Discrete mathematics plays an important role in mathematical and computing sciences. The objective of this course is to provide the fundamentals of disctere mathematics.
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.
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
Intercultural skills | Communication skills | ✔ Specialist skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
The lectures provide the fundamentals of discrete mathematics.
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. |
Not specified.
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
By scores of reports.
None.