Discrete Mathematics 2

Course title

L0007000

Course description

Following "Discrete Mathematics 1", students will acquire the mathematical concepts, notation, and reasoning necessary for computer Science. In particular, in this course, students will learn in detail about the concept of graphs, which are used in various fields of computer Science. The aim is to understand the basic concepts and properties of graph theory, and can construct simple proofs on your own.

Purpose of class

Computer Science is a study that deals with abstract things called information, and requires abstract notation and logical thinking among various subjects. By taking this subject following "Discrete Mathematics 1," students will be able to acquire the basic knowledge necessary to study the specialized subjects of this department.

Goals and objectives

The student understand basic concepts related to graphs and can explain them using examples.
The student understand proofs of basic properties of graphs and can explain them using concrete examples.
The student can construct proofs of simple properties of graphs (particularly those using contrarianism and mathematical induction) by oneself.

Relationship between 'Goals and Objectives' and 'Course Outcomes'

	Midterm exam	Final exam	Total.
1.	25%	25%	50%
2.	15%	15%	30%
3.	10%	10%	20%
Total.	50%	50%	-

Evaluation method and criteria

100 points are calculated from 50% of the midterm exam, exercises and reports, and 50% of the final exam, and a total score of 60 points or higher is considered passing.

The passing standard (60 points) is to be able to correctly execute "selection of basic concepts of graph theory" and "argument leading to a solution" for given problems.

Language

Japanese

Class schedule

	Class schedule	HW assignments (Including preparation and review of the class.)	Amount of Time Required
1.	Overview of graph theory：on graph theory, specific example of graph	Check the syllabus.	90minutes
2.	Basic concept (1)：vertex, edge, degree, isomorphic	Read section 4.1 of the textbook.	90minutes
2.	Basic concept (1)：vertex, edge, degree, isomorphic	Solve the relevant practice problems.	110minutes
3.	Basic concept (2)：regular graph, complete graph, subgraph	Read section 4.1 of the textbook.	90minutes
3.	Basic concept (2)：regular graph, complete graph, subgraph	Solve the relevant practice problems.	110minutes
4.	Path and Cycle（1）：path, cycle, simple path, basic path	Read section 4.2.1 of the textbook.	90minutes
4.	Path and Cycle（1）：path, cycle, simple path, basic path	Solve the relevant practice problems.	110minutes
5.	Path and Cycle（2）：Adjacency matrix, distance, eccentricity, diameter	Read section 4.2.1 of the textbook.	90minutes
5.		Solve the relevant practice problems.	110minutes
6.	Integrated problem practice（1）	Review lectures from 1st to 5th.	90minutes
6.	Integrated problem practice（1）	Solve the relevant practice problems.	100minutes
7.	Midterm exam and its explanation	Review lectures from 1st to 6th.	200minutes
8.	Connected graph（1）：　connected, connected component, properties of connected graphs	Read section 4.2.2 of the textbook.	90minutes
8.		Solve the relevant practice problems.	110minutes
9.	Connected graph（2）：cut vertex, cut edge, 2-connected graph	Read section 4.2.3 of the textbook.	90minutes
9.	Connected graph（2）：cut vertex, cut edge, 2-connected graph	Solve the relevant practice problems.	110minutes
10.	Tree（1）：forest, tree, properties of trees	Read section 4.3.6 of the textbook.	90minutes
10.	Tree（1）：forest, tree, properties of trees	Solve the relevant practice problems.	110minutes
11.	Tree（2）：rooted tree, subtree, n-ary tree	Read section 4.3.6 of the textbook.	90minutes
11.	Tree（2）：rooted tree, subtree, n-ary tree	Solve the relevant practice problems.	110minutes
12.	Digraph：definition of a digraph, degree, path and cycle, connectivity	Read section 3.4 of the textbook.	90minutes
12.		Solve the relevant practice problems.	110minutes
13.	Integrated problem practice（2）	Review lectures from 8th to 12th.	90minutes
13.	Integrated problem practice（2）	Solve the relevant practice problems.	100minutes
14.	Final exam and its explanation	Prepare for the final exam.	200minutes
Total.	-	-	2670minutes

Feedback on exams, assignments, etc.

ways of feedback	specific contents about "Other"
Feedback in the class

Textbooks and reference materials

Textbook：「離散数学入門」守屋悦朗著　サイエンス社

Prerequisites

It is desirable to have taken Discrete Mathematics 1.

Office hours and How to contact professors for questions

In the classroom after class.
In my office, during Tuesday 3rd period.
I also accept questions and consultations via email at any time.

Regionally-oriented

Non-regionally-oriented course

Development of social and professional independence

Course that cultivates an ability for utilizing knowledge

Active-learning course

N/A

Course by professor with work experience

Work experience	Work experience and relevance to the course content if applicable
N/A	Not applicable

Education related SDGs:the Sustainable Development Goals

4.QUALITY EDUCATION

Last modified : Thu Mar 06 10:01:23 JST 2025