# Paul S. WangKent State University | KSU · Department of Computer Science

Paul S. Wang

PhD

## About

149

Publications

79,305

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Introduction

Additional affiliations

June 2012 - present

June 2002 - May 2003

June 1986 - May 1987

Education

August 1967 - May 1971

## Publications

Publications (149)

The complexity of a mathematical expression is a measure that can be used to compare the expression with other mathematical expressions and judge which one is simpler. In the paper, we analyze three effect factors for the complexity of a mathematical expression: representational length, computational time, and intelligibility. Mainly, the paper int...

本书为教育部大学计算机课程改革项目成果，通过讲授计算机科学和技术中最基本的内容，来介绍有关计算思维 (Computational Thinking 或 CT) 的一些概念。目的是让读者通过知识学习体会思考问题和解决问题的新方法，培养计算思维能力。
本书共分10章，包括了计算机基本原理、操作系统与应用软件、网络与网页、计算机安全、算法与数据管理等方面的丰富内容。本书不教编程语言， 读者也不需要有编程经验。
本书采用新的角度组织教学内容，在广泛性、实用性、思想性方面具有显著特点，可作为高校“大学计算机”课程的配套教材使用，适合非专业生计算入门课， 也可供对计算机学科或计算思维感兴趣的人员阅读。
See: http://ct.hfut.edu.cn/

Concepts, techniques, and analytical abilities from the field of computing can make anyone more efficient in the information age. Furthermore, their understanding can give us powerful mental tools in general for solving problems, performing tasks, planing, working with others, anticipating problems, troubleshooting, and more. We refer to this menta...

GeometryTouch is a dynamic geometry software system with touch operation. Developed by JavaScript and SVG, GeometryTouch is a Web-based application which can run on browsers of mobile devices. When using GeometryTouch, users can draw geometric figures and create or modify geometry-based interactive manipulatives. A virtual cursor is designed to imp...

MathEdit is an interactive tool for creating and editing mathematical expressions on the Web. It is an open-source program implemented in standard XHTML and JavaScript to run in regular browsers. The tool supports both WYSIWYG editing and command-line editing operations. Recently, a touch version of MathEdit is under development. In MathEdit touch...

This book provides a comprehensive and up-to-date guide to Web programming concepts, principles, standard technologies, HTML5 and its associated APIs. The text helps you master Web development techniques with a well-organized set of topics. Practical examples are used to illustrate and demonstrate how to combine and use what you learn in realistic...

This book provides a comprehensive and up-to-date guide to Linux concepts, usage, and programming. The text helps you master Linux with a well-selected set of topics. Hands-on practice is encouraged; it is the only way to gain familiarity with an operating system. A primer gets you started quickly. Then, the chapters lead you from user interfaces,...

Introduced is a Web-based intelligent mathematics assessment system, MathPASS. MathPASS can generate random mathematical test questions based on pre-determined question prototypes, let users enter their answers in either a WYSIWYG or a character-string input environment, and check user answers with the help of a computer algebra system (CAS). 1 Mat...

A Web-based intelligent mathematics assessment system, as a part of education system, is extremely useful to assess the ability of students. The paper mainly focuses on three research topics in the intelligent mathematics assessment system: answer input methods, generating of random question, and answer checking. The paper discusses the design meth...

The paper contributes a solution for creating and editing mathematical formula, graphics and geometry object for Web-based application of e-Science. The solution includes two useful program packages: MathEdit, a Web-based WYSIWYG mathematical expression editor, and GeometryEditor, a Web-based interactive tool for drawing geometry graphics. The two...

This comprehensive and in-depth textbook covers Java and object-oriented as well as generic programming for an upper-level undergraduate or beginning graduate course. This book is ideal for students who have some programming experience, who wish to really learn Java and OOP well.

Assessing student performance and understanding is very important in education generally and in Mathematics education in particular. DMAS is a Web-based Distributed Mathematics Assessment system that can be of great value to teachers and students of Mathematics. Features of DMAS include: DMAD (the core Distributed Mathematics Assessment database),...

