|
|
|
||
|
Inclusion-exclusion principle and its applications.
Generating functions.
Finite projective planes, latin squares.
Hall theorem and its applications.
Flows in digraphs.
k-connectivity of graphs.
Ramsey theory.
Last update: PANGRAC/MFF.CUNI.CZ (08.04.2010)
|
|
||
|
Irena Penev (Winter 2020/2021): To obtain tutorial credit, students must obtain at least 40% total on HW assignments. The lowest two HW scores will be dropped. To take the exam, students must first obtain tutorial credit. Last update: Penev Irena, Ph.D. (29.09.2020)
|
|
||
|
J. Matoušek, J. Nešetřil: Invitation to Discrete Mathematics, Oxford University Press (1998)
R. Diestel: Graph Theory (4th edition), Springer (2010) Last update: Jelínek Vít, doc. RNDr., Ph.D. (22.11.2012)
|
|
||
|
Irena Penev (Winter 2020/2021): To take the exam, students must first obtain tutorial credit. The exam will be written, and it will consist of problems similar to HW problems from the tutorial (English section). It will be possible to take the exam online (over Zoom). Depending on the COVID-19 situation, it may or may not be possible to take the exam in person at the Department. Last update: Penev Irena, Ph.D. (29.09.2020)
|
|
||
|
Double Counting: Sperner Theorem, The maximum number of edges in a graph without C4 and without K3. Number of spanning trees (determinant proof) and electrical networks. Generating functions (understood as Taylor series), applications: Catalan, Fibonacci numbers, solving recurrences, asymptotics of the solution. Finite projective planes. Error-correcting codes, basic properties. Hammnig code, Hadamard code. Existence of asymptotically good codes (Gilbert-Varshamov). Hamming's lower bound. Maximum matching in graphs, Hall's theorem and its applications (Birkhoff-von Neumann theorem), Tutte theorem. k-connectivity, Menger's theorem. Ear lemma, structure of 2-connected graphs. Ramsey theorem, Ramsey theorem for p-tuples, Ramsey infinite theorem. König's theorem on the infinite branch.
Course web page (Irena Penev, Winter 2020/2021): https://iuuk.mff.cuni.cz/~ipenev/NDMI011.html Last update: Jelínek Vít, doc. RNDr., Ph.D. (06.09.2023)
|