Mathematics and Engineering in Computer Science
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Developing Scientific Computing Software: Current Processes And
DEVELOPING: SGIENffl&Pifli|ii^Mp| CURRENT PROCESSES" WMWiiiiia DEVELOPING SCIENTIFIC COMPUTING SOFTWARE MASTER OF APPLIED SCIENCE(2008) McMaster University COMPUTING AND SOFTWARE Hamilton, Ontario TITLE: Developing Scientific Computing Software: Current Processes and Future Directions AUTHOR: Jin Tang, M.M. (Nanjing University) SUPERVISOR: Dr. Spencer Smith NUMBER OF PAGERS: xxii, 216 n Abstract Considerable emphasis in scientific computing (SC) software development has been placed on the software qualities of performance and correctness. How ever, other software qualities have received less attention, such as the qualities of usability, maintainability, testability and reusability. Presented in this work is a survey titled "Survey on Developing Scien tific Computing Software, which is apparently the first conducted to explore the current approaches to SC software development and to determine which qualities of SC software are in most need of improvement. From the survey. we found that systematic development process is frequently not adopted in the SC software community, since 58% of respondents mentioned that their entire development process potentially consists only of coding and debugging. Moreover, semi-formal and formal specification is rarely used when developing SC software, which is suggested by the fact that 70% of respondents indicate that they only use informal specification. In terms of the problems in SC software development, which are dis covered by analyzing the survey results, a solution is proposed to improve the quality of SC software by using SE methodologies, concretely, using a modified Parnas' Rational Design Process (PRDP) and the Unified Software Development Process (USDP). A comparison of the two candidate processes is provided to help SC software practitioners determine which of the two pro cesses fits their particular situation. -
The Guide to Available Mathematical Software Problem Classification System
The Guide to Available Mathematical Software Problem Classification System Ronald F. Boisvert, Sally E. Howe and David K. Kahaner November 1990 U.S. DEPARTMENT OF COMMERCE National Institute of Standards and Technology Gaithersburg, MD 20899 100 U56 //4475 1990 C.2 NATIONAL, INSrrnJTE OF STANDARDS & TECHNOLOGY / THE GUIDE TO AVAILABLE MATHEMATICAL SOFTWARE PROBLEM CLASSIFICATION SYSTEM Ronald F. Boisvert Sally E. Howe David K. Kahaner U.S. DEPARTMENT OF COMMERCE National InstHute of Standards and Technology Center for Computing and Applied Mathematics Gaithersburg, MO 20899 November 1990 U.S. DEPARTMENT OF COMMERCE Robert A. Mosbacher, Secretary NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY John W. Lyons, Director 2 Boisvert, Howe and Kahaner own manuals or on-line documentation system. In order to determine what software is avail- able to solve a particular problem, users must search through a very large, heterogeneous collection of information. This is a tedious and error-prone process. As a result, there has been much interest in the development of automated advisory systems to help users select software. Keyword search is a popular technique used for this purpose. In such a system keywords or phrases are assigned to each piece of software to succinctly define its purpose, and the set of aU such keywords axe entered into a database. Keyword-based selection systems query users for a set of keywords and then present a fist of software modules which contain them. A major difficulty with such systems is that users often have trouble in providing the appropriate keywords for a given mathematical or statistical problem. There is such a wealth of alternate mathematical and statistical terminology that it would be a rare occurrence for two separate knowledgeable persons to assign the same set of keywords to a given software module. -
A Comparison of Six Numerical Software Packages for Educational Use in the Chemical Engineering Curriculum
SESSION 2520 A COMPARISON OF SIX NUMERICAL SOFTWARE PACKAGES FOR EDUCATIONAL USE IN THE CHEMICAL ENGINEERING CURRICULUM Mordechai Shacham Department of Chemical Engineering Ben-Gurion University of the Negev P. O. Box 653 Beer Sheva 84105, Israel Tel: (972) 7-6461481 Fax: (972) 7-6472916 E-mail: [email protected] Michael B. Cutlip Department of Chemical Engineering University of Connecticut Box U-222 Storrs, CT 06269-3222 Tel: (860)486-0321 Fax: (860)486-2959 E-mail: [email protected] INTRODUCTION Until the early 1980’s, computer use in Chemical Engineering Education involved mainly FORTRAN and less frequently CSMP programming. A typical com- puter assignment in that era would require the student to carry out the following tasks: 1.) Derive the model equations for the problem at hand, 2.) Find an appropri- ate numerical method to solve the model (mostly NLE’s or ODE’s), 3.) Write and debug a FORTRAN program to solve the problem using the selected numerical algo- rithm, and 4.) Analyze the results for validity and precision. It was soon recognized that the second and third tasks of the solution were minor contributions to the learning of the subject material in most chemical engi- neering courses, but they were actually the most time consuming and frustrating parts of computer assignments. The computer indeed enabled the students to solve realistic problems, but the time spent on technical details which were of minor rele- vance to the subject matter was much too long. In order to solve this difficulty, there was a tendency to provide the students with computer programs that could solve one particular type of a problem. -
