Applications of Mathematical in Computer Science

Current Science, 2005

Mathematics has been an important intellectual preoccupation of man for a long time. Computer science as a formal discipline is about seven decades young. However, one thing in common between all users and producers of mathematical thought is the almost involuntary use of computing. In this article, we bring to fore the many close connections and parallels between the two sciences of mathematics and computing. We show that, unlike in the other branches of human inquiry where mathematics is merely utilized or applied, computer science also returns additional value to mathematics by introducing certain new computational paradigms and methodologies and also by posing new foundational questions. We emphasize the strong interplay and interactions by looking at some exciting contemporary results from number theory and combinatorial mathematics and algorithms of computer science.

trung, 2019

Social Science Research Network, 2024

In this article we highlight some of the very interesting and important applications of mathematics, mainly in the fields of computer science, data science, and engineering. We discuss how fundamental concepts of mathematics, including functions, transformations, and mathematical structures have been influential in shaping the backbones of various digital technologies of the twenty first century. Furthermore, we look back into the twentieth century and review some milestones and key moments in the history of modern mathematics, that led to emergence and development of computer science and its subfields. By looking back into previous applications of mathematics, we try to provide insights on how and where mathematical concepts can be useful for future applications (particularly for establishing new math-based technological applications as well as for solving open problems in engineering domains such as artificial intelligence). This article will cover the contents in an easy-to-understand language; so that it can be interesting and insightful for the general audience. We believe and hope that it will help researchers to have a better understanding of how subtle properties of mathematical concepts and structures have been used for solving various engineering problems and for developing new branches of technology (e.g., blockchain as well as digital and math-based money systems such as Bitcoin).

Journal of Computing Sciences in Colleges, 2019

Mathematics has a vital role in the development of computer science, electronic systems, and numerous practical applications. The objective of this poster is to review several advanced mathematical concepts and methods (modular arithmetic; Galois fields; graph theory; singular differential equations; strange attractors; fuzzy logic, and projective geometry) that contribute into the development of applications in cryptography, numerical methods, code complexity reduction, atmospheric dynamics, expert systems, computational visualization, and other areas. The mathematical concepts, algorithms, and codes are examined by undergraduate and graduate students in various courses taught by the author. These concepts have paved the roads for students' research projects on various applications. Each student works on a selected project analyzing algorithms, creating computer codes (in Python, MATLAB, C/C++ or Java), running them at various parameters, comparing numerical results with known data, and presenting the findings to classmates and the research community. Many students published project summaries in the Rivier Academic Journal [1] and conference proceedings available from the web [2]. The opinions on why computer science students need general knowledge of mathematical concepts have been widely discussed in academia [3]. Several scholars [8] even recommended long lists of mathematical methods and formulas (ironically named as "Computer Science Cheat Sheets") that every computer science student should be familiar with. These "Cheat Sheets" cover mostly basic mathematical concepts (e.g.

arXiv preprint arXiv:0805.0585, 2008

Abstract: These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural deduction system``a la Prawitz''. The rest of the material is more or less traditional but I emphasize partial functions more than usual (after all, programs may not terminate for all input) and I provide a fairly complete account of the basic concepts of graph theory.

Philosophical Transactions of The Royal Society A: Mathematical, Physical and Engineering Sciences, 2005

Progress in the foundations of mathematics has made it possible to formulate all thinkable mathematical concepts, algorithms and proofs in one language and in an impeccable way. This not in spite of, but partially based on the famous results of Gödel and Turing. In this way statements are about mathematical objects and algorithms, proofs show the correctness of statements and computations, and computations are dealing with objects and proofs. Interactive computer systems for a full integration of defining, computing and proving are based on this. The human defines concepts, constructs algorithms and provides proofs, while the machine checks that the definitions are well-formed and the proofs and computations are correct. Results formalised so far demonstrate the feasibility of this 'Computer Mathematics'. Also there are very good applications. The challenge is to make the systems more mathematician-friendly, by building libraries and tools. The eventual goal is to help humans to learn, develop, communicate, referee and apply mathematics.

2

1999

The following is the catalog description of the course: Discussion of discrete structures frequently encountered in computer science and engineering, with an emphasis in problem solving skills and algorithms. Topics include set theory, proof techniques, graphs and trees, functions, recursive functions and procedures, inductively defined sets, grammars, equivalence, inductive proof, counting, discrete probability, and their applications to computing problems.

2006

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