzzy metric space presents a fruitful application of mathematics in computer science and engineering. In this paper, we direct the concept of fuzzy metric space towards the graph theory using altering distance function. Here, to find fixed point, we define a new contraction $$\mathcal {J}$$ - $$\psi $$ -fuzzy contraction in fuzzy metric space $$(K,\mathcal {F},*)$$ endowed with a graph.

Mathematics in Computer Science: After 10 Years

Mathematics in Computer Science: After 10 Years

Modelling computer systems: mathematics for computer science

Modelling computer systems: mathematics for computer science

The roles of mathematics in computer science

research-article Share on The roles of mathematics in computer science Authors: Douglas Baldwin SUNY Geneseo, Geneseo, New York SUNY Geneseo, Geneseo, New YorkView Profile , Henry M. Walker Grinnell College, Grinnell, Iowa Grinnell College, Grinnell, IowaView Profile , Peter B. Henderson Butler University, Indianapolis, Indiana Butler University, Indianapolis, IndianaView Profile Authors Info & Claims ACM InroadsVolume 4Issue 4December 2013 pp 74–80https://doi.org/10.1145/2537753.2537777Online:01 December 2013Publication History 43citation1,570DownloadsMetricsTotal Citations43Total Downloads1,570Last 12 Months153Last 6 weeks18 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

Foreword to the Special Focus on Mathematics, Data and Knowledge

There is a growing interest in applying mathematical theories and methods from topology, computational geometry, differential equations, fluid dynamics, quantum statistics, etc. to describe and to analyze scientific regularities of diverse, massive, complex, nonlinear, and fast changing data accumulated continuously around the world and in discovering and revealing valid, insightful, and valuable knowledge that data imply. With increasingly solid mathematical foundations, various methods and techniques have been studied and developed for data mining, modeling, and processing, and knowledge representation, organization, and verification; different systems and mechanisms have been designed to perform data-intensive tasks in many application fields for classification, predication, recommendation, ranking, filtering, etc. This special focus of Mathematics in Computer Science is organized to stimulate original research on the interaction of mathematics with data and knowledge, in particular the exploration of new mathematical theories and methodologies for data modeling and analysis and knowledge discovery and management, the study of mathematical models of big data and complex knowledge, and the development of novel solutions and strategies to enhance the performance of existing systems and mechanisms for data and knowledge processing. The present foreword provides a short review of some key ideas and techniques on how mathematics interacts with data and knowledge, together with a few selected research directions and problems and a brief introduction to the four papers published in the focus.

PENGKLASIFIKASIAN DEBITUR DENGAN MENGGUNAKAN ALGORITMA GRAHAM SCAN DALAM PENGAPLIKASIAN CONVEX HULL

Computational geometry is the mathematical science of computation by using the algorithm analysis to solve the problems of geometry. The problems of computational include polygon triangulations, convex hulls, Voronoi diagrams, and motion planning. Convex hull is the set of points that form a convex polygon that covers the entire set of points. The algorithms for determining the convex hull, among others, Graham Scan, Jarvis March, and Divide and Conquer. In the two-dimensional case, Graham Scan algorithm is highly efficient in the use of time complexity. This article discusses the quest convex hull of the data bank debtors, some of the data used to look at the classification accuracy of the convex hull formed. The coordinates of all the data found by using principal component analysis.After the data are analyzed, we get the accuracy of classification by 74%.

Behavior of the Fiber and the Base Points of Parametrizations Under Projections

This is the author’s version of a work that was accepted for publication in Mathematics in Computer Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Mathematics in Computer Science Volume 7, Issue 2 (2013), Page 167-184 DOI 10.1007/s11786-013-0139-8

Reviews of the book "Discrete Mathematics for Computer Science, Part I: Elementary combinatorics'' by J. Jaworskiego, Z. Palki and J. Szymańskiego

T he book under review is based on discrete mathematics lectures conducted for students of mathematics and computer science. This is the first of two planned volumes. Published volume is dedicated to combinatorics , announced the second volume will cover the most important graph theory and algorithms. The second volume will be discussed in the pages of Mathematica Applicanda after his release .

Indian Women and Mathematics for Computer Science

To sum up, the case study of female students in India has shown that because they perform well in mathematics, they have high self efficacy for enrolling and remaining in CS. The new domain of CS builds on prior skills in mathematics. This suggests that CS and mathematics share skills. There is a need to carry out a comparative study of how mathematics is taught to girls and boys in the U.S. and India in order to understand issues related to gender and mathematics.

Decision procedures for extensions of the theory of arrays

The theory of arrays, introduced by McCarthy in his seminal paper "Towards a mathematical science of computation," is central to Computer Science. Unfortunately, the theory alone is not sufficient for many important verification applications such as program analysis. Motivated by this observation, we study extensions of the theory of arrays whose satisfiability problem (i.e., checking the satisfiability of conjunctions of ground literals) is decidable. In particular, we consider extensions where the indexes of arrays have the algebraic structure of Presburger arithmetic and the theory of arrays is augmented with axioms characterizing additional symbols such as dimension, sortedness, or the domain of definition of arrays. We provide methods for integrating available decision procedures for the theory of arrays and Presburger arithmetic with automatic instantiation strategies which allow us to reduce the satisfiability problem for the extension of the theory of arrays to that of the theories decided by the available procedures. Our approach aims to re-use as much as possible existing techniques so as to ease the implementation of the proposed methods. To this end, we show how to use model-theoretic, rewriting-based theorem proving (i.e., superposition), and techniques developed in the Satisfiability Modulo Theories communities to implement the decision procedures for the various extensions.