Study Guide

Objective

After completing the course the student can
- apply logical rules and notation
- compute and apply permutations and combinations
- apply the concepts and properties of divisibility and congruence
- process arithmetic and geometric sequences and sums
- calculate the sum of a converging infinite geometric series
- form Taylor polynomials and utilize them in numerical computation
- determine coefficients for Fourier-series expansions using mathematical computation tools

Content

- Fundamentals of logic
- Basics od number theory with applications
- Basics of combinatorics with applications
- Sequences and series
- Taylor series
- Fourier series

Materials

Lecture notes, homework and MATLAB exercises will be published in Itslearning.

Teaching methods

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

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

Exam schedules

Midterm exam, on Part 1 on week 7, retake on week 9.
Midterm exam, part 2 on week 15, retakes on week 16. Exact dates and times in the schedule.

Note. Homework and exercises must be submitted in time, there is no way to complement or "retake" them later.

Student workload

Lessons 46 h
Exams + preparing for them 20 h
Self-study (homework, installing and learning Matlab etc.) 70 h so approx. 6 h per week.

Content scheduling

Spring semester 2024, according to the schedule.
Part 1, weeks 2-9
Part 2, weeks 10-16

Further information

We use MATLAB, for which TUAS has a campus licence. You can to download it to your own device or use MATLAB online.

Taking the self-study course MATLAB Basics for ICT is highly recommended prior to the start of Sequences and Series part (Part 2).

Evaluation scale

H-5

Assessment methods and criteria

Submit in time at least 25 % of the homework/exercises for both modules.

Active participation in classroom and exercise sessions (at least 75 % attendance for both modules).

Achieve at least 6/15 points in both Midterm exams or retakes.

Assessment criteria, fail (0)

Less than 25 % of homework exercises submitted in time.
More than 25 % (unauthorized) non-attendance from lectures and exercise sessions.
Less than 6/15 points in one or both of the Midterm exams or retakes.

Student has not demonstrated achieving the learning objectives of the course. They recognize and can use only few of the concepts of the course topics, and show no skills to apply them.

Assessment criteria, satisfactory (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.

Assessment criteria, good (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.

Assessment criteria, excellent (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.

Qualifications

Previous mathematics courses of ICT engineering curriculum (or equivalent skills):
Introduction to Engineering Mathematics
Calculus

Objective

After completing the course the student can
- apply logical rules and notation
- compute and apply permutations and combinations
- apply the concepts and properties of divisibility and congruence
- process arithmetic and geometric sequences and sums
- calculate the sum of a converging infinite geometric series
- form Taylor polynomials and utilize them in numerical computation
- determine coefficients for Fourier-series expansions using mathematical computation tools

Content

- Fundamentals of logic
- Basics od number theory with applications
- Basics of combinatorics with applications
- Sequences and series
- Taylor series
- Fourier series

Materials

Itslearning-sivulta löytyvät:
Luentomuistiinpanot
Laskuharjoitusten tehtävät
MATLAB-ohjeet

Teaching methods

Luennot
Laskuharjoitukset
Kokeet

Exam schedules

Tietotekniikan matematiikka:
- Osakoe
- Puolivälissä kurssia (Helmi-Maaliskuun vaihde)

Sarjat:
- Osakoe
- Huhtikuun lopulla

Uusinta:
- Toukokuussa
- Voi tehdä jomman kumman osakokeista

Student workload

Tietotekninen matematiikka:
10*2h tietotekniikan matematiikan luennot
5*2h laskuharjoitukset
2h tietotekninen matematiikka -koe

Sarjat:
5*2h sarjat-luennot
5*2h Matlab harjoitukset. Matlab harjoituksissa on läsnäolo pakko
2h sarjat -koe

loppu opiskelijan itsenäistä opiskelua

Content scheduling

Tammikuu-Helmikuu, tietotekniikan matematiikka:
- Logiikka
- Kombinatoriikka; yhteenlasku/kertolaskusääntö, permutaatiot, kombinaatiot
- Kombinatoriikan sovelluksia todennäköisyyslaskentaan
- Lukuteoria: alkuluvut, syt/pym, Eukleideen algoritmi, kongruenssi/modulolaskenta, hajautusfunktiot, jäännösluokkarengas, RSA-algoritmi


Maaliskuu-Huhtikuu, sarjat:
- Lukujonot, aritmeettinen ja geometrinen lukujono, lukujonon raja-arvo
- Lukujonon summat, aritmeettinen ja geometrinen summa
- Sarjat, geometrinen sarja ja suppeneminen
- Taylorin sarja
- Fourierin sarja
- Fourierin muunnos

Evaluation scale

H-5

Assessment methods and criteria

Osakokeista täytyy saada tietty määrä pisteitä päästäkseen läpi.
Laskuharjoituksista saatavat pisteet parantavat arvosanaa
Sarjat osion laskuharjoituksissa on läsnäolopakko.
Arvosanataulukko löytyy Itslearning-sivulta.