GeometryEditor (previous code name: GeoSVG) is a Web-based environment for authoring interactive geometry manipulatives. Users may create on-line manipulatives to illustrate mathematical concepts for a hands-on learning environment. GeometryEditor provides standard authoring features, such as sketching, measurements, calculation, macros, iteration,...

The ability for users online creating and editing mathematical expressions is very important for Science Computing Systems, Science Communication Systems, and Web-based Mathematics Education Systems. Lanzhou university/China and Kent University/USA are jointly developing a mathematical expression editor. The editor MathEdit, implemented in JavaScri...

The public converter will translate mathematical expression from one encoding standard to another. This technical report will talk about several different encoding standards; compare their merits and de-faults; and explain why we need a public converter component for these representations. Then we'll focus on how to build such a converter. 1 Backgr...

MathEdit (Su et al., 2006) is a browser-based tool implemented in JavaScript that provides a convenient and intuitive graphical user interface for creating and editing mathematical expressions as well as a well-defined API for interoperating with its containing Web page. MathEdit can produce MathML Content and Presentation Markup as well as infix e...

The design and implementation of a software system for automatically generating code for finite element analysis are described. Exact symbolic computational techniques are employed to derive strain-displacement matrices and element stiffness matrices. Methods for dealing with the excessive growth of symbolic expressions in practical computations ar...

In a recently published paper [4] the author described a new algorithm for multivariate polynomial factorization over the integers. One important feature of this algorithm is the variable-by-variable p-adic construction of all factors in parallel. To perform such p-adic construction of the factors, a second p-adic construction for multivariate "cor...

Classroom trials at Kimpton Middle School demonstrated advantages of the WME (Web-based Mathematics Education) system and obtained positive feedback as well as suggestions from teachers and students. Based on the prototype site for Kimpton, an interdisciplinary team is developing a model WME site making it directly deployable in different schools....

Several factorization properties of Chebyshev are reported here. Studying the euclidean division of two Chebyshev, we observe that the remainder is either zero or (up to a sign) another Chebyshev polynomial. This lead to explicit computation of the greatest common divisor of two Chebyshev. We also obtain conditions for determining when a Chebyshev...

An ongoing project creates a Web-based mathematics education (WME) system by an innovative combination of standard Web technologies. WME delivers classroom-ready lessons that are well-prepared, interesting, effective, as well as interoperable. Lesson pages contain easy to use special-purpose manipulatives to help students understand and explore mat...

Assessment of student understanding and performance is important in education. Hence we are building a DMAD for our WME (Web-based mathematics education) system. DMAD consists of databases located at individual WME websites. Each local DMAD database collects assessment questions contributed by teachers to be shared with others. Teachers can search...

The Web-based mathematics education framework (WME) aims to create a Web for mathematics education. WME empowers mathematics teachers, learning content developers, as well as dynamic mathematics computation and education service providers, to deliver an unprecedented mathematics learning environment to students and educators. Main WME components in...

The Internet Accessible Mathematical Computation (IAMC) framework aims to make it easy to supply mathematical computing powers
over the Internet/Web. The protocol-based IAMC framework enables developers to create interoperable clients and servers easily
and independently. Presented are conceptual and experimental work on the IAMC framework architec...

One of the first to introduce Web design and programming in an integrated manner, this text covers visual communication design (VCD) and computer programming together. The text addresses style and coding of website development, and more importantly, their combination. (http://sofpower.com/wdp/main.html)

Reported is an approach for Web-based Mathematics Education (WME). The WME framework is a distributed system that aims to create a Web for mathematics education. Components of the WME framework include the Mathematics Education Markup Language (MeML) for page markup, regular Web servers to deliver pages, WME Page Processors to enable common Web bro...

The Mathematics Education Markup Language (MeML) is central to the Web-based Math- ematics Education (WME) (12) framework (see Figure 1) under investigation at ICM/Kent. Defined in XML syntax, MeML provides effective and expressive markup elements to repre- sent and structure mathematics education pages that may also contain XHTML and MathML (6) el...

An approach for Web-based Mathematics Education (WME) is considered. It aims to establish a framework to support authoring of dynamic and interactive mathematics education pages, end-user access through regular Web browsers, and supplying mathematical and educational capabilities through interoperable WME servers. The WME architecture we envision b...

