Discrete Algebraic Structures - Lecture 6

Themen:

• Kombinationen
• Permutationen
• Mengentheoretische Partitionen

Computational Biology - Lecture 6

• Hidden Markov model

• Example: CpG islands.

Seminar: Constructive Algebraic Geometry

Topics:

• Functions on affine varieties
• rings of regular functions
• valuation rings and basic properties.

Discrete Algebraic Structures - Lecture 5

Themen:

• Überabzählbarkeit der Menge der reellen Zahlen
• Kontinuumshypothese
• Elementare Zählprinzipien
• Doppelte Abzählung, Inklusion-Exklusion
• k-Kombinationen von n, Binomialzahl.

Computational Biology - Lecture 5

Topics:

• General algebraic statistical models, DiaNA
• maximum likelihood estimation (MLE)
• fully observed toric Markov model
• fully observed Markov model, MLE.

Seminar. Constructive Algebraic Geometry

Topics:

• graded rings and homogeneous ideals
• graded modules and graded homomorphisms
• graded resolutions and Hilbert's syzygy theorem
• Hilbert function and Hilbert polynomial.

Discrete Algebraic Structures - Lecture 4

Themen:

• Permutationen vom Grad n, Zykeldarstellung, Signum
• vollständige Induktion
• Peano-Axiome, Aufbau der natürlichen Zahlen
• Abzählbarkeit
• 1. Diagonalisierungsmethode (Cantor).