Soveltava matematiikka (5 op)

Arviointiasteikko

H-5

Sisällön jaksotus

Fundamentals of logic
- Number theory
- Power series
- Fourier series
- On Fourier transformation

Tavoitteet

Opintojakson suoritettuaan opiskelija osaa
- soveltaa logiikan sääntöjä ja merkintöjä mm. ehtolauseissa ja matemaattisissa todistuksissa
- laskea ja soveltaa permutaatioita ja kombinaatioita
- soveltaa jaollisuuden ja kongruenssin käsitteitä ja ominaisuuksia
- laskea suppenevan geometrisen sarjan summan
- muodostaa funktioiden potenssisarjakehitelmiä ja soveltaa niitä numeerisessa laskemisessa
- laskea Fourier-sarjojen kertoimia matematiikkaohjelmien avulla

Sisältö

- logiikan perusteita
- kombinatoriikkaa
- lukuteoriaa
- potenssisarjoista
- Fourier-sarja
- Fourier-muunnoksesta

Oppimateriaalit

1. Discrete Mathematics and Its Applications, Kenneth H. Rose, Sixth Edition
2. Theory and Problems of Discrete Mathematics, Seymour Lipschutz, Marc Lars Lipson. Schaum’s Outline Series, Third Edition
3. Engineering Mathematics (6th edition), K.A. Stroud [MACMILLAN PRESS LTD]
4. Formula book: Technical formulas

Opetusmenetelmät

Teacher-directed classroom activities, group work and independent work; project work, reports, task-based (homework)

Pedagogiset toimintatavat ja kestävä kehitys

The contents of the course give understanding of the applied mathematics and help students to apply logical rules and notation in e.g. conditional expressions and mathematical proofs, compute and apply permutations and combinations, apply the concepts and properties of divisibility and congruence, calculate the sum of a converging infinite geometric series, find power series for a function and utilize them in numerical computation
and determine coefficients for Fourier-series expansions using mathematical computation tools.
The students will team up for a project work and writing reports on some current and relevant aspect of basic math, which gives everyone an opportunity to understand the topic; all students will develop their mathematical proficiency.
Task-based assessment supports learning and is continuous throughout the course. Studying in an international group develops students’ ability to intercultural communication and multicultural collaboration.

Opiskelijan ajankäyttö ja kuormitus

Classroom activities: Classroom activities participation 50 h
Homework: Working on homework sets 1-6. 30 h
Project work Research, presentation material, presentation 20h
Final exam: Preparing for the final exam 25 h

Arviointimenetelmät ja arvioinnin perusteet

Homework sets 1-6, 30 %, Total of thirty homework exercises based on reading material and classroom notes diagnostic/formative
self / teacher evaluation in connection with each homework set return session
Project work, reports,
presentations 40 %, Each outcome of the project work is assessed independently (assessment criteria is specified in Optima), peer feedback
summative teacher feedback at the end of the course
Final exam, 30 %, A written exam (1,5 hrs) on specified material Summative
teacher evaluation at the end of the course

Esitietovaatimukset

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

Lisätiedot

All practical information on timetables, project work, grading etc., as well as links to web materials are provided in Optima.