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Mathematics (minor) (Bachelor level)
Basic information
Code:
SCI3033
Extent:
20–25
ECTS
Curriculum:
2026–2028
2024–2026
2022–2024
Previous curricula
Level:
Intermediate studies
Language of learning:
English
Finnish
Target group:
All Aalto students
Teacher in charge:
Riikka Korte
Administrative contact:
Suvi Saviniemi
Organising department:
Department of Mathematics and Systems Analysis
Organiser:
School of Science
Prerequisites:
-
Quotas and restrictions:
-
Application process:
-
Content and structure of the minor
About the minor
Target group: All students in the schools of technology. Also other students of Aalto University interested in mathematics. The minor is intended for students who do not have Mathematics and Systems Sciences as their major.
This minor is designed for students willing to develop their general mathematical thinking and problem solving skills, and to learn mathematical and statistical methods that can be applied in science, technology, arts, and business.
Due to the wide range of possible applications for mathematics in different fields of technology, the student assembles an individual package of courses together with a professor of mathematics.
The courses are chosen mainly from the list below according to the student’s background, interests and needs. In addition, master’s level courses in mathematics (MS-E1***) can be included in the minor. It is also possible to choose some courses in statistics and systems sciences (MS-C2*** and MS-E2***).
Content
| Code | Course name | ECTS | Teaching |
|---|---|---|---|
| MS-A00** |
Matriisilaskenta / Matrisräkning / Matrix Algebra |
5 |
I, II or III Finnish II Swedish II English |
| MS-A01** |
Differentiaali- ja integraalilaskenta 1 / Differential- och integralkalkyl 1 / Differential and Integral Calculus 1 |
5 |
I, II or IV Finnish I Swedish I English |
| MS-A02** |
Differentiaali- ja integraalilaskenta 2 / Differential- och integralkalkyl 2 / Differential and Integral Calculus 2 |
5 |
I, III, IV or summer Finnish III Swedish III English |
| MS-A03** |
Differentiaali- ja integraalilaskenta 3 / Differential- och integralkalkyl 3 / Differential and Integral Calculus 3 |
5 |
I or IV Finnish IV Swedish IV English |
| MS-A0401 |
Diskreetin matematiikan perusteet / Grundkurs i diskret matematik / Foundations of Discrete Mathematics |
5 |
I Finnish I Swedish IV English |
| MS-A050* |
Todennäköisyyslaskennan ja tilastotieteen peruskurssi / Grundkurs i sannolikhetskalkyl och statistik / First Course in Probability and Statistics |
5 |
I, II, IV or summer Finnish III Swedish III English |
| MS-C1001 | Shapes in Action | 5 |
2026-2027: I English 2027-2028: no teaching |
| MS-C1081 | Abstract Algebra | 5 | III English |
| MS-C1300 | Complex Analysis | 5 | II English |
| MS-C1342 | Lineaarialgebra / Linear Algebra | 5 | II Finnish, V English |
| MS-C1350 | Partial Differential Equations | 5 | I-II English |
| MS-C1420 | Fourier-analyysi | 5 | I Finnish |
| MS-C1530 | Curves and Surfaces | 5 |
2026-2027: no teaching 2027-2028: I English |
| MS-C1541 | Metric Spaces | 5 | III English |
| MS-C1650 | Numerical Analysis | 5 | V English |
| MS-C2105 | Introduction to Optimization | 5 | IV English |
| MS-C2111 | Stochastic Processes | 5 | II English |
* Teaching language is Finnish.
By choosing the following three courses, the minor can be completed with an orientation in integrating mathematics with visual arts, design and architecture:
| Code | Course name | ECTS | Teaching |
|---|---|---|---|
| MS-C1001 | Shapes in Action | 5 |
2026-2027: I English 2027-2028: no teaching |
| MS-E1000 | Crystal Flowers in Halls of Mirrors: Mathematics Meets Art and Architecture D | 5–15 |
2026-2027: III-V English 2027-2028: no teaching |
| AXM-E0411 | Spatial Structures | 6 | I-II English |
More information about this orientation can be found at http://matharts.aalto.fi/.
Previous curricula
Koodi: SCI3033
Laajuus: 20–25 ECTS
Opetussuunnitelma: 2024–2026 2022–2024 2020–2022 Aiemmat opintosuunnitelmat
Taso: Aineopinnot
Suorituskieli: Englanti Suomi
Teema: Matematiikka ja tutkimusmenetelmät
Kohderyhmä: Kaikki Aallon opiskelijat
Sivuaineen vastuuopettaja: Riikka Korte
Sivuaineen koordinaattori: Suvi Saviniemi
Järjestävä laitos: Matematiikan ja systeemianalyysin laitos
Korkeakoulu: Perustieteiden korkeakoulu
Esitiedot: -
Kiintiöt ja rajoitukset: -
Haku: -
Sivuaineen sisältö ja rakenne
Tietoa sivuaineesta
Sivuaineen kuvaus
Kohderyhmä: Tekniikan alan opiskelijat. Myös muiden koulujen opiskelijat, jotka ovat kiinnostuneita matematiikasta. Matematiikan sivuaine on tarkoitettu muille kuin matematiikan ja systeemitieteiden pääaineopiskelijoille.
