MATA120 Number Fields (4 cr)
Description
Integers, rational, real and complex numbers. Construction of binary operations and order relations. Cauchy sequences. Fundamental theorem of algebra.
Learning outcomes
- 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
Method 2
Teaching (4 cr)
28h luentoja, 7 harjoituskertaa
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
Exam (4 cr)
Independent study and final exam
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