Qualifications

Previous mathematics courses of ICT engineering curriculum (or equivalent skills):
Introduction to Engineering Mathematics
Calculus

Objective

After completing the course the student can
- apply logical rules and notation
- compute and apply permutations and combinations
- apply the concepts and properties of divisibility and congruence
- process arithmetic and geometric sequences and sums
- calculate the sum of a converging infinite geometric series
- form Taylor polynomials and utilize them in numerical computation
- determine coefficients for Fourier-series expansions using mathematical computation tools

Content

- Fundamentals of logic
- Basics od number theory with applications
- Basics of combinatorics with applications
- Sequences and series
- Taylor series
- Fourier series

Materials

ITSL-sivulta löytyvät:
Luentomuistiinpanot
Laskuharjoitusten tehtävät ja mallivastaukset
MATLAB-ohjeet
Harjoituskoe

Teaching methods

Luennot
Laskuharjoitukset
Kokeet
Vapaaehtoinen harjoitustyö

Exam schedules

Sarjat:
Osakoe ennen syyslomaa ja uusinta sen jälkeen.
Tietotekniikan matematiikka:
Osakoe ja sen uusinta ennen joululomaa

Lopullinen uusinta seuraavan vuoden tammikuussa:
voi tehdä jomman kumman tai kummatkin osakokeista

Completion alternatives

Pelkät osakokeet ilman pisteitä laskuharjoituksista (sarjat tehtävistä 25 kpl pakollisia)
Vapaaehtoinen harjoitustyö, + 2op

Student workload

5*2h sarjat-luennot, joissa yhteensä 50 kpl tehtäviä
10*2h tietotekniikan matematiikan luennot
5*1h laskuharjoitukset, joissa yhteensä 50 kpl tehtäviä
2*2h kokeet
loppu opiskelijan itsenäistä opiskelua
vapaaehtoinen harjoitustyö, + 2op

Content scheduling

Syyskuu-lokakuu, sarjat:
- Lukujonot, aritmeettinen ja geometrinen lukujono, lukujonon raja-arvo
- Lukujonon summat, aritmeettinen ja geometrinen summa
- Sarjat, geometrinen sarja ja suppeneminen
- Taylorin sarja
- Fourierin sarja
- Fourierin muunnos (vapaaehtoinen)

Lokakuu-joulukuu, tietotekniikan matematiikka:
- Logiikka
- Kombinatoriikka; yhteenlasku/kertolaskusääntö, permutaatiot, kombinaatiot
- Kombinatoriikan sovelluksia todennäköisyyslaskentaan
- Lukuteoria: alkuluvut, syt/pym, Eukleideen algoritmi, kongruenssi/modulolaskenta, hajautusfunktiot, jäännösluokkarengas, RSA-algoritmi

Further information

Sähköposti.

Evaluation scale

H-5

Assessment methods and criteria

Osakokeista täytyy saada tietty määrä pisteitä päästäkseen läpi.
Laskuharjoituksista saatavat lisäpisteet parantavat arvosanaa (sarjat tehtävistä 25 kpl pakollisia)
Arvosanataulukko löytyy ITSL-sivulta.

Assessment criteria, fail (0)

Ei tarpeeksi pisteitä kokeista.

Assessment criteria, satisfactory (1-2)

Arvosanataulukko löytyy ITSL-sivulta.

Assessment criteria, good (3-4)

Arvosanataulukko löytyy ITSL-sivulta.

Assessment criteria, excellent (5)

Arvosanataulukko löytyy ITSL-sivulta.

Qualifications

Previous mathematics courses of ICT engineering curriculum (or equivalent skills):
Introduction to Engineering Mathematics
Calculus

Objective

After completing the course the student can
- apply logical rules and notation
- compute and apply permutations and combinations
- apply the concepts and properties of divisibility and congruence
- process arithmetic and geometric sequences and sums
- calculate the sum of a converging infinite geometric series
- form Taylor polynomials and utilize them in numerical computation
- determine coefficients for Fourier-series expansions using mathematical computation tools

Content

- Fundamentals of logic
- Basics od number theory with applications
- Basics of combinatorics with applications
- Sequences and series
- Taylor series
- Fourier series

Materials

Lecture notes, homework and MATLAB exercises will be published in Itslearning.

