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2019　Discrete Mathematics

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Academic unit or major
Undergraduate major in Mathematical and Computing Science
Instructor(s)
Suzuki Sakie  Umehara Masaaki  Nishibata Shinya  Miura Hideyuki  Murofushi Toshiaki  Tsuchioka Shunsuke 
Class Format
Lecture     
Media-enhanced courses
Day/Period(Room No.)
Mon1-2(W833)  Thr1-2(W833)  
Group
-
Course number
MCS.T331
Credits
2
Academic year
2019
Offered quarter
2Q
Syllabus updated
2019/4/10
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 disctere 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, 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 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 5 The last half of volume 1 of Elements (Parallelogram, Area, The Pythagorean theorem) Understand the contents covered by the lecture.
Class 6 Euclidean Geometry to Modern Geometry （Hyperbolic Geometry，The Gauss-Bonnet Theorem） Understand the contents covered by the lecture.
Class 7 Lattices - Part 1 Understand the contents covered by the lecture.
Class 8 Lattieces - Part 2 Understand the contents covered by the lecture.
Class 9 Formal Concept Analysis Understand the contents covered by the lecture.
Class 10 Integer partitions and Young diagrams Understand the contents covered by the lecture.
Class 11 Generating functions and enumerative/analytic combinatorics Understand the contents covered by the lecture.
Class 12 Hyperbolic summation Understand the contents covered by the lecture.
Class 13 Groebner basis Understand the contents covered by the lecture.
Class 14 Experimental mathematics Understand the contents covered by the lecture.

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 Softwares, and Applications,
Journal of Japan Society for Fuzzy Theory and Intelligent Informatics, vol. 19, no. 2 (2007) pp. 103-142.
G.E.Andrews and K.Eriksson, Integer partitions, Cambridge University Press, 2004

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.

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