Osion kuvaus

  • Further materials


    All the lectures for this year's course will be on campus. However, I understand there may be some students who are unable to attend. For this purpose, you can find in this page last year's Zoom videos by Ragnar Freij-Hollanti, and his lecture slides (disc_slides.pdf below). In this year we will follow very closely same structure as Ragnar and we do not deviate from the material. The main addition to this year are the new lecture notes (see Materials), which are basically a modification of the slides below.

    Videos from last year. The videos follow roughly the following schedule (including references to Kenneth H. Rosen: Discrete mathematics and its applications):
    1: Sets (2.1-3,5 ; Slides 1-31)
    2: Formal logic (1.1-6 ; Slides 32-51)
    3: Proof methods (1.7-8, 5.1 ; Slides 52-67)
    4: Equivalence relations, partitions, partial orders (9.1,3,5,6 ; Slides 68-86)
    5. Functions and cardinalities (2.3,5 ; Slides 87-116)
    6: Enumerative combinatorics: multiplication rule, binomial coefficients (6.1-4 ; Slides 117-135)
    7: Enumerative combinatorics: inclusion-exclusion principle (8.5-6 ; Slides 136-155)
    8: Permutations and groups (Bogart 6.1 ; Slides 156-179)
    9: Graph theory: concepts (10.1-3, 11.1 ; Slides 180-205)
    10: Graph theory: algorithms (10.6,8, 11.4-5 ; Slides 206-225)
    11: Number theory: Divisibility and Diophantine equations (4.1-3 ; Slides 226-256)
    12: Number theory: Modular arithmetics and Fermat's little theorem (4.4-6 ; Slides 257-273)
    Bonus lecture: RSA cryptography (Slides 274-285)

    • Lecture slides by Ragnar Freij-Hollanti used in the videos (disc_slides.pdf below).

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