ELIMINO is a new computer-mathematics research system developed to support Wu's method for computing characteristic sets of polynomials and other related operations. By implementing OMEI as its application programming interface, ELIMINO could make itself IAMC compliant, gain access to the graphical user interface Dragonfly locally and remotely, and...

Introduction 5 is a new symbolic computation system being developed at the Institute of Systems Science of the Chinese Academy of Sciences. Capabilities of ELIMINO include manipulation of multi-precision numbers and polynomials, computation of characteristic set in Wu's method , polynomial equation solving, geometric theorem proving, etc.. To make...

An approach for Web-based Mathematics Education (WME) is presented. WME aims to establish a framework to support authoring of dynamic and interactive mathematics educa- tion pages, end-user access through regular Web browsers, and interoperable back-end WME servers. The WME architecture builds on emerging Web standards, and defines an XML-based aut...

ECT NKBRSF G1998030609 AND 863 PROJECT 2001AA144030 + WORK REPORTED HEREIN HAS BEEN SUPPORTED IN PART BY THE NATIONAL SCIENCE FOUNDATION UNDER GRANT CCR-9721343 AND INT-9722919, AND IN PART BY THE OHIO BOARD OF REGENTS COMPUTER SCIENCE ENHANCEMENT FUNDS. can be made available on the Web/Internet by an IAMC server. Due to the vulnerabilities of pres...

PVM-ET is a set of tools to enhance the usage of PVM: initializing a new user, compiling applications, creating and distributing executables, reducing start-up times for applications, and otherwise managing apvm. A centralized #le organization and simpli#ed steps to setup a new user's PVM environment are also described. A Common Lisp to PVM interfa...

Introduction Polynomial factorization is one of the most striking successes of Symbolic Computation. Take a polynomial, f(x)over the integers Z, and ask a computer to factor it. The result, a list of irreducible factors, comes back within a few seconds, provided that the polynomial is not too big. Modern symbolic computation systems factor equally...

Two aspects of parallelism as related to symbolic computing are presented: (1) the implementation of parallel programs for the factorization of polynomials, and (2) the automatic derivation and generation of parallel codes for nite element analysis. The former illustrates the use of parallel programming to speed up symbolic manipulation. The latter...

The Internet Accessible Mathematical Computation (IAMC) framework aims to make it easy to supply mathematical computing powers over the Internet/Web. The Mathematical Computa- tion Protocol (MCP), the core part in the IAMC framework, enables developers to create interoper- able clients and servers easily and independently. Presented are the specica...

Internet Accessible Mathematical Computation (IAMC) is a distributed framework to supply mathematical computing powers over the Internet. Presented are conceptual and experimental work on the IAMC architecture, a client prototype (Dragonfly), client GUI, a server prototype (Starfish), the Mathematical Computation Protocol (MCP), mathematical data e...

Open Mathematical Engine Interface (OMEI) aims to establish a uniform application programming interface specification (API) for heterogeneous mathematical computation systems. OMEI can play an essential role in making mathematical engines easily accessible by front-ends, tools, and servers. The interface enables the development of individual applic...

Mathematical computing can become easily accessible on the Internet. The distributed Internet Accessible Mathematical Computation (IAMC) system can supply mathematical computing power widely through TCP/IP, the Web, or email. A key enabling technology for distributed and parallel mathematical computation is a standard protocol for exchanging mathem...

We present the details and some experimental results of our parallel implementation of the CS (Characteristic Sets) method under the environment of PVM and SACLIB. PVM is used for data conversion, task scheduling and inter-task communications. SACLIB is used for developing the basic algorithms of CS method. In our parallel implementation of the CS...

Introduction The Internet and the World-Wide Web make many kinds of information and services easily accessible. Ad-hoc methods have been used to make mathematical computing available on the Internet#Web. On SymbolicNet for example, one can #nd demonstrations of mathematical computations ranging from differentiation, integration, polynomial factoriz...