Teaching methods

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

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

Exam schedules

Midterm exam, on Part 1 on week 41, retake on week 43.
Midterm exam, part 2 on week 49, retakes on week 50. Exact dates and times in the schedule.

Note. Homework and exercises must be submitted in time, there is no way to complement or "retake" them later.

Student workload

Lessons 46 h
Exams + preparing for them 20 h
Self-study (homework, installing and learning Matlab etc.) 70 h so approx. 6 h per week.

Content scheduling

Fall semester 2023, according to the schedule.
Part 1, weeks 36-41
Part 2, weeks 43-50

Further information

We use MATLAB, for which TUAS has a campus licence. You'll need to download it to your laptops.

Taking the self-study course MATLAB Basics for ICT is highly recommended prior to the start of Sequences and Series part (Part 2).

Evaluation scale

H-5

Assessment methods and criteria

Submit in time at least 25 % of the homework/exercises for both modules.

Active participation in classroom and exercise sessions (at least 75 % attendance for both modules).

Achieve at least 6/15 points in both Midterm exams or retakes.

Assessment criteria, fail (0)

Less than 25 % of homework exercises submitted in time.
More than 25 % (unauthorized) non-attendance from lectures and exercise sessions.
Less than 6/15 points in one or both of the Midterm exams or retakes.

Student has not demonstrated achieving the learning objectives of the course. They recognize and can use only few of the concepts of the course topics, and show no skills to apply them.

Assessment criteria, satisfactory (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.

Assessment criteria, good (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.

Assessment criteria, excellent (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.

Qualifications

Previous mathematics courses of ICT engineering curriculum (or equivalent skills):
Introduction to Engineering Mathematics
Calculus

Objective

After completing the course the student can
- apply logical rules and notation
- compute and apply permutations and combinations
- apply the concepts and properties of divisibility and congruence
- process arithmetic and geometric sequences and sums
- calculate the sum of a converging infinite geometric series
- form Taylor polynomials and utilize them in numerical computation
- determine coefficients for Fourier-series expansions using mathematical computation tools

Content

- Fundamentals of logic
- Basics od number theory with applications
- Basics of combinatorics with applications
- Sequences and series
- Taylor series
- Fourier series

Materials

Lecture notes, homework and MATLAB exercises will be published in Itslearning.

Teaching methods

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

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

Exam schedules

Midterm exam, part 1 on week 7, retake on week 9. Midterm exam, part 2 on week 16, retakes on week 17. Exact dates and times in the schedule.

Note. Homework and exercises must be returned in time, there is no way to complement or "retake" them later.

Student workload

Lessons 49 h
Exams + preparing for them 26 h
Self-study (homework, Matlab etc.) 60 h so approx. 5 h per week.

Content scheduling

Spring 2023, according to the schedule.

Further information

We will use MATLAB, for which TUAS has a campus licence. You'll need to download it to your laptops.

Taking the self-study course MATLAB Basics for ICT is highly recommended prior to the start of Sequences and Series part.

Evaluation scale

H-5

Assessment methods and criteria

Submit in time at least 25 % of the homework/exercises for both modules.

Active participation in classroom and exercise sessions (at least 80 % attendance).

Achieve at least 6/15 points in both Midterm exams or retakes.

Assessment criteria, fail (0)

Less than 25 % of homework exercises submitted in time.
More than 20 % (unauthorized) non-attendance from lectures and exercise sessions.
Less than 6/15 points in one or both of the Midterm exams or retakes.

Student has not achieved the learning objectives of the course. They recognize and can use only few of the concepts of the course topics, and show no skills to apply them.

Assessment criteria, satisfactory (1-2)

Student has 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.

Assessment criteria, good (3-4)

Student has 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.

Assessment criteria, excellent (5)

Student has 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.

