### MS-A0402 - Foundations of Discrete Mathematics, 01.03.2021-15.04.2021

Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.

#### LEARNING OUTCOMES

After passing the course the student
- understands the concept of proof and its necessity
- knows the basics of sets, functions, and relations
- has adopted the central mathematical notations
- masters the elements of combinatorics, the integers, modular arithmetic, and graph theory
- knows how to manipulate permutation groups

Credits: 5

Schedule: 01.03.2021 - 15.04.2021

Teacher in charge (valid 01.08.2020-31.07.2022): Ragnar Freij-Hollanti

Teacher in charge (applies in this implementation): Ragnar Freij-Hollanti

Contact information for the course (valid 25.01.2021-21.12.2112):

Lecturer and responsible teacher: Ragnar Freij-Hollanti, Y242b, ragnar.freij@aalto.fi,

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English

##### Content
• Valid 01.08.2020-31.07.2022:

logic, sets, functions, relations, combinatorics, induction and recursion, modular arithmetic, permutation groups and symmetry groups, graphs.

• Applies in this implementation:

• Set theory and formal logic
• Graph theory
• Enumerative combinatorics
• Permutations and symmetries
• Modular arithmetics

But more importantly:

• The elementary notions and techniques of mathematics (definition, theorem, proof, example...)

##### Assessment Methods and Criteria
• Valid 01.08.2020-31.07.2022:

lectures, exercises, midterm exams/final exam.

• Applies in this implementation:

The course can be completed in two different ways:

Alternative 1 (recommended):

Final exam (60%): Written, Thursday 15.4. 9:00-12:00, or Friday 4.6. 13:00-16:00.

Homework (40%): During the course, five homework sheets will be given (one per week, except the first week). Written solutions are handed in via MyCourses, after which you will evaluate the work of two other students. Points will be given both for your own solutions (8p per week) and for grading (2p per week). The four best results (out of five) are counted.

Alternative 2: Final exam (100%) Thursday 15.4. 9:00-12:00, or Friday 4.6. 13:00-16:00, or September (date to be decided).

Note thus, that homework counts towards the final grade only for the exams in April and June.

• Valid 01.08.2020-31.07.2022:

24+24 (4+4).

• Applies in this implementation:

Lectures (24 h)

Exercise sessions (24 h)

Reporting and grading homework (8-16 h)

Other self study (20-36 h)

Exam preparantion and participation (4-12 h)

#### DETAILS

##### Study Material
• Applies in this implementation:

Kenneth Rosen: Discrete Mathematics and its Applications.

Preparatory exercises: Published on the course homepage every Friday.

Tentative lecture slides: Published on the course homepage in advance of the course.

Annotated lecture slides: Published on the course homepage after each lecture.

##### Substitutes for Courses
• Valid 01.08.2020-31.07.2022:

Substitutes the course Mat-1.2991 Discrete mathematics.

Together with the course MS-A00XX Matrix algebra substitutes the course Mat-1.1110 or together with the course MS-A02XX Differential and integral calculus 2 substitutes the course Mat-1.1120.

Substitutes the courses MS-A04XX Foundations of discrete mathematics.

##### Prerequisites
• Valid 01.08.2020-31.07.2022:

high school mathematics

#### FURTHER INFORMATION

##### Details on the schedule
• Applies in this implementation:

First exercise sessions: 1.3. or 2.3.

Wednesdays and Thursdays 3.3.-8.4., 8:15-10:00 : Lectures. https://aalto.zoom.us/j/67216065161

Homework deadlines: Saturdays 13.3., 20.3., 27.3., 3.4., 10.4., 18:00.