 강의 개요
이산수학(Discrete
Mathematics)이란 연속적성질을
갖는
대상과는 달리 이산적인 양 또는 이산구조를 갖는
대상에
대하여수학적으로 분류하고 정리하며, 논리적으로
사고하여
문제를 해결하는 여러 이론을 통틀어 다루는
학문을
말한다. 또,구체적이고 이산적인 여러 문제를
다루므로
Concrete Mathematics 라고도 한다.
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학습 목표
본
강좌에서는 이산수학의 여러 이론 중에서 전통적
조합론의 영역인 선택과
배열의 다양한 이론과 유한체이론
위에서의 유한평면기하학,
그래프이론, recursion,
알고리즘, 디자인과
초등암호이론, 최적화문제 등을 학습
함으로써 현대수학의
새로운 영역으로 여러 가지 중요한
응용을 갖고 있는
이산수학 또는 조합론의 기초를 익히고
동시에 다양한 내용을
공부하는 데 그 중점을 둔다. |
Course Perspective
Interests in computer science and the use of computer applications,
together with connections to many real-world situations, have helped
make topics of discrete mathematics more commonplace in school
and university curricula. A topic of widespread application
and interest is combinatorics,
the study of counting techniques. Enumeration, or counting,
may strike one as an obvious process that a student learns when
first studying arithmetic. But then, it seems, very little attention
is paid to further developments in counting as the student turns
to "more difficult" areas in mathematics, such as algebra,
geometry, trigonometry, and calculus. . . . Enumeration [however]
does not end with arithmetic. It also has applications in such areas
as coding theory, probability, and statistics (in mathematics) and
in the analysis of algorithms (in computer science). [Ralph P. Grimaldi,
in Discrete and Combinatorial Mathematics, 1994, p. 3]
Combinatorial Analysis is an area
of mathematics concerned with solving problems for which the number
of possibilities is finite (though possibly quite large). These
problems may be broken into three main categories: determining existence,
counting, and optimization. Sometimes it is not clear whether a
problem has a solution or not. This is a question of existence.
In other cases solutions are known to exist, but we want to know
how many there are. This is a counting problem. Or a solution may
be desired that is "best" in some sense. This is an optimization
problem. [John A. Dossey, Albert D. Otto, Lawrence E. Spence, &
Charles V. Eynden, in Discrete Mathematics, 1987, p. 1]
Current documents that support
the reform of school mathematics education suggest the need for
increased attention to topics in discrete mathematics as well as
in probability and statistics. The topic of combinatorics--counting--is
mentioned in the National Council of Teachers of Mathematics standards
documents and in the Mathematical Association of America's recommendations
for teacher preparation as a topic area worthy of study by middle
school and high school teachers.
This quarter, we will study
and apply combinatorial techniques in a variety of settings. In
doing so, we will make connections to algebra, probability, and
many other topics in mathematics. During the course, we may also
study the process of proof by induction, the use of recursion, and
the graph theory and knot theory and more.
Contact Information
Room 82-105 충북대학교 사범대학
Wednesday 3:00-5:00 pm
email: wkkim@cbucc.chungbuk.ac.kr
Course Requirements and Grading Scale
Problem Sets & Quizzes (20%)
These will be weekly assignments by webboard, and several
quizzes during the course.
Test (20%)
Three exams will be given during the course.
The test is tentatively scheduled for the mid week of the Quarter.
Final Examination (60%)
The test is scheduled for the last week of the
Quarter.
강의 일정
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