Sivuaineen nimi muilla kielillä: Matematik, Mathematics
Osaamistavoitteet
Tämän sivuaineen suorittamalla opiskelijat voivat kehittää matemaattista ajatteluaan ja ongelmanratkaisutaitoja, sekä oppia matematiikan ja tilastotieteen menetelmiä, joista on hyötyä tieteessä, teknologiassa, taiteissa ja kauppatieteissä.
Sisällön kuvaus
Matematiikalla on sovelluksia kaikilla tekniikan aloilla, ja tästä laaja-alaisuudesta johtuen sivuaineen opiskelija laatii matematiikan vastuuprofessorin kanssa 20 tai 25 opintopisteen kokoisen henkilökohtaisen kurssipaketin.
Pakettiin valitaan kursseja pääasiassa alla olevasta listasta huomioiden opiskelijan tausta, kiinnostukset ja muiden opintojen tarpeet. Lisäksi matematiikan maisteritason kursseja (MS-E1***) saa vapaasti sisällyttää sivuaineeseen esitietovaatimusten täyttyessä. Myös tilastotieteen ja systeemitieteen opintojen (MS-C2*** ja MS-E2***) sisällyttäminen kurssipakettiin on mahdollista.
Opintojaksojen kuvaukset löydät Sisusta joko oman opintosuunnitelmasi kautta valitsemalla opintojakson ja klikkaamalla sen koodia tai hakemalla opintojaksoja koodilla tai nimellä. Opintojaksojen työtilat löydät MyCoursesista joko hakemalla tai ilmoittautumisen jälkeen kohdasta "omat kurssini".
Sisältö
| Koodi | Opintojakson nimi | Op | Periodi |
|---|---|---|---|
| MS-A00** |
Matriisilaskenta / Matrisräkning / Matrix algebra |
5 | Fi: I, II, III, / Sv: II / En: II |
| MS-A01** |
Differentiaali- ja integraalilaskenta 1 / Differential- och integralkalkyl 1 / Differential and integral calculus 1 |
5 | Fi: I, II, IV / Sv: I / En: I |
| MS-A02** |
Differentiaali- ja integraalilaskenta 2 / Differential- och integralkalkyl 2 / Differential and integral calculus 2 |
5 | Fi: I, III, IV, kesä / Sv: III / En: III |
| MS-A03** |
Differentiaali- ja integraalilaskenta 3 / Differential- och integralkalkyl 3 / Differential and integral calculus 3 |
5 | Fi: I, IV / Sv: IV / En: IV |
| MS-A040* |
Diskreetin matematiikan perusteet / Grundkurs i diskret matematik / Foundations of discrete mathematics |
5 | Fi: I / Sv: I / En: IV |
| MS-A050* |
Todennäköisyyslaskennan ja tilastotieteen peruskurssi / Grundkurs i sannolikhetskalkyl och statistik / First course in probability and statistics |
5 | Fi: I, II, IV, kesä / Sv: III / En: III |
| MS-C1001 | Shapes in Action | 5 | I (2024-2025) |
| MS-C1081 | Abstract Algebra | 5 | III |
| MS-C1300 | Complex Analysis | 5 | II |
| MS-C1342 | Linear Algebra | 5 | V |
| MS-C1350 | Partial Differential Equations | 5 | I-II |
| MS-C1420 | Fourier-analyysi | 5 | I |
| MS-C1530 | Curves and Surfaces | 5 | I (2025-2026) |
| MS-C1541 | Metric Spaces | 5 | III |
| MS-C1650 | Numerical Analysis | 5 | V |
| MS-C2105 | Introduction to Optimization | 5 | IV |
| MS-C2111 | Stochastic Processes | 5 | II |
Valitsemalla seuraavat kolme kurssia sivuaineen voi suorittaa painottuen matematiikan, kuvataiteiden, muotoilun ja arkkitehtuurin yhteyksiin:
Basic information
Code: SCI3033
Extent: 20–25 ECTS
Language of instruction: English Finnish
Level: Bachelor
Theme: Mathematics and research methods
Curriculum: 2022–2024
Target group: All Aalto students
Teacher in charge: Riikka Korte
Administrative contact: Suvi Saviniemi
Organising department: Department of Mathematics and Systems Analysis
Prerequisites: No prerequisites.
Quotas and restrictions: No quotas or restrictions.
Application process: The minor is open for all students of Aalto University. (No separate call.)