The text is a new edition of the C++/OOP book by the same author to cover the new ANSI/ISO Standard and to include other improvements. New Standard C++ features are integrated in a strong Object-Oriented approach for solving problems. The text keeps the same sound basic approach of the C++/OOP text which was rated best by ACM Computing Reviews: "Fo...

An approach to make mathematical computing easily accessible and conveniently usable on the Internet is reported. The distributed Internet Accessible Mathematical Computation (IAMC) system aims to supply mathematical computing powers widely through TCP/IP, the Web, or email. The overall IAMC architecture, a feasibility study, elements of the Mathem...

Mathematical computing can become easily accessible on the Internet. The dis- tributed Internet Accessible Mathematical Compu- tation (IAMC) system can supply mathematical computing power widely through TCP/IP, the Web, or email. A key enabling technology for distributed and parallel mathematical computation is a stan- dard protocol for exchanging...

. There are several advantages to providing communication links between independent scientific applications. Important problems to solve include data and control integration. Solving these problems separately is an essential aspect of the design and implementation of a protocol for mathematics. The Multi Protocol (MP) specification addresses the ex...

IAMC aims to make mathematical computation services easily accessible on the Internet. The IAMC design leverages existing technologies and makes it possible to access services through TCP#IP, the Web, or email. The overall IAMC architecture, the object-oriented design of a prototype IAMC client and server, as well as the initial speci#cation of the...

. Grobner Bases are certain finite sets of multivariate polynomials. Grobner Bases Algorithm is a technique that provides algorithmic solutions to a variety of problems in commutative algebra and algebraic geometry. In this introductory tutorial, the theory of Grobner Bases is discussed in details, algorithms for computing a Grobner basis are prese...

The complete factorization of Chebyshev polynomials, of the rst and sec-ond kind, into irreducible factors over the integers Z is described. Conditions are given for determining when a Chebyshev polynomial is divisible by another. And, if non-zero, the remainder is again a Chebyshev polynomial, up to a sign. Algorithms are also speciied to nd two i...

The Multi Project is an ongoing research effort at Kent State University aimed at providing an environment for distributed scientific computing. An integral part of this environment is the Multi Protocol (MP) which is designed to support efficient communication of mathematical data between scientifically-oriented software tools. MP exchanges data i...

PvmJobs is a general bag-of-jobs library for PVM that works with
any user created job structure in a master/slave paradigm. A master can
spawn slave processes, schedule and dispatch jobs to slaves, coordinate
and synchronize the activities. A slave process obtains a job from the
master, performs a set of prescribed tasks, returns results to the
mas...

PVM-based parallel/distributed computation tools have been
designed, implemented, and applied to two important mathematical
algorithms. The tools make PVM easier to use and applicable to a wider
class of computations. The application shows how advanced algebraic
algorithms can take advantage of modern parallel/distributed computing
with the aid of...

A set of software tools for connecting heterogeneous tasks on networked computers as well as MIMD prmllel machines is described. The purpose is to provide a convenient and practical approach to connect mathematical/scientific computing tasks, to build complex syetems by integrating exieting ones, and to perform parallel/distributed processing in sy...

Parallel Polynomial Operations 1 SMP-based parallel algorithms and implementations for polynomial factoring and GCD are overviewed. Topics include polynomial factoring modulo small primes, univariate and multivariate p-adic lifting, and reformulation of lift basis. Sparse polynomial GCD is also covered.

Parallel Virtual Machine (PVM) is a software package that integrates a heterogeneous network of computers to form a single parallel/concurrent computing facility [2]. PVM consists of two parts: a run-time server and a set of library functions. A user sets up a hostfile that lists the names of the hosts constituting the parallel virtual machine (pvm...

CL-PVM is a set of Common Lisp functions that interfaces Com-mon Lisp KCL, AKCL, or GCL to the C-based library of PVM. Generally, there is one CL interface function to each PVM C library function. The CL function calls its C-based counter part and relays data to and from the C function. This interface is complete and allows Lisp-based programs to t...

Chains of Recurrences (CR's) are introduced as an effective method to evaluate functions at regular intervals. Algebraic properties of CR's are examined and an algorithm that constructs a CR for a given function is explained. Finally, an implementation of the method in MAXIMA/Common Lisp is discussed. 1 Introduction Given a closed-form function G(x...