Software for Numerical Computation
Purdue University Purdue e-Pubs Department of Computer Science Technical Reports Department of Computer Science 1977 Software for Numerical Computation John R. Rice Purdue University, [email protected] Report Number: 77-214 Rice, John R., "Software for Numerical Computation" (1977). Department of Computer Science Technical Reports. Paper 154. https://docs.lib.purdue.edu/cstech/154 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. SOFTWARE FOR NUMERICAL COMPUTATION John R. Rice Department of Computer Sciences Purdue University West Lafayette, IN 47907 CSD TR #214 January 1977 SOFTWARE FOR NUMERICAL COMPUTATION John R. Rice Mathematical Sciences Purdue University CSD-TR 214 January 12, 1977 Article to appear in the book: Research Directions in Software Technology. SOFTWARE FOR NUMERICAL COMPUTATION John R. Rice Mathematical Sciences Purdue University INTRODUCTION AND MOTIVATING PROBLEMS. The purpose of this article is to examine the research developments in software for numerical computation. Research and development of numerical methods is not intended to be discussed for two reasons. First, a reasonable survey of the research in numerical methods would require a book. The COSERS report [Rice et al, 1977] on Numerical Computation does such a survey in about 100 printed pages and even so the discussion of many important fields (never mind topics) is limited to a few paragraphs. Second, the present book is focused on software and thus it is natural to attempt to separate software research from numerical computation research. This, of course, is not easy as the two are intimately intertwined. -
RESOURCES in NUMERICAL ANALYSIS Kendall E
RESOURCES IN NUMERICAL ANALYSIS Kendall E. Atkinson University of Iowa Introduction I. General Numerical Analysis A. Introductory Sources B. Advanced Introductory Texts with Broad Coverage C. Books With a Sampling of Introductory Topics D. Major Journals and Serial Publications 1. General Surveys 2. Leading journals with a general coverage in numerical analysis. 3. Other journals with a general coverage in numerical analysis. E. Other Printed Resources F. Online Resources II. Numerical Linear Algebra, Nonlinear Algebra, and Optimization A. Numerical Linear Algebra 1. General references 2. Eigenvalue problems 3. Iterative methods 4. Applications on parallel and vector computers 5. Over-determined linear systems. B. Numerical Solution of Nonlinear Systems 1. Single equations 2. Multivariate problems C. Optimization III. Approximation Theory A. Approximation of Functions 1. General references 2. Algorithms and software 3. Special topics 4. Multivariate approximation theory 5. Wavelets B. Interpolation Theory 1. Multivariable interpolation 2. Spline functions C. Numerical Integration and Differentiation 1. General references 2. Multivariate numerical integration IV. Solving Differential and Integral Equations A. Ordinary Differential Equations B. Partial Differential Equations C. Integral Equations V. Miscellaneous Important References VI. History of Numerical Analysis INTRODUCTION Numerical analysis is the area of mathematics and computer science that creates, analyzes, and implements algorithms for solving numerically the problems of continuous mathematics. Such problems originate generally from real-world applications of algebra, geometry, and calculus, and they involve variables that vary continuously; these problems occur throughout the natural sciences, social sciences, engineering, medicine, and business. During the second half of the twentieth century and continuing up to the present day, digital computers have grown in power and availability. -
A Combinatorial Analysis of Finite Boolean Algebras
A Combinatorial Analysis of Finite Boolean Algebras Kevin Halasz [email protected] May 1, 2013 Copyright c Kevin Halasz. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license can be found at http://www.gnu.org/copyleft/fdl.html. 1 Contents 1 Introduction 3 2 Basic Concepts 3 2.1 Chains . .3 2.2 Antichains . .6 3 Dilworth's Chain Decomposition Theorem 6 4 Boolean Algebras 8 5 Sperner's Theorem 9 5.1 The Sperner Property . .9 5.2 Sperner's Theorem . 10 6 Extensions 12 6.1 Maximally Sized Antichains . 12 6.2 The Erdos-Ko-Rado Theorem . 13 7 Conclusion 14 2 1 Introduction Boolean algebras serve an important purpose in the study of algebraic systems, providing algebraic structure to the notions of order, inequality, and inclusion. The algebraist is always trying to understand some structured set using symbol manipulation. Boolean algebras are then used to study the relationships that hold between such algebraic structures while still using basic techniques of symbol manipulation. In this paper we will take a step back from the standard algebraic practices, and analyze these fascinating algebraic structures from a different point of view. Using combinatorial tools, we will provide an in-depth analysis of the structure of finite Boolean algebras. We will start by introducing several ways of analyzing poset substructure from a com- binatorial point of view. -
