Print

2023　Discrete Mathematics

Font size  SML

Register update notification mail Add to favorite lecture list
Academic unit or major
Undergraduate major in Mathematical and Computing Science
Instructor(s)
Umehara Masaaki  Murofushi Toshiaki  Nishibata Shinya  Miura Hideyuki  Suzuki Sakie  Tsuchioka Shunsuke 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Mon7-8(W8E-308(W834))  Thr7-8(W8E-308(W834))  
Group
-
Course number
MCS.T331
Credits
2
Academic year
2023
Offered quarter
2Q
Syllabus updated
2023/3/20
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

Discrete mathematics plays an important role in mathematical and computing sciences. The objective of this course is to provide the fundamentals of discrete mathematics.

Student learning outcomes

The students are expected to understand the fundamentals of discrete mathematics appeared in mathematical and computing sciences and also to be able to apply them to practical problems.

Keywords

Euler characteristic, Four color problem, Euclidean Geometry to Modern Geometry, Partially ordered sets, Lattices, Formal Concept Analysis, Generating function, Integer partitions, Representation theory, Hyperbolic summation, Groebner basis, Experimental mathematics

Competencies that will be developed

✔ Specialist skills Intercultural skills Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

Class flow

The lectures provide the fundamentals of discrete mathematics.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Curvature and Euler characteristic Understand the contents covered by the lecture.
Class 2 Four color problem I Understand the contents covered by the lecture.
Class 3 Four color problem II Understand the contents covered by the lecture.
Class 4 Knots and invariants Understand the contents covered by the lecture.
Class 5 Jones polynomial Understand the contents covered by the lecture.
Class 6 The first half of volume 1 of Elements (The axiom of parallel lines, sum of interior angles of a triangle) Understand the contents covered by the lecture.
Class 7 The last half of volume 1 of Elements (Parallelogram, area, the Pythagorean theorem) Understand the contents covered by the lecture.
Class 8 Hyperbolic geometry as non-Euclidean geometry (Negation of parallel postulate, hyperbolic geometry） Understand the contents covered by the lecture.
Class 9 Partially ordered sets Understand the contents covered by the lecture.
Class 10 Lattices Understand the contents covered by the lecture.
Class 11 Formal Concept Analysis Understand the contents covered by the lecture.
Class 12 Integer partitions and Young diagrams Understand the contents covered by the lecture.
Class 13 Analytic combinatorics Understand the contents covered by the lecture.
Class 14 Modular forms Understand the contents covered by the lecture.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

Not specified.

Reference books, course materials, etc.

B. A. Davey & H. A. Priestley, “Introduction to Lattices and Order”, 2nd ed., Cambridge Univ. Press, 2002,
B. Ganter & R. Wille, “Formal Concept Analysis — Mathematical Foundations”, Springer, 1999
O. Suzuki, T. Murofushi, Formal Concept Analysis: Introduction, Support Software, and Applications,
Journal of Japan Society for Fuzzy Theory and Intelligent Informatics, vol. 19, no. 2 (2007) pp. 103-142.

Assessment criteria and methods

By scores of reports.

Related courses

  • MCS.T231 ： Algebra
  • MCS.T201 ： Set and Topology I
  • MCS.T202 ： Exercises in Set and Topology I

Prerequisites (i.e., required knowledge, skills, courses, etc.)

None.

Page Top