- Profs: Ueli Maurer
- Website: https://crypto.ethz.ch/teaching/DM24/
- Exercises: https://dm.crypto.ethz.ch/
- Admin: Admin
- Material: Material
- Videos: Videos ETHZ
Discrete mathematics provides the mathematical foundations for computer science. It covers topics such as logic, set theory, functions, relations, and combinatorics. Students learn to apply these concepts to computer science problems, including proof techniques and the basics of graph theory, which are essential for understanding algorithms and data structures.
Lecture Notes
- 01 Intro and Statements
- 02 Propositional Logic and Formulas
- 03 Logical Equivalence, Tautological Implication and Modus Ponens
- 04 Quantifiers
- 05 Proof Types
- 06 Set Theory and Russels Paradox
- 07 Equality, Ordered Pairs, Cartesian Product, Power Set and Relationships
- 08 Relations, Compositions and Properties
- 09 Equivalency Relation and Classes, Partitions, Partially Ordered Sets
- 10 Posets, Hasse Diagrams, Lexicographical Ordering, Special Elements, Functions, Countability, Infinities
- 11 Functions, Relations, Cardinality, Countability, Cantor’s Diagonalization Argument
- 12 Cardinality, Number Theory, Rings, Euclidian Rings, Ideal, Congruence, Modular Arithmetic, Diophantine Equations
- 13 Modular Arithmetics, Set of Residues, Diffie-Hellman, Multiplicative Inverse, Chinese Remainder Theorem
- 14 Algebraic Structures and Operations, Monoids, Inverses, Groups, Group Properties, Landscape of Groups
- 15 Groups, Homomorphism, Isomorphism, Preservation of Identity and Inverses
- 16 Isomorphism, Powers, Order, Generators, Lagrange’s Theorem, Multiplicative Groups, Euler’s Totient Function, RSA
