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, Partially ordered sets，Lattices, Formal Concept Analysis, Generating function, Integer partitions, Representation theory, Hyperbolic summation, Groebner basis, Experimental mathematics
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
The lectures provide the fundamentals of discrete mathematics.
Course schedule | Required learning | |
---|---|---|
Class 1 | The last half of volume 1 of Elements (Parallelogram, area, the Pythagorean theorem) | Understand the contents covered by the lecture. |
Class 2 | The last half of volume 1 of Elements (Parallelogram, area, the Pythagorean theorem) | Understand the contents covered by the lecture. |
Class 3 | Hyperbolic geomtry as non-Euclidean geometry (Negation of parallel postulate, hyperbolic geometry） | Understand the contents covered by the lecture. |
Class 4 | Projective geometry (Properties of figures preserving under the projections, Desargues's theorem, Pascal's theorem) | Understand the contents covered by the lecture. |
Class 5 | Geometry of Moebius strips (orientability of surfaces, Moebius strips as flat surfaces) | Understand the contents covered by the lecture. |
Class 6 | Preliminaries from logic, sets, and relations | Understand the contents covered by the lecture. |
Class 7 | Partially ordered sets | Understand the contents covered by the lecture. |
Class 8 | Lattices | 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 | Hypergeometric 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. |
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.
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.
By scores of reports.
None.