Content and structure of the minor
Target group: All students in the schools of technology. Also other students of Aalto University interested in mathematics. The minor is intended for students who do not have Mathematics and Systems Sciences as their major.
Due to the wide range of possible applications for mathematics in different fields of technology, the student assembles an individual package of courses together with a professor of mathematics.
The courses are chosen mainly from the list below according to the student’s background, interests and needs. In addition, master’s level courses in mathematics (MS-E1***) can be included in the minor. It is also possible to choose some courses in statistics and systems sciences (MS-C2*** and MS-E2***).
Structure of the minor
| Code | Course name | ECTS credits | Period |
|---|---|---|---|
| MS-A00** |
Matriisilaskenta / Matrisräkning / Matrix algebra |
5 | Fi: I, II, III, / Sv: II / En: II |
| MS-A01** |
Differentiaali- ja integraalilaskenta 1 / Differential- och integralkalkyl 1 / Differential and integral calculus 1 |
5 | Fi: I, II, IV / Sv: I / En: I |
| MS-A02** |
Differentiaali- ja integraalilaskenta 2 / Differential- och integralkalkyl 2 / Differential and integral calculus 2 |
5 | Fi: I, III, IV, kesä / Sv: III / En: III |
| MS-A03** |
Differentiaali- ja integraalilaskenta 3 / Differential- och integralkalkyl 3 / Differential and integral calculus 3 |
5 | Fi: I, IV / Sv: IV / En: IV |
| MS-A040* |
Diskreetin matematiikan perusteet / Grundkurs i diskret matematik / Foundations of discrete mathematics |
5 | Fi: I / Sv: II / En: IV |
| MS-A050* |
Todennäköisyyslaskennan ja tilastotieteen peruskurssi / Grundkurs i sannolikhetskalkyl och statistik / First course in probability and statistics |
5 |
Fi: I, II, IV, kesä / Sv: III / En: III |
| MS-C1001 | Shapes in Action | 5 | I |
| MS-C1081 | Abstract Algebra | 5 | III |
| MS-C1300 | Complex Analysis | 5 | II |
| MS-C1342 | Linear Algebra | 5 | V |
| MS-C1350 | Partial Differential Equations | 5 | I-II |
| MS-C1420 | Fourier-analyysi | 5 | I |
| MS-C1530 | Curves and Surfaces | 5 | I |
| MS-C1541 | Metric Spaces | 5 | III |
| MS-C1650 | Numerical Analysis | 5 | V |
By choosing the following three courses, the minor can be completed with an orientation in integrating mathematics with visual arts, design and architecture:
| Code | Course name | ECTS credits | Period |
|---|---|---|---|
| MS-C1001 | Shapes in Action | 5 | I |
| MS-E1000 | Crystal Flowers in Halls of Mirrors: Mathematics Meets Art and Architecture D | 5–15 | III-IV |
| AXM-E0411 | Spatial Structures | 6 | I-II |
More information about this orientation can be found at http://matharts.aalto.fi/.
Basic information
Code: SCI3033
Extent: 20-25 op
Language: Finnish and English
Teacher in charge: Riikka Korte
Administrative contact: Johanna Bovellán
Target group: All students in the Schools of Technology. Also other students of Aalto University interested in mathematics. The minor is intended for students who do not have Mathematics and Systems Sciences as their major.
Application process: The minor is open for all students of Aalto University. (No separate call.)
Quotas and restrictions: No quotas or restrictions.
Prerequisites: No prerequisites.
Name of the minor in other languages: Matematiikka, Matematik
Content and structure of the minor
Due to the wide range of possible applications for mathematics in different fields of technology, the student assembles an individual package of courses together with a professor of mathematics.
The courses are chosen mainly from the list below according to the student’s background, interests and needs. In addition, master’s level courses in mathematics (MS-E1***) can be included in the minor. It is also possible to choose some courses in statistics and systems sciences (MS-C2*** and MS-E2***).
