Information Mathematics Ⅱ

Course Information

College	Tsuyama College	Year	2024
Course Title	Information Mathematics Ⅱ
Course Code	0074	Course Category	Specialized / Compulsory
Class Format	Lecture	Credits	School Credit: 1
Department	Department of Computer and Information Engineering	Student Grade	5th
Term	Second Semester	Classes per Week	2
Textbook and/or Teaching Materials	Textbooks : Material on Teams(LMS), Reference books : Seymour Lipschutz etal., "Schaum’s outline of Theory and Problems of Discrete mathematics, 3rd Ed."（McGraw-Hill）, IBARAKI Toshihide,"Discrete Mathematics for AI era(Japanese)"(Ohmusha)
Instructor	FANG Guanshen

Course Objectives

Learning purposes :
The purposes of this course are understanding the basic notion of sets, functions, properties of integers, logic, graph theory, automata, and formal language as the theoretical basis of information engineering.

Course Objectives :
1. To understand the basic concept of a set and can execute operations of a set.
2. To be able to explain basic concept of a function.
3. To be able to explain basic concept of information theory.
4. To be able to explain basic concept of logical algebra and predicate logic.
5. To be able to explain basic concept of graph theory.
6. To be able to explain basic concept of automata and formal language.

Rubric

	Excellent	Good	Acceptable	Not acceptable
Achievement 1	The students understand basic concept of set, and can execute set operation and calculate cardinality of set using inclusion-exclusion principle.	The students understand basic concept of set, and can execute set operation and calculate cardinality of set.	The students understand basic concept of set and can execute set operation.	The students do not understand basic concept of set, nor can execute set operation.
Achievement 2	The students can explain correspondence and basic concept of function and prove some theorems using these concepts.	The students can explain correspondence and basic concept of function and prove bijection of set using these notion.	For given function, the students can judge whether the function is surjective or injective or neither.	For given function, the students cannot judge whether the function is surjective or injective or neither.
Achievement 3	The students can explain basic notion of information theory and prove simple theorems.	The students can explain basic notion of information theory.	The students can explain entropy.	The students can not explain entropy.
Achievement 4	The student can explain basic notion of logical algebra and predicate logic and use them daily life.	The student can explain basic notion of logical algebra and predicate logic.	The student can explain basic notion of logical algebra.	The student can not explain basic notion of logical algebra.
Achievement 5	The student can explain basic notion of graph theory and prove simple theorem. They can also model problem on graph.	The student can explain basic notion of graph theory and prove simple theorem.	The student can explain basic notion of graph theory.	The student can not explain basic notion of graph theory.
Achievement 6	The student can explain basic notion of automata and formal language and prove simple theorem.	The student can explain basic notion of automata and formal language and make state transition diagram.	The student can explain basic notion of automata and formal language.	The student can not explain basic notion of automata and formal language

Teaching Method

Outline:

※Relationship with practice: This course is provided by a teacher who worked at another institute (IMAI Quantum Computation and Information Project and Quantum Computation and Information Project Solution Oriented Research for Science and Technology. The purpose of this course is to use teacher's experience in understanding the basic idea of information theory as the basis of information engineering. This course is given in lecture format.

General or Specialized : Specialized
Foundational academic disciplines : Integrated Disciplines/Informatics/Principles of Informatics
Field of learning : Infromation system・Programming・Network
Relationship with Educational Objectives :This class is equivalent to "(3) Acquire deep foundation knowledge of the major subject area".

MCC Goals(Based on the guidelie 4/28/2017 version, number in brackets is MCC level)： V-D-7 Information mathematics・Information theory/Discrete mathematics(4), Applied discrete mathematics(4), Information theory(4).

Relationship with JABEE programs :
The main goal of learning / education in this class are "A A-1" also "A-2" is involved.

Course outline :
This course provides understanding theoretical basis of information engeering, through leraningbasic mathematics concerned with information engineering. This course deal with discrete mathematics mainly.

Style:

Course method :
1: Lectures is given using textbooks and prints.
2: Lectures repeat cycle of presentation of teacher and exercises. Imposing assignment submissions as appropriate.
3: Publish of materials of lecture and assign assignments through Teams,.

Grade evaluation method :
1: Evaluation is based on 2 times' examinations, and submissions(20%). As a general, retaking exams can not performed.
2: Bringing textbook and notebook at examination is not permitted but depending on the situation.
3: Assignment submissions will be imposed during class and during long vacations.
Generally, re-examination will not be conducted.

Notice:

Precautions on the enrollment : English is used in classrooom mainly.

Course advice :
1: Prepare and review the content before and after every lecture.
2: Submit every answer or report .
3: Most of the contents are basic and many exercises appear on textbook. Since all exercise may not solve in classroom from a temporal restriction, the students should solve them by themselves after lecture.

Foundational subjects : Mathematical Information(4th year)

Attendance advice :
1:Attendance is confirmed before every lecture. Three times of late is counted as 1 hour's absence.
2: Submit absentee notice or official absenteeism notice.
3: Make sure the answers or reports are submitted in time.

Characteristics of Class / Division in Learning

Aided by ICT

Applicable to Remote Class

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Course Plan

			Theme	Goals
2nd Semester
	3rd Quarter
		1st	Guidance
		2nd	Set theory	Understand set theory, carry out calculation of set.
		3rd	Logic and propositional calculus	Understand logic and propositional calculus, judge the truth value using truth table.
		4th	Relations	Understand relations among sets, prove the equivalence relation.
		5th	Function and algorithm	Understand function and algorithm, deeply understand the feature of bijection.
		6th	Graph theory	Deeply understand graph, understand the application of Discrete Mathematics in design of algorithm.
		7th	Directed graphs	Deeply understand directed graphs, and its difference with graphs.
		8th	mid-term exam
	4th Quarter
		9th	Return and explaination of mid-term exam
		10th	Binary trees	Deeply understand at least one algorithm using binary trees.
		11th	Languages, automata	Deeply understand Pump lemma, understand the application of Discrete Mathematics in design of algorithm.
		12th	Finite state machine and Turing machines	Understand and draw state transition diagram. Understand the application of Discrete Mathematics in design of algorithm.
		13th	Information theory 1	Understand information entropy and information compression.
		14th	Information theory 2	Understand channel coding.
		15th	Final exam
		16th	Return and explaination of final exam

Evaluation Method and Weight (%)

	Examination	Presentation	Mutual Evaluations between students	Behavior	Portfolio	Other	Total
Subtotal	80	0	0	0	20	0	100
Basic Proficiency	0	0	0	0	0	0	0
Specialized Proficiency	80	0	0	0	20	0	100
Cross Area Proficiency	0	0	0	0	0	0	0