Hiroshima University Syllabus

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Japanese
Academic Year 2022Year School/Graduate School School of Informatics and Data Science
Lecture Code KA101001 Subject Classification Specialized Education
Subject Name 離散数学I
Subject Name
(Katakana)
リサンスウガク1
Subject Name in
English
Discrete Mathematics I
Instructor IMAI KATSUNOBU
Instructor
(Katakana)
イマイ カツノブ
Campus Higashi-Hiroshima Semester/Term 1st-Year,  First Semester,  2Term
Days, Periods, and Classrooms (2T) Tues5-6,Thur5-6:ENG 219
Lesson Style Lecture Lesson Style
(More Details)
 
Lecture 
Credits 2.0 Class Hours/Week   Language of Instruction B : Japanese/English
Course Level 2 : Undergraduate Low-Intermediate
Course Area(Area) 25 : Science and Technology
Course Area(Discipline) 01 : Mathematics/Statistics
Eligible Students 1st-year (School of Informatics and Data Science), 2nd-year (Electrical, Electronic and Systems Engineering)
Keywords Logic, Set theory, Graph theory, Elementary number theory, Algebraic systems 
Special Subject for Teacher Education   Special Subject  
Class Status
within Educational
Program
 
Criterion referenced
Evaluation
Integrated Arts and Sciences
(Knowledge and Understanding)
・Knowledge and understanding of the importance and characteristics of each discipline and basic theoretical framework.
(Abilities and Skills)
・The ability and skills to specify necessary theories and methods for consideration of issues.

Program of Electrical,Systems and Information Engineering
(Abilities and Skills)
・Mathematical methods required for professionals in electrical,  systems, and information engineering.

Computer Science Program
(Abilities and Skills)
・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value.
・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis.

Data Science Program
(Abilities and Skills)
・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value.
・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis.

Intelligence Science Program
(Abilities and Skills)
・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value.
・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis. 
Class Objectives
/Class Outline
The purpose of this lecture is to understand the fundamentals of discrete mathematics used in the field of information science.  
Class Schedule lesson 1: Guidance, Fundamentals of formal logic (1) Logic puzzles and propositional logic
lesson 2: Fundamentals of formal logic (2) Propositional logic and Inference
lesson 3: Fundamentals of formal logic (3) Predicate logic
lesson 4: Set theory (1) Sets and Relations
lesson 5: Set theory (2) Equivalent Relations
lesson 6: Set theory (3) The Principle of Inclusion and Exclusion
lesson 7: Graph theory (1): Definitions and Graph Isomorphism
lesson 8: Graph theory (2): Adjacency Matrices and Trees
lesson 9: Graph theory (3): Net work
lesson 10: Elementary number theory (1) Prime Numbers and Indeterminate Equations
lesson 11: Elementary number theory (2) The Integers Modulo n
lesson 12: Elementary number theory (3) Fermat’ s Theorem
lesson 13: Elementary number theory (4) Euler’s Theorem and the RSA  Cryptosystem
lesson 14: Introduction to algebraic systems (1) Groups and Examples
lesson 15: Introduction to algebraic systems (2) Lagrange’s Theorem and its Applications

lesson 16: Final exam 
Text/Reference
Books,etc.
Text Book: Lecture notes (PDF) 
PC or AV used in
Class,etc.
 
(More Details) Lecture and web based materials including movies and documents (PDF) 
Learning techniques to be incorporated  
Suggestions on
Preparation and
Review
Students are advised to ruminate the new ideas apperae in each class. 
Requirements  
Grading Method The course unit is decided by exercises (40%), tests (30%) and the final exam (30%).  
Practical Experience  
Summary of Practical Experience and Class Contents based on it  
Message It does not assume much of high school math (especially Math III). Enjoy it in a new mood. 
Other   
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. 
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