“离散数学”教学的探讨与思考
“离散数学”教学的探讨与思考
文章编号:1672-5913(2009)10-0127-03
摘要:“离散数学”是计算机及相关专业的一门重要课程。该课程概念多、理论性强、高度抽象。在教学过程中,教师要强调课程的实用价值和重要性,引起学生足够的重视,在教学中注重反例的作用,做到一题多解,举一反三,注重特殊与一般相结合及时归纳与小结,提升教学质量。
关键词:离散数学;举一反三;启发式教学
中图分类号:G642
文献标识码:B
1引言
“离散数学”是计算机科学与技术专业的重要专业基础课程,在计算机科学中有着广泛的应用。它不仅是许多计算机专业课,如“数据结构”、“操作系统”、“编译原理”、“数据库原理”、“人工智能”、“数字逻辑”等的必备基础,也对培养学生抽象思维能力和逻辑推理能力起着重要作用。该课程由计算机科学与工程实践中所需要的数学理论和方法所组成,概念多、理论性强、高度抽象。学生在学习该课程时,往往看不到离散数学的知识在计算机科学中的具体应用,因而不仅不重视离散数学的学习,还怕学这门课程。因此如何提高离散数学课程的教学水平和质量,对学生后续课程的学习和毕业以后的科学研究和实践有重要意义。在离散数学的教学实践过程中,笔者积累了一些实际效果较好的做法,现提出供大家商榷。
2强调实用价值和重要性,引起学生足够重视
近年来,计算机学科的发展与离散数学的主要内容如数理逻辑、集合论和图论等都有非常紧密的联系。数理逻辑是研究推理的学科,在人工智能、数据库理论等的研究中有着重要的应用;图论和集合论为数据结构和数据表示理论奠定了数学基础,也为许多问题从算法角度加以解决提供了抽象和描述的重要方法。因此,在实际教学过程中,教师更应注重让学生了解离散数学在现实应用中的主要作用,有意识地引导学生运用所学理论分析和解决实际问题,从而让学生充分感受到这门课程的魅力和实用价值。例如在讲授平面图时,可以给出它们在印刷电路板、集成电路等方面的应用。
数理逻辑部分在计算机的硬件设计中应用非常突出,我们可以利用命题中各个联结词运算规律,把由高低电平表示的各信号之间的转换与二进制之间的运算连接起来,用数学方法解决电路设计的问题,使得整个设计过程更加系统化。很多学生在解决这样的问题时已经使用了离散数学知识,但并没有意识到自己使用了离散数学中的数理逻辑。针对这样的问题,教师在讲授课程过程中,一定要将每部分离散数学知识是怎样应用到计算机科学中说清楚,让学生充分认识到离散数学的重要性。
再如,在介绍图论中根树时,可将根树中求最优树的方法运用到计算机通讯中,以使信息在传输过程中既准确无误又节省二进制位。在讲解数理逻辑部分时,可以将真值表部分的内容运用到逻辑电路的设计上,在此基础上进一步启发学生运用这部分知识设计简单的表决器、抢答器等。这样不仅激发了学生学习离散数学的积极性,还进一步加强了学生理论联系实际的能力。
3一题多解,举一反三
离散数学具有多样性的特点,同一个概念可以给出不同的描述方法,例如,讲解二元关系的性质时给出如下定义:
设R为定义在集合A上的二元关系。
① 若 x(x A→
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