MATA120 Number Fields (4 cr)

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

• 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

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

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