# MATA120 Number Fields (4 cr)

Study level:
Intermediate studies
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023

## Description

Integers, rational, real and complex numbers. Construction of binary operations and order relations. Cauchy sequences. Fundamental theorem of algebra.

## Learning outcomes

After completing the course, the student
• Knows the constructs of number systems Z, Q, R and C from natural numbers
• Can prove the basic properties of operations and order relations in different number systems
• Knows the definition of equivalence relation and is able to apply it in constructing number systems
• Knows the definition of the Cauchy sequence and their connection to completeness
• Understands geometric interpretations of complex numbers calculations
• Can apply the solution formula of the third degree equation
• Knows the content of the Fundamental theorem of algebra and main ideas of its proof

## Description of prerequisites

Introduction to mathematical analysis 1-2, Linear algebra and geometry 1

## Study materials

Lecture notes (in Finnish)

I. Stewart and D. Tall: The Foundations of Mathematics, chapters 2, 9, 10, and 11
H.-D. Ebbinghaus et. al.: Numbers, chapters 1.2-1.4 ; 2.3-2.5 ; 3.2-3.4, 3.6 ; 4.3

## Completion methods

### Method 1

Evaluation criteria:
Course exam and homework
Select all marked parts

### Method 2

Evaluation criteria:
Final exam
Select all marked parts
Parts of the completion methods
x

### Teaching (4 cr)

Type:
Participation in teaching
0-5
Evaluation criteria:
Language:
Finnish
Study methods:

28h luentoja, 7 harjoituskertaa

Study materials:

Luentomoniste

Opintojaksoa vastaavia sisältöjä löytyy teoksista
I. Stewart ja D. Tall: The Foundations of Mathematics, Luvut 2,9,10,11
H.-D. Ebbinghaus et. al.: Numbers, Luvut 1.2-1.4 ; 2.3-2.5 ; 3.2-3.4, 3.6 ; 4.3

x

### Exam (4 cr)

Type:
Exam
0-5
Evaluation criteria:
Final exam
Language:
English, Finnish
Study methods:

Independent study and final exam

Study materials:

I. Stewart ja D. Tall: The Foundations of Mathematics, chap. 2, 9, 10, and 11
H.-D. Ebbinghaus et. al.: Numbers, chapters 1.2-1.4 ; 2.3-2.5 ; 3.2-3.4, 3.6 ; 4.3