General

  • General

    The course MS-A0402 is given in Period 4, starting with exercise sessions on Monday 24.2 and Tuesday 25.2.

    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.

    Welcome on board!

    Teachers:
    Ragnar Freij-Hollanti, Lecturer and responsible teacher
    Miika Leinonen, H01
    Laura Jakobsson, H02 and head assistant
    Antti Immonen, H03

    Course evaluation: 

    There will be an online quiz that can be taken at any point during the exam week (6.-10.4.). You can get the grade "PASS" if you satisfy one of the following:

    • You get a total of at least 18 points (out of 30) on the homeworks AND 50% of the points on the quiz.
    • or You get at least 75% of the points on the quiz.


    A numerical grade (1-5) can be obtained in two different ways. The one that gives a student the better grade is automatically chosen for that student. You can only get a numerical grade after writing a final exam. At the time of writing, it is not clear when this will be organized the next time.
    • Homework + final exam. In this case, the best four (out of five) homework scores are counted, and account together for 40% of the grade. The remaining 60% is determined by the final exam. Homeworks are reported in writing, and graded in the second exercise session of each week. To get points from the homework, it is thus necessary to participate in the exercise sessions. by a fellow student via MyCourses.
    • Course exam. In this case, the exam result directly determines the grade.

    Lectures are given in Hall D, Wednesdays and Thursdays 8:15-10:00

    Tentative schedule, including references to the book: (Subject to change. The schedule is updated as the course goes on)

    26.2. Sets (Hammack 1, Slides 1-31)
    27.2. Formal logic (Hammack 2, Slides 32-48)
    4.3. Proof techniques and relations (Hammack 11, Slides 49-66)
    5.3. Equivalence relations and partial orders (Rosen 9.5-6, Slides 67-82)
    11.3. Functions and cardinalities (Rosen 2.3,5, Slides 83-108)
    12.3. Enumerative combinatorics (Rosen 6.1-4, Slides 109-128)
    18.3. Inclusion/exclusion (Rosen 8.5-6, Slides 129-152, 179-184)
    19.3. Permutations (Bogart 6.1, Slides 153-170)
    25.3. Graphs and adjacency matrices (Rosen 10.2-3, Slides 171-178, 185-200)
    26.3. Graph colourings and algorithms (Rosen 10.2-3, Slides 201-220)
    1.4. Divisibility and Diophantine equations (Rosen 4.1,3, Slides 221-243)
    2.4. Modular arithmetic (Rosen 4.4-6)


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