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# IX1303 Algebra and Geometry 7.5 credits

### For course offering

Spring 2025 Start 17 Mar 2025 programme students

### Target group

Open for all master programmes as long as it can be included in your programme.

P4 (7.5 hp)

17 Mar 2025
2 Jun 2025

50%

Normal Daytime

Swedish

KTH Campus

Min: 25

## Application

### For course offering

Spring 2025 Start 17 Mar 2025 programme students

60073

## Contact

### For course offering

Spring 2025 Start 17 Mar 2025 programme students

### Examiner

No information inserted

### Course coordinator

No information inserted

### Teachers

No information inserted
Headings with content from the Course syllabus IX1303 (Spring 2021–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

Basic logic and set theory; different number fields; complex numbers; linear equation systems; matrices and matrix algebra; determinants; the matrix, vectors and vector algebra in R2 of inverse and R3; coordinate system and change of basis; inner product and cross product with geometric applications; affine reproductions; solution to over determined, under determined and sparse systems; eigenvalue problem; applications to computer graphics and image processing.

### Intended learning outcomes

Aim that the student should have achieved on completion of the course:

The student should be able to formulate, analyse and solve problems within algebra and geometry that are of significance within the ICT-subject area; apply and develop mathematical models within algebra and geometry by means of a mathematical programming language; critically review and comment on a given solution to a problem ; analyse how sensitive a solution is for variations in input.

On completion of the course, the student should be able to use logical symbols and formalism in set theory in a correct way in problem-solving; formulate mathematical models and solve problems where linear equation systems, matrices and determinants are included; model geometric vectors and vector algebra in R2 and R3, for example within computer graphics; carry out change of basis in orders to simplify a model; explain the relevance of eigenvalues and eigenvectors at certain applications for example rotations; solve linear equation systems (also over determined, under determined and sparse); handle vectors, matrices and determinants; solve eigenvalue problems; handle graphical objects with linear algebra especially with affine reproductions; explain how and explain why the number system is expanded to complex numbers; count with complex numbers written in different forms; model and solve problem in R2 with complex numbers.

## Literature and preparations

### Specific prerequisites

No information inserted

IX1304 Calculus

### Equipment

No information inserted

### Literature

No information inserted

## Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

A, B, C, D, E, FX, F

### Examination

• PRO1 - Project work, 1.5 credits, grading scale: P, F
• TENB - Exam, 6.0 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

## Further information

### Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

### Main field of study

Mathematics, Technology

First cycle