MATP121 Linear Algebra and Geometry 1 (7 cr)

Open the course unit brochure on Sisu
Study level:
Basic studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023

Description

Linear algebra and geometry of euclidean spaces. Main themes: Systems of linear equations, linear independence, subspaces, basis, dimension, orthogonality, matrices, determinants.

The contents correspond to

Lay: Linear algebra and its applications, 2nd edition chapters 1-4 and 6

Learning outcomes

After completing the course, the student- is able to solve multivariate linear equations using the the method of Gauss and Jordan, and to analyze the solutions sets.

  • knows the linear structure of Euclidean space, especially subspaces, as well as inner product and norm
  • is able to handle linear mappings, matrices and determinants, and knows the relationships between them
  • is able to determine whether a given set of vectors is linearly independent
  • can form a base for a given subspace and determine the dimension of the subspace
  • knows how to use the geometric structure provided by Euclidean inner product, is able to form an orthonormal base for a given subspace using the Gram and Schmidt orthogonalization method, and knows how to compute the orthogonal projection to a subspace
  • knows the definitions of the key concepts of linear algebra and is able to produce proofs

Description of prerequisites

Good command of the long mathematics curriculum of high school.

Literature

  • Steven J. Leon, Linear Algebra with Applications, Pearson Education, Inc. (kaikki painokset käyvät); ISBN: 0-13-200306-6
  • Gilbert Strang, Introduction to Linear Algebra, Wellesley-Cambrige Press. (kaikki painokset käyvät); ISBN: 978-09802327-7-6
  • Stanley I. Grossman, Elementary Linear Algebra, Wadswoth Publishing Company. (kaikki painokset käyvät).; ISBN: 0-534-07422-7
  • Roland E. Larson ja Bruce H. Edwards, Elementary Linear Algebra, D.C. Heath and Company. (kaikki painokset käyvät); ISBN: 0-669-14583-1
  • David C. Lay, Linear Algebra and Its Applications, Pearson Education, Inc. (kaikki painokset käyvät); ISBN: 0-321-14992-0

Completion methods

Method 1

Description:
Suoritustavassa opintojakso suoritetaan välikokeilla (2kpl kurssin aikana). Suoritustapaan liittyy viikottaisten harjoitustehtävien tekemistä. Osa harjoitustehtävistä voi olla kirjallisesti palautettavia. Välikokeisiin saa lisäpisteitä tehdyistä harjoitustehtävistä. Tarkemmat tiedot opetusohjelmassa.
Evaluation criteria:
Grading is based on points from mid exams and weekly exercises
Time of teaching:
Period 1, Period 2
Select all marked parts

Method 2

Description:
Suoritustapana itsenäinen opiskelu ja lopputentti.
Evaluation criteria:
Grading is based on points from the final exam
Select all marked parts
Parts of the completion methods
x

Teaching (7 cr)

Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
Opintojakson arvosana määräytyy välikokeiden yhteispistemäärän ja laskuharjoitustehtävistä saatavien pisteiden perusteella.
Language:
Finnish
Study methods:

Lectures 48 h (in Finnish), exercises

Study materials:

Luennoilla jaettava luentomateriaali.

Teaching

x

Exam (7 cr)

Type:
Exam
Grading scale:
0-5
Evaluation criteria:
Opintojakson arvosana määräytyy lopputentin pistemäärän perusteella. Hyväksyttyyn arvolauseeseen vaaditaan vähintään puolet maksimipistemäärästä.
Language:
English, Finnish
Study methods:

Itsenäinen opiskelu ja lopputentti.

Teaching