Du som ska skriva examensarbete i matematik kan hitta förslag på lämpliga ämnen här. Kontakta exjobbssamordnare Håkan Granath eller studievägledare Anders Hedin för mer information om hur du går till väga.

Gauss's Theorem Egregium

The Gauss curvature of a regular surface in the Euclidian 3-space is an intrinsic property of the surface i.e. it depends only of the coefficients E,F,G of the metric tensor of the surface. Avancerad nivå 30 hp.

Handledare: Ilie Barza

 

Limit and Continuity on the Real Axis – The Gate to General Topology.

Avancerad nivå 30 hp.

Handledare: Ilie Barza

 

Gauss-Bonnet Formula for Area of the Hyperbolic Triangle

Avancerad nivå 30 hp.

Handledare: Ilie Barza

 

Krökning och Torsion för kurvor i R³

Grundnivå 15 hp.

Handledare: Ilie Barza

 

On the concept of primitive/antiderivative function

Grundnivå 15 hp eller avancerad nivå 30 hp, beroende på djup och omfattning.

Handledare: Ilie Barza

 

The intermediate value property

It is a well-known fact that all continuous functions defined on an intervall have the intermediate value property (called also Darboux property). The consequences of this result are not less important. The aim of this thesis is to study the relations between the class of functions with intermediate value property and other important classes of functions, to give some new applications and solve some problems.

Handledare: Sorina Barza

 

Convex functions

The aim of this thesis is to present a detailed study of convex functions, to give characterizations of this class of functions and to prove some of their properties. Functional operatations which are closed to "convexity" will be also pointed out. Some applications will be also given.

Handledare: Sorina Barza

 

Dini derivatives

Dini derivatives characterize the behaviour of an arbitrary real-valued function and play an important role in Analysis. The objective of the work is to study the basic properties of these derivatives and to solve some problems. Reference: R. Kannan, Carole King Krueger, Advanced Analysis, Springer, 1996.

Handledare: Viktor Kolyada

 

The Riemann integral

The Riemann integral is one of the main conceptions of the classical Mathematical Analysis. The objective of the work is to study different criteria of the Riemann integrability and to solve related problems. Reference: B.S. Thomson, J.B. Bruckner, A.M. Bruckner, Elementary Real Analysis, Prentice-Hall, 2001.

Handledare: Viktor Kolyada

 

On the cardinality of sets

The notion of a cardinality of an infinite set is a generalization of a number of elements of a finite set. The objective of the work is to study basic results in this area and to solve related problems. References: I.P. Natanson, Theory of functions of a real variable. K. Kuratowski, Introduction to set theory and topology.

Handledare: Viktor Kolyada