Consider any degree-n polynomial u(x) ∈ Z[x] that is square-free and an * an a0 ≠ 0. An efficient algorithm is given to test if u(x) is ring-ordinary. Let[EQUATION]

Automatic generation of sequential and parallel programs can bring the power of modern computers to more engineers and scientists. The project investigated parallel code generation and automatic derivation of parallel finite element routines. Software packages GENCRAY, a code translator producing Cray Fortran, and PIER, a finite element code deriva...

A priori bound for the size of coefficients of the desired factors is important for modern polynomial factoring algorithms. Experts have long suspected that the maximum coefficient size in a given polynomial, called the height, is a good heuristic bound. Developed are sufficient conditions under which the simple height bound is actually valid. Effi...

The Multi Protocol (MP) is designed for integrating symbolic, numeric, graphics, document processing, and other tools for scientific computation, into a single distributed problem-solving environment. MP is layered, reflecting the logically distinct aspects of tool integration. Data representation issues are addressed by specifying a set of basic d...

Reported are experiences and practical results from parallelizing the modular GCD algorithm for sparse multivariate polynomials. The strategy is to identify key computation steps in the sequential algorithm and implement them in parallel. The two major steps of the sequential algorithm—computing the GCD modulo several primes and applying the Chines...

In this paper we describe a coupled symbolic-numeric approach for solving PDE-based mathematical models on sequential and parallel computers. PIER, an experimental software system that we are developing, synthesizes F77 subroutines for finite element modeling directly from very-high level user input specifications. The system is being developed in...

A new coefficient bound is established for factoring univariate polynomials over the integers. Unlike an overall bound, the new bound limits the size of the coefficients of at least one irreducible factor of the given polynomial. The single-factor bound is derived from the weighted norm introduced in Beauzamy et al. (1990) and is almost optimal. Ef...

One way to combine the powers of symbolic computing with numeric computing is to automaticaly derive and produce numeric code. This approach has important applications in science and engineering. Once the desired formulas and procedures are derived in a symbolic manipulation system, they can be translated into a target numeric language by a code ge...

Parallelization of univariate p-adic lifting, a procedure important in modern gcd and factorization algorithms, is presented. The strategy is to take the fastest known sequential algorithm and parallelize its key steps: lift basis, residue, correction coefficients, updating factors, detecting true factors, and reformulation for continued lifting. B...

Symbolic computation is employed to automatically derive formulas in nite element analysis (FEA) and to generate parallel numeric code. Key FEA computations parallelized include ele- ment stiness computations and solution of global system of equations. An element-by-element preconditioned conjugate gradient method is used to solve the global system...

The research presented here is part of an effort to establish state-of-the-art factoring routines for polynomials. The foundation of such algorithms lies in the efficient factorization over a finite field GF(p k ). The Cantor-Zassenhaus algorithm together with innovative ideas suggested by others is compared with the Berlekamp algorithm. The studie...

Using parallelism afforded by shared-memory multiprocessors to speed up systems for polynomial factorization is discussed. The approach is to take the fastest known factoring algorithm for practical purposes and parallelize key parts of it. The univariate factoring algorithm consists of two major tasks (a) factoring modulo small integer primes and...

SIG is a compact graphics system for the display of curves and surfaces defined by mathematical formulas in a symbolic system. It is available from Kent State University. SIG consists of two parts: xgraph and mgraph that run as concurrent processes. Xgraph is a stand-alone graphics facility written in C to work with the X Window System. Mgraph is t...

Using parallelism afforded by shared-memory multiprocessors to speed up systems for polynomial factorization is discussed. The approach is to take the fastest known factoring algorithm for practical purposes and parallelize key parts of it. The univariate factoring algorithm consists of two major tasks (a) factoring modulo small integer primes and...

The design and implementation of a Scientific User Interface is presented. Written in the C language, SUI is a window-menu-mouse oriented graphical user interface that is designed to provide a modern and integrated computing environment for scientific work. SUI can serve multiple client systems in parallel including symbolic, numeric, graphics and...