Qualifications

Previous mathematics courses of ICT engineering curriculum (or equivalent skills):
Introduction to Engineering Mathematics
Calculus

Objective

After completing the course the student can
- apply logical rules and notation
- compute and apply permutations and combinations
- apply the concepts and properties of divisibility and congruence
- process arithmetic and geometric sequences and sums
- calculate the sum of a converging infinite geometric series
- form Taylor polynomials and utilize them in numerical computation
- determine coefficients for Fourier-series expansions using mathematical computation tools

Content

- Fundamentals of logic
- Basics od number theory with applications
- Basics of combinatorics with applications
- Sequences and series
- Taylor series
- Fourier series

Materials

ITSL-sivulta löytyvät:
Luentomuistiinpanot
Laskuharjoitusten tehtävät
MATLAB-ohjeet

Teaching methods

Luennot
Laskuharjoitukset
Kokeet

Exam schedules

Tietotekniikan matematiikka:
Osakoe ennen syyslomaa

Sarjat:
Osakoe ennen joululomaa

Lopullinen uusinta seuraavan vuoden tammikuussa:
voi tehdä jomman kumman tai kummatkin osakokeista

Student workload

Tietotekninen matematiikka:
10*2h tietotekniikan matematiikan luennot
5*2h laskuharjoitukset
2h tietotekninen matematiikka -koe
Sarjat:
5*2h sarjat-luennot
6*2h matlab työskentelyä
2h sarjat -koe

loppu opiskelijan itsenäistä opiskelua

Content scheduling

Elokuu-Lokakuu, tietotekniikan matematiikka:
- Logiikka
- Kombinatoriikka; yhteenlasku/kertolaskusääntö, permutaatiot, kombinaatiot
- Kombinatoriikan sovelluksia todennäköisyyslaskentaan
- Lukuteoria: alkuluvut, syt/pym, Eukleideen algoritmi, kongruenssi/modulolaskenta, hajautusfunktiot, jäännösluokkarengas, RSA-algoritmi


Lokakuu-Joulukuu, sarjat:
- Lukujonot, aritmeettinen ja geometrinen lukujono, lukujonon raja-arvo
- Lukujonon summat, aritmeettinen ja geometrinen summa
- Sarjat, geometrinen sarja ja suppeneminen
- Taylorin sarja
- Fourierin sarja
- Fourierin muunnos (vapaaehtoinen)

Evaluation scale

H-5

Assessment methods and criteria

Osakokeista täytyy saada tietty määrä pisteitä päästäkseen läpi.
Laskuharjoituksista saatavat lisäpisteet parantavat arvosanaa (sarjat tehtävistä 25 kpl pakollisia)
Arvosanataulukko löytyy ITSL-sivulta.

Qualifications

Previous mathematics courses of ICT engineering curriculum (or equivalent skills):
Introduction to Engineering Mathematics
Calculus

Objective

After completing the course the student can
- apply logical rules and notation
- compute and apply permutations and combinations
- apply the concepts and properties of divisibility and congruence
- process arithmetic and geometric sequences and sums
- calculate the sum of a converging infinite geometric series
- form Taylor polynomials and utilize them in numerical computation
- determine coefficients for Fourier-series expansions using mathematical computation tools

Content

- Fundamentals of logic
- Basics od number theory with applications
- Basics of combinatorics with applications
- Sequences and series
- Taylor series
- Fourier series

Materials

ITSL-sivulta löytyvät:
Luentomuistiinpanot
Laskuharjoitusten tehtävät ja mallivastaukset
MATLAB-ohjeet
Harjoituskoe

Teaching methods

Luennot
Laskuharjoitukset
Kokeet
Vapaaehtoinen harjoitustyö

Exam schedules

Sarjat:
Osakoe ja sen uusinta ennen syyslomaa
Tietotekniikan matematiikka:
Osakoe ja sen uusinta ennen joululomaa

Lopullinen uusinta seuraavan vuoden tammikuussa:
voi tehdä jomman kumman tai kummatkin osakokeista

Completion alternatives

Pelkät osakokeet ilman pisteitä laskuharjoituksista (sarjat osuuden tehtävistä 25 kpl pakollisia)
Vapaaehtoinen harjoitustyö, + 1op

Student workload

5*2h sarjat-luennot, joissa yhteensä 50 kpl tehtäviä
10*2h tietotekniikan matematiikan luennot
5*2h laskuharjoitukset, joissa yhteensä 50 kpl tehtäviä
2*2h kokeet
loppu opiskelijan itsenäistä opiskelua
vapaaehtoinen harjoitustyö, + 1op

Content scheduling

Elokuu-lokakuu, sarjat:
- Lukujonot, aritmeettinen ja geometrinen lukujono, lukujonon raja-arvo
- Lukujonon summat, aritmeettinen ja geometrinen summa
- Sarjat, geometrinen sarja ja suppeneminen
- Taylorin sarja
- Fourierin sarja
- Fourierin muunnos (vapaaehtoinen)

