Mathematical Modeling for Practical Problems

2021

Studies in Computational Intelligence, 2013

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International Journal for Research in Applied Science & Engineering Technology (IJRASET), 2023

Mathematics (The QUEEN's mother of all Sciences), is the foundation of Computer Science. Mathematics 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. Scientists and researchers cannot ideally accomplish their work without the inclusion of mathematics. Mathematics is sociable for analytical skills needed in Computer Disciplines like; 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 accessional emergence of new concepts like machine learning, artificial intelligence, virtual reality and augmented reality make the future of mathematics grow endless. Mathematics has been an important intellectual preoccupation of man for a long time. Computer Science as a formal discipline is about seven decades young. Is the almost spontaneous use of computing? In this article, this paper convey to the frontage the many close connections and parallels between the Mother and daughter sciences. The paper underscores the strong interplay and interactions by looking at some exciting contemporary results from number theory and combinatorial mathematics and algorithms of computer science.

Extensive Journal of Applied Sciences, 2014

This research features the execution of security program utilizing the USB program to secure and discover entrance program. This allows using USB to discover and secure the entrance or anything that requires locking mechanism. Right now considering door (door can be of any room or cupboard or bank safe) as an example having a code number along with a number of mathematical expressions. This study mainly focuses on the mathematical algorithm running behind that system. Unlike mechanical locks, which use keys that are prone to duplication. This characteristic ensures the reliability of USB door locks, providing a secure access control.

UNITEXT, 2020

Based on a translation from the Italian language edition: I delfini delle Eolie, i battiti del cuore, i motori di ricerca by Alfio Quarteroni, Paola Gervasio © Zanichelli 2019 All rights Reserved.

2013

Introduction to fundamental techniques for designing and analyzing algorithms, including asymptotic analysis; divide-and-conquer algorithms and disjoint set operations; graph algorithms; backtracking algorithms; greedy algorithms; dynamic programming; and branch and bound algorithms; NP-Hard and NP-Complete problems; II. PREREQUISITE(S): 1. Problem Solving Skills 2. Basic Programming 3. Data Structures 4. Formal Languages and Automata Theory III. COURSE OBJECTIVES: 1 To analyze performance of algorithms. 2 To choose the appropriate data structure and algorithm design method for a specified application. 3 To understand how the choice of data structures and algorithm design methods impacts the performance of programs. 4 To solve problems using algorithm design methods such as the greedy method, divide and conquer, dynamic programming, backtracking and branch and bound. 5 To understand the differences between tractable and intractable problems. 6 To introduce P and NP classes. IV. COURSE OUTCOMES: S.No Description Bloom's Taxonomy Level 1 Ability to analyze the performance of algorithms. Analyze (level 4) 2 Ability to choose appropriate algorithm design techniques for solving problems. Knowledge, Application (level 1, level 3) 3 Ability to understand how the choice of data structures and the algorithm design methods impact the performance of programs. Understanding, Synthesis (Level 2, level 5) V. HOW PROGRAM OUTCOMES ARE ASSESSED: Program Outcomes (PO) Level Proficiency assessed by PO1 Engineering knowledge: Apply the knowledge of mathematics, science, engineering fundamentals, and an engineering specialization to the solution of complex engineering problems related to Computer Science and Engineering. 3 Assignments PO2 Problem analysis: Identify, formulate, review research literature, and analyze complex engineering problems related to Computer Science and Engineering and reaching substantiated conclusions using first principles of mathematics, natural sciences, and engineering sciences. 3 Assignments PO3 Design/development of solutions: Design solutions for complex engineering problems related to Computer Science and Engineering and design system components or processes that meet the specified needs with appropriate consideration for the public health and 2 Assignments safety, and the cultural, societal, and environmental considerations. PO4 Conduct investigations of complex problems: Use research-based knowledge and research methods including design of experiments, analysis and interpretation of data, and synthesis of the information to provide valid conclusions. 2 Assignments PO5 Modern tool usage: Create, select, and apply appropriate techniques, resources, and modern engineering and IT tools including prediction and modeling to complex engineering activities with an understanding of the limitations.

2018

All computer science disciplines have deep roots in various areas of mathematics, and students and engineers should be familiar with corresponding mathematical concepts and their implementations in real-world applications. This paper reviews several areas of computer science theory and its applications (e.g., computational fluid dynamics, modern encryption algorithms, code development and testing, and system simulation and modeling), where “traditional” and non-trivial mathematical methods (the analysis of singular differential equations, strange attractors, the group theory, modular arithmetic, the theory of graphs, and statistical modeling of rarefied-gas flows with the Direct Simulation Monte-Carlo technique) play key roles.