Soveltava matematiikka (5op)

Arviointiasteikko

H-5

Sisällön jaksotus

PART1
1. Logic
2. Combinatorics
3. Permutations
4. Combinations
5. Divisibility
6. Euclidean algorithm
7. Congruence
8. Residue class ring
9. Hash functions and RSA
PART 2
10. Sequence
11. Sum
12. Series
13. Recursive equation
14. Graph theory

Tavoitteet

Opintojakson suoritettuaan opiskelija osaa
- soveltaa logiikan sääntöjä ja merkintöjä
- laskea ja soveltaa permutaatioita ja kombinaatioita
- soveltaa jaollisuuden ja kongruenssin käsitteitä ja ominaisuuksia
- käsitellä aritmeettisia ja geometrisia lukujonoja ja summia
- laskea suppenevan geometrisen sarjan summan
- muodostaa Taylorin polynomeja ja soveltaa niitä numeerisessa laskemisessa
- laskea Fourier-sarjojen kertoimia matematiikkaohjelmien avulla

Sisältö

- Logiikan perusteita
- Lukuteorian perusteita ja sovelluksia
- Kombinatoriikan perusteita ja sovelluksia
- Lukujono ja sarja
- Taylorin sarja
- Fourier-sarja

Oppimateriaalit

All course materials will be published in Itslearning.

Opetusmenetelmät

Part 1, Logic, combinatorics and number theory:
lectures, homework, self-study, exam

Part 2, Sequences and series:
lectures, MATLAB exercises, homework sessions, self-study, exam

Tenttien ajankohdat ja uusintamahdollisuudet

Assessment Schedule

Midterm Exam – Part 1: 28 October 2025
First Retake: 4 November 2025

Midterm Exam – Part 2: 16 December 2025
First Retake: (Date listed as 2025 — please verify and update if needed)

Final Retake Exam (for both parts): 13 January 2026
Exact times for all exams will be published in the official schedule.

Important:
Homework and exercises must be submitted by the specified deadlines. Late submissions will not be accepted, and there are no options to make up or retake missed tasks.

Opiskelijan ajankäyttö ja kuormitus

Part 1:
Intro 1h
Lectures 9*2h
Exam 2h
Self-study (homework, preparing for exams etc.) ~46h.

Part 2:
Lectures 5*2h
Homework sessions 5*2h (Mandatory attendance)
Exam 2h
Self-study (homework, preparing for exams etc.) ~46h.

Arviointimenetelmät ja arvioinnin perusteet

Achieve at least 50% of the points in both Midterm exams or retakes.
Submit at least 30% of the exercises is mandatory to pass the course.


Additional points from homework will improve your grade.

Hylätty (0)

Less than 50% of the points in one or both of the Midterm exams or retakes.

Unauthorized non-attendance exceeds 30% of homework sessions.

The student has not demonstrated sufficient achievement of the course learning objectives. They recognize and apply only a limited number of course concepts and lack the necessary skills to implement them effectively.

Additionally, the course will be failed if any instance of academic misconduct is detected. The first occurrence—whether misconduct or an attempt—will result in the rejection of the affected exam or assignment. A second offense will lead to failure of the entire course.

Arviointikriteerit, tyydyttävä (1-2)

Student has demonstrated having achieved the learning objectives of the course on satisfactory level. They recognize and can to some extent use most of the concepts of the course topics.

Arviointikriteerit, hyvä (3-4)

Student has demonstrated having achieved the learning objectives of the course well.
They recognize and can use most of the concepts of the course topics, and are able to apply them on various study and work contexts.

Arviointikriteerit, kiitettävä (5)

Student has demonstrated having achieved the learning objectives of the course on excellent level. They master the concepts of the course topics, and are able to fluently apply them on study and work contexts.

Esitietovaatimukset

Tieto- ja viestintätekniikan koulutuksen edeltävät matematiikan opintojaksot (tai vastaavat tiedot ja taidot):
Insinöörimatematiikan perusteet
Calculus

Lisätiedot

Itslearning and email