Lokakuu-joulukuu, tietotekniikan matematiikka:
- Logiikka
- Kombinatoriikka; yhteenlasku/kertolaskusääntö, permutaatiot, kombinaatiot
- Kombinatoriikan sovelluksia todennäköisyyslaskentaan
- Lukuteoria: alkuluvut, syt/pym, Eukleideen algoritmi, kongruenssi/modulolaskenta, hajautusfunktiot, jäännösluokkarengas, RSA-algoritmi

Evaluation scale

H-5

Assessment methods and criteria

Osakokeista täytyy saada tietty määrä pisteitä päästäkseen läpi.
Laskuharjoituksista saatavat lisäpisteet parantavat arvosanaa (sarjat tehtävistä 25 kpl pakollisia)
Arvosanataulukko löytyy ITSL-sivulta.

Assessment criteria, fail (0)

Ei tarpeeksi pisteitä kokeista.

Assessment criteria, satisfactory (1-2)

Arvosanataulukko löytyy ITSL-sivulta.

Assessment criteria, good (3-4)

Arvosanataulukko löytyy ITSL-sivulta.

Assessment criteria, excellent (5)

Arvosanataulukko löytyy ITSL-sivulta.

Qualifications

Previous mathematics courses of ICT engineering curriculum (or equivalent skills):
Introduction to Engineering Mathematics
Calculus

Objective

After completing the course the student can
- apply logical rules and notation
- compute and apply permutations and combinations
- apply the concepts and properties of divisibility and congruence
- process arithmetic and geometric sequences and sums
- calculate the sum of a converging infinite geometric series
- form Taylor polynomials and utilize them in numerical computation
- determine coefficients for Fourier-series expansions using mathematical computation tools

Content

- Fundamentals of logic
- Basics od number theory with applications
- Basics of combinatorics with applications
- Sequences and series
- Taylor series
- Fourier series

Evaluation scale

H-5

Qualifications

Previous mathematics courses of ICT engineering curriculum (or equivalent skills):
Introduction to Engineering Mathematics
Calculus

Objective

After completing the course the student can
- apply logical rules and notation
- compute and apply permutations and combinations
- apply the concepts and properties of divisibility and congruence
- process arithmetic and geometric sequences and sums
- calculate the sum of a converging infinite geometric series
- form Taylor polynomials and utilize them in numerical computation
- determine coefficients for Fourier-series expansions using mathematical computation tools

Content

- Fundamentals of logic
- Basics od number theory with applications
- Basics of combinatorics with applications
- Sequences and series
- Taylor series
- Fourier series

Materials

Lecture notes, homework and MATLAB exercises will be published in Itslearning.

Teaching methods

Part 1, Sequences and series:
lectures, MATLAB exercises, self-study, exercises/homework

Part 2, Logic, combinatorics and number theory:
lectures and demonstrations, self-study, homework

Exam schedules

Midterm exam, part 1 on week 41, Midterm exam, part 2 on week 49, retakes on week 50. Exact dates and times in the schedule.

Note. Homework and exercises must be returned in time, there is no way to complement or "retake" them later

Student workload

Lessons 49 h
Exams + preparing for them 26 h
Self-study (homework, Matlab etc.) 60 h so approx. 5 h per week.

Content scheduling

Fall 2022, according to the schedule.

Further information

We will use MATLAB, for which TUAS has a campus licence. You'll need to download it to your laptops.

Taking the self-study course MATLAB Basics for ICT is highly recommended prior to the start of Sequences and Series part (by week 43).

Evaluation scale

H-5

Assessment methods and criteria

Submit in time at least 25 % of the homework/exercises for both modules.

Active participation in MATLAB exercises.

Achieve at least 6/15 points in both Midterm exams or retakes.

Assessment criteria, fail (0)

Less than 25 % of homework exercises submitted in time.
More than 20 % (unauthorized) non-attendance from MATLAB exercises
Less than 6/15 points in one or both of the Midterm exams or retakes.

Student has not achieved the learning objectives of the course. They recognize and can use only few of the concepts of the course topics, and show no skills to apply them.

Assessment criteria, satisfactory (1-2)

Student has 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.

Assessment criteria, good (3-4)

Student has 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.

Assessment criteria, excellent (5)

Student has 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.

Qualifications

Previous mathematics courses of ICT engineering curriculum (or equivalent skills):
Introduction to Engineering Mathematics
Calculus