Discrete Mathematics is the mathematics of finite and countable structures, or loosely speaking the mathematics of sets where there is no notion of "convergence". Methods from discrete mathematics play a large role in many other subjects, in particular in computer engineering and data science.
In this course we cover the foundations of discrete mathematics (graphs, enumeration, modular arithmetic) as well as as the foundations of all mathematics on university level (set logic and proof techniques). We also study some modern applications of the theory, in cryptography and networks theory.
The course is suitable for all Aalto students; no other prerequisites than high school mathematics are necessary.
Tentative schedule, including references to the book: (Subject to change. The schedule is updated as the course goes on)
27.2. Sets (Hammack 1) (slides: 1-30)
28.2. Formal logic (Hammack 2) (slides: 31-48)
6.3. Relations (Hammack 11) (slides: 49-71)
7.3. Functions and cardinalities (Hammack 12, 13) (slides: 72-91)
13.3. Graphs and graph isomorphisms (Rosen 10.2-3) (slides: 92-114)
14.3. Paths and circuits (Rosen 10.4-5) (slides: 115-135)
20.3. Planar graphs and graph colorings (Rosen 10.7-8) (slides: 136-152)
21.3. Combinatorics (Hammack 3.1-5) (slides: 153-177)
27.3. Combinatorics (Hammack 3.1-5) (slides: 178-200)
28.3. Diophantine equations (slides: 201-221)
3.4. Modular arithmetic (slides: 222-238)
4.4. Repetition and curiosities (slides: 239-246)
Ragnar Freij-Hollanti, Lectures and responsible teacher
Jaakko Visti, H01
Anton Vavilov, H02
Matthias Grezet, H03 and head assistant
Richard Hammack: Book of Proof.
Oscar Levin: Discrete Mathematics, an Open Introduction.
Kenneth Rosen: Discrete Mathematics and its Applications.
Explorative exercises, homework exercises, and slides updated weekly on the course homepage under Materials.