A Boolean Algebra and K-Map Approach
Proceedings of the International Conference on Industrial Engineering and Operations Management Washington DC, USA, September 27-29, 2018 Reliability Assessment of Bufferless Production System: A Boolean Algebra and K-Map Approach Firas Sallumi ([email protected]) and Walid Abdul-Kader ([email protected]) Industrial and Manufacturing Systems Engineering University of Windsor, Windsor (ON) Canada Abstract In this paper, system reliability is determined based on a K-map (Karnaugh map) and the Boolean algebra theory. The proposed methodology incorporates the K-map technique for system level reliability, and Boolean analysis for interactions. It considers not only the configuration of the production line, but also effectively incorporates the interactions between the machines composing the line. Through the K-map, a binary argument is used for considering the interactions between the machines and a probability expression is found to assess the reliability of a bufferless production system. The paper covers three main system design configurations: series, parallel and hybrid (mix of series and parallel). In the parallel production system section, three strategies or methods are presented to find the system reliability. These are the Split, the Overlap, and the Zeros methods. A real-world case study from the automotive industry is presented to demonstrate the applicability of the approach used in this research work. Keywords: Series, Series-Parallel, Hybrid, Bufferless, Production Line, Reliability, K-Map, Boolean algebra 1. Introduction Presently, the global economy is forcing companies to have their production systems maintain low inventory and provide short delivery times. Therefore, production systems are required to be reliable and productive to make products at rates which are changing with the demand. -
Course Description for Computer Science.Pdf
COURSE DESCRIPTIONS FOR COMPUTER SCIENCE The Department of Mathematics and Computer Science requires that, prior to enrolling in any departmental course, students should earn a grade of “C” or better in all course prerequisites. CSDP 100 Computer Science Orientation Credit 1 This course is a survey of Computer Science with special emphasis on topics of importance to computer scientists. It also provides an exploration of skills required and resources available to students majoring Computer Science. Topics include nature of problems, hardware, human factors, security, social, ethical and legal issues, familiarization of various aspects of computing and networks. This course must be taken by all Computer Science major and minor students. CSDP 120 Introduction to Computing Credit 3 This course is for students new to Computer Science. The goal is to introduce students to different general computing aspects of the computer systems. Course topics include overview of the history of computing machines, computing codes and ethics, computing algorithms, programming languages, and mathematical software packages. Prerequisite: High school mathematics. CSDP 120 does not satisfy the General Education Area III Requirement. CSDP 121 Microcomputer Applications Credit 3 This course is designed for non-technical majors in different applications of modern computing systems. The course surveys computing hardware and software systems and introduces students to the present state-of-the-art word processing, spreadsheet, and database software. Applications to other disciplines, such as medicine, administration, accounting, social sciences and humanities, will be considered. Prerequisite: High School Mathematics. CSDP 121 does not satisfy the General Education Area III Requirement. CSDP 150 Office Automation Workshop Credit 1 This course is an introduction to current progress in word processing and/or office automation. -
Sage: Unifying Mathematical Software for Scientists, Engineers, and Mathematicians
Sage: Unifying Mathematical Software for Scientists, Engineers, and Mathematicians 1 Introduction The goal of this proposal is to further the development of Sage, which is comprehensive unified open source software for mathematical and scientific computing that builds on high-quality mainstream methodologies and tools. Sage [12] uses Python, one of the world's most popular general-purpose interpreted programming languages, to create a system that scales to modern interdisciplinary prob- lems. Sage is also Internet friendly, featuring a web-based interface (see http://www.sagenb.org) that can be used from any computer with a web browser (PC's, Macs, iPhones, Android cell phones, etc.), and has sophisticated interfaces to nearly all other mathematics software, includ- ing the commercial programs Mathematica, Maple, MATLAB and Magma. Sage is not tied to any particular commercial mathematics software platform, is open source, and is completely free. With sufficient new work, Sage has the potential to have a transformative impact on the compu- tational sciences, by helping to set a high standard for reproducible computational research and peer reviewed publication of code. Our vision is that Sage will have a broad impact by supporting cutting edge research in a wide range of areas of computational mathematics, ranging from applied numerical computation to the most abstract realms of number theory. Already, Sage combines several hundred thousand lines of new code with over 5 million lines of code from other projects. Thousands of researchers use Sage in their work to find new conjectures and results (see [13] for a list of over 75 publications that use Sage). -
