一個(gè)離散數(shù)學(xué)輔助教學(xué)軟件的設(shè)計(jì)與開發(fā)

周曉聰　趙清　謝揚(yáng)　周宇　喬海燕

摘? 要：離散數(shù)學(xué)是計(jì)算機(jī)專業(yè)的核心基礎(chǔ)課程，通常包括邏輯、證明、集合、關(guān)系、函數(shù)、組合計(jì)數(shù)、圖論和代數(shù)等多個(gè)模塊。一個(gè)能求解離散數(shù)學(xué)問題的計(jì)算機(jī)軟件對(duì)離散數(shù)學(xué)課程的教學(xué)和學(xué)習(xí)都有很好的輔助作用。本文使用面向?qū)ο蠓椒ㄔO(shè)計(jì)和開發(fā)了一個(gè)包含能求解邏輯、集合、組合計(jì)數(shù)、圖論與代數(shù)等離散數(shù)學(xué)課程模塊中問題的教學(xué)輔助軟件。該軟件不僅能展示離散數(shù)學(xué)問題求解的詳細(xì)過程，還能隨機(jī)生成問題供學(xué)生練習(xí)。對(duì)學(xué)生試用后的調(diào)查表明，該軟件對(duì)學(xué)生學(xué)習(xí)離散數(shù)學(xué)課程很有幫助，也有助于培養(yǎng)學(xué)生的計(jì)算思維。

關(guān)鍵詞：離散數(shù)學(xué);輔助教學(xué)軟件;面向?qū)ο笤O(shè)計(jì)

中圖分類號(hào)：TP31? ? ?文獻(xiàn)標(biāo)識(shí)碼：A

Design and Development of an Aided Instruction Software for Discrete Mathematics

ZHOU Xiaocong， ZHAO Qing， XIE Yang， ZHOU Yu， QIAO Haiyan

（School of Computer Science and Engineering， Sun Yat-Sen University， Guangzhou 510006， China）

isszxc@mail.sysu.edu.cn; zhaoq78@mail2.sysu.edu.cn; xiey233@mail2.sysu.edu.cn;

zhouy635@mail2.sysu.edu.cn; qiaohy@mail.sysu.edu.cn

Abstract： Discrete mathematics is a core basic course of computer majors， which usually includes multiple modules such as logic， proof， set， relation， function， combinatorial counting， graph theory and algebra. A computer software that can solve discrete mathematics problems motivates teaching and learning of discrete mathematics. By using object-oriented method， this paper proposes to design and develop an aided instruction software to solve problems in discrete mathematics course modules， such as logic， sets， combinatorial counting， graph theory and algebra. The proposed software can not only show the detailed process of solving problems， but also randomly generate instances of such problems for students to practice. Post-trial survey of students shows that the proposed software is helpful for students to learn discrete mathematics， and good for cultivating students' computational thinking as well.

Keywords： discrete mathematics; aided instruction software; object-oriented design

1? ?引言（Introduction）

離散數(shù)學(xué)是計(jì)算機(jī)專業(yè)的核心基礎(chǔ)課程，通常包括邏輯、證明、集合、關(guān)系、函數(shù)、組合計(jì)數(shù)、圖論和代數(shù)等多個(gè)模塊。離散數(shù)學(xué)課程的內(nèi)容抽象，概念眾多，教師希望能有很多可選的例子幫助講解相關(guān)內(nèi)容，學(xué)生也希望有更多的例子幫助理解和做更多的練習(xí)，但教材受篇幅所限通常不會(huì)提供太多的例題和習(xí)題，對(duì)于例題的求解過程有時(shí)也不會(huì)寫得非常詳細(xì)。教師自己想擬出更多例子時(shí)，卻由于思維的某種局限性，往往擬出的例子與已有例子非常相似，例子的復(fù)雜性和代表性都可能不夠。因此，一款能夠隨機(jī)生成例子并給出詳細(xì)求解過程的計(jì)算機(jī)軟件對(duì)離散數(shù)學(xué)課程的教學(xué)和學(xué)習(xí)都會(huì)非常有幫助[1]。……