Structure of the minor
| Code | Course name | ECTS credits | Period |
|---|---|---|---|
| MS-A00** |
Matriisilaskenta / Matrisräkning / Matrix algebra |
5 | Fi: I, II, III, kesä / Sv: II / En: II |
| MS-A01** |
Differentiaali- ja integraalilaskenta 1 / Differential- och integralkalkyl 1 / Differential and integral calculus 1 |
5 | Fi: I, II, IV / Sv: I / En: I |
| MS-A02** |
Differentiaali- ja integraalilaskenta 2 / Differential- och integralkalkyl 2 / Differential and integral calculus 2 |
5 | Fi: I, III, IV, kesä / Sv: III / En: III |
| MS-A03** |
Differentiaali- ja integraalilaskenta 3 / Differential- och integralkalkyl 3 / Differential and integral calculus 3 |
5 | Fi: I, IV / Sv: IV / En: IV |
| MS-A040* |
Diskreetin matematiikan perusteet / Grundkurs i diskret matematik / Foundations of discrete mathematics |
5 | Fi: I / Sv: II / En: IV |
| MS-A050* |
Todennäköisyyslaskennan ja tilastotieteen peruskurssi / Grundkurs i sannolikhetskalkyl och statistik / First course in probability and statistics |
5 |
Fi: I, II, IV / Sv: III / En: III |
| MS-C1001 | Shapes in action | 5 | I |
| MS-C1081 | Abstract algebra | 5 | III |
| MS-C1300 | Complex analysis | 5 | II |
| MS-C1342 | Linear algebra | 5 | V |
| MS-C1350 | Partial differential equations | 5 | I-II |
| MS-C1420 | Fourier-analyysi | 5 | I |
| MS-C1530 | Curves and surfaces | 5 | I |
| MS-C1541 | Metric spaces | 5 | III |
| MS-C1650 | Numerical analysis | 5 | V |
By choosing the following three courses, the minor can be completed with an orientation in integrating mathematics with visual arts, design and architecture:
| Code | Course name | ECTS credits | Period |
|---|---|---|---|
| MS-C1001 | Shapes in action | 5 | I |
| MS-E1000 | Crystal Flowers in Halls of Mirrors: Mathematics meets Art and Architecture | 5-15 | III-IV |
| AXM-E0411 | Spatial structures | 5 | III-IV |
More information about this orientation can be found at http://matharts.aalto.fi/.
Basic information
Code: SCI3033
Extent: 20-25 op
Language: Finnish and English
Teacher in charge: Juha Kinnunen
Administrative contact: Johanna Bovellán
Target group: All students in the Schools of Technology. Also other students of Aalto University interested in mathematics. The minor is intended for students who do not have Mathematics and Systems Sciences as their major.
Application process: The minor is open for all students of Aalto University. (No separate call.)
Quotas and restrictions: No quotas or restrictions.
Prerequisites: No prerequisites.
Name of the minor in other languages: Matematiikka, Matematik
Content and structure of the minor
Due to the wide range of possible applications for mathematics in different fields of technology, the student assembles an individual package of courses together with a professor of mathematics.
The courses are chosen mainly from the list below according to the student’s background, interests and needs. In addition, master’s level courses in mathematics (MS-E1***) can be included in the minor. It is also possible to choose some courses in statistics and systems sciences (MS-C2*** and MS-E2***).
Structure of the minor
| Code | Course name | ECTS credits | Period |
|---|---|---|---|
| MS-A00** |
Matriisilaskenta / Matrisräkning / Matrix algebra |
5 | I, II, III / II / II |
| MS-A01** |
Differentiaali- ja integraalilaskenta 1 / Differential- och integralkalkyl 1 / Differential and integral calculus 1 |
5 | I, II, IV / I / I |
| MS-A02** |
Differentiaali- ja integraalilaskenta 2 / Differential- och integralkalkyl 2 / Differential and integral calculus 2 |
5 | I, III, IV / III / IV |
| MS-A03** |
Differentiaali- ja integraalilaskenta 3 / Differential- och integralkalkyl 3 / Differential and integral calculus 3 |
5 | I, IV / IV / V |
| MS-A040* |
Diskreetin matematiikan perusteet / Grundkurs i diskret matematik / Foundations of discrete mathematics |
5 | I / II / IV |
| MS-A050* |
Todennäköisyyslaskennan ja tilastotieteen peruskurssi / Grundkurs i sannolikhetskalkyl och statistik / First course in probability and statistics |
5 |
I, II, IV / III / III |
| MS-C1001 | Shapes in action | 5 | I |
| MS-C1081 | Abstract algebra | 5 | III |
| MS-C1300 | Kompleksianalyysi | 5 | II |
| MS-C134* |
Lineaarialgebra / Linear algebra |
5 | V / I |
| MS-C1350 | Partial differential equations | 5 | I-II |
| MS-C142* |
Fourier-analyysi / Fourier analysis |
5 | I / IV |
| MS-C1530 | Curves and surfaces | 5 | I |
| MS-C1540 | Euklidiset avaruudet | 5 | III |
| MS-C1650 | Numeerinen analyysi | 5 | V |
By choosing the following three courses, the minor can be completed with an orientation in integrating mathematics with visual arts, design and architecture:
| Code | Course name | ECTS credits | Period |
|---|---|---|---|
| MS-C1001 | Shapes in action | 5 | I |
| MS-E1000 | Crystal Flowers in Halls of Mirrors: Mathematics meets Art and Architecture | 5-15 | III-IV |
| UWAS-C0014 | Spatial structures | 5 | III-IV |
More information about this orientation can be found at http://matharts.aalto.fi/.
Only available in Finnish.