Sets and Boolean Algebra
MATHEMATICAL THEORY FOR SOCIAL SCIENTISTS SETS AND SUBSETS Denitions (1) A set A in any collection of objects which have a common characteristic. If an object x has the characteristic, then we say that it is an element or a member of the set and we write x ∈ A.Ifxis not a member of the set A, then we write x/∈A. It may be possible to specify a set by writing down all of its elements. If x, y, z are the only elements of the set A, then the set can be written as (2) A = {x, y, z}. Similarly, if A is a nite set comprising n elements, then it can be denoted by (3) A = {x1,x2,...,xn}. The three dots, which stand for the phase “and so on”, are called an ellipsis. The subscripts which are applied to the x’s place them in a one-to-one cor- respondence with set of integers {1, 2,...,n} which constitutes the so-called index set. However, this indexing imposes no necessary order on the elements of the set; and its only pupose is to make it easier to reference the elements. Sometimes we write an expression in the form of (4) A = {x1,x2,...}. Here the implication is that the set A may have an innite number of elements; in which case a correspondence is indicated between the elements of the set and the set of natural numbers or positive integers which we shall denote by (5) Z = {1, 2,...}. (Here the letter Z, which denotes the set of natural numbers, derives from the German verb zahlen: to count) An alternative way of denoting a set is to specify the characteristic which is common to its elements. -
Bachelor of Engineering Program in Robotics Engineering and Automation System
Bachelor of Engineering Program in Robotics Engineering and Automation System Production Engineering Department, Faculty of Engineering King Mongkut's University of Technology North Bangkok 1518 Pracharad 1 Rd., Wongsawang, Bangsue, Bangkok 10800 Thailand Tel. 02-555-2000 ext 8208 Fax 02-587-0029 Brief History Since founded in 1984, Production Engineering Department has offered only one undergraduate curriculum. With ample available resources, the department identifies the next step as a new curriculum responding to industrial needs. PE Students become so skillful that they have won many prizes in various robot competitions. Curriculum Objectives Produce graduates in Robotics Engineering and Automation System for industry and ASEAN. Produce students with skills and knowledge to proudly represent KMUTNB uniqueness. Support innovative creation according to KMUTNB philosophy Program of Study for Robotics Engineering & Automation System ( . 2556) Total = 143 Credits Semester 1 Semester 2 Semester 3 Semester 4 Semester 5 Semester 6 Summer Semester 7 Semester 8 = 18 Credits = 20 Credits = 22 Credits = 21 Credits = 18 Credits = 19 Credits = 240 hours = 11 Credits = 14 Credits 040203111 3(3-0-6) 040203112 3(3-0-6) 040203211 3(3-0-6) 010243102 3(3-0-6) 010243xxx 3(x-x-x) 010243xxx 3(x-x-x) 010243210 1(0-2-1) 010243211 3(0-6-3) Engineering Engineering Engineering Mechanics of Technical Elective Technical Elective p RE Project I RE Project II Course I Course II ) Mathematics I Mathematics II Mathematics III i Materials 0 - h 0 s 4 n 2 r - 0 e -
Boolean Algebras
CHAPTER 8 Boolean Algebras 8.1. Combinatorial Circuits 8.1.1. Introduction. At their lowest level digital computers han- dle only binary signals, represented with the symbols 0 and 1. The most elementary circuits that combine those signals are called gates. Figure 8.1 shows three gates: OR, AND and NOT. x1 OR GATE x1 x2 x2 x1 AND GATE x1 x2 x2 NOT GATE x x Figure 8.1. Gates. Their outputs can be expressed as a function of their inputs by the following logic tables: x1 x2 x1 x2 1 1 ∨1 1 0 1 0 1 1 0 0 0 OR GATE 118 8.1. COMBINATORIAL CIRCUITS 119 x1 x2 x1 x2 1 1 ∧1 1 0 0 0 1 0 0 0 0 AND GATE x x¯ 1 0 0 1 NOT GATE These are examples of combinatorial circuits. A combinatorial cir- cuit is a circuit whose output is uniquely defined by its inputs. They do not have memory, previous inputs do not affect their outputs. Some combinations of gates can be used to make more complicated combi- natorial circuits. For instance figure 8.2 is combinatorial circuit with the logic table shown below, representing the values of the Boolean expression y = (x x ) x . 1 ∨ 2 ∧ 3 x1 x2 y x3 Figure 8.2. A combinatorial circuit. x1 x2 x3 y = (x1 x2) x3 1 1 1 ∨0 ∧ 1 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1 0 0 1 1 0 0 0 1 However the circuit in figure 8.3 is not a combinatorial circuit.