I komplex analys finns det ett antal olika konvergenser varav vi tittar närmare på några här. Bland annat hur likformig konvergens medför punktvis konvergens men att det omvända ej gäller. Vi tittar också på vad de har för samband med lokal likformig konvergens och normal konvergens dvs. likformig konvergens på kompakta delmängder. Slutligen kommer vi att se på vad som gäller för familjer och kommer då in på lokalt begränsad, ekvikontinuitet, Arzela/Ascoli, Montels och Runges satser.

Chinese Remainder Theorem is used to solving problems in computing, coding and cryptography. In computing we can compute with shorter numbers instead of large numbers and this will make the computing-process faster and easier. In coding it can be used for error-searching and error-regulating.Cryptography means that we can send a coded message and that no one will be able to read it without the decode-key which is based on prim-numbers. I am writing about the history of mathematics and how the number- and decimal number-system is used in Babylon, Egypt, Greece and in China. Abacus was a very important aid to calculate advanced mathematical problems.

This paper explains the basis for impartial games and the classicgame Nim. Nim is complicated by a modular Muller twist and thesolution for this game is described by a simple theorem. The modularMuller twist means that at the end of each move the player selects a kand the number of sticks the next player leaves in the pile, where thedraw is made, must be congruent with k modulo m. The number m isfixed throughout the game..

Gravitational lenses are unlike ordinary optical lenses, a phenomenon corrupting our optical view of the cosmos. When we look out intospace we see celestial bodies lying with astronomical distance from Earth. There is no guarantee that what we see out there in space is actually there where we are observing it, and it may be that we see multiple images of the same star! Studies have shown that thenumber of distorted images of an n-mass (n > 1) plane lens can not exceed 5(n -1) for lighter lenses or 5n for more massive lens. This mathematical thesis covers gravitational lensing and their properties that distort light rays coming towards us from distant celestial bodies. In addition of gravitational lensing, its properties and the proof of the maximum number of distorted images, a bigger part of this work even cover two very interesting mathematical tools - the so-called Schwarz function and Bezout theorem..

In several scientific and technical educations today we meet mathematical studies in differential- and integral calculus. The classic mechanics is a foundation for the physics and it has made it possible for today's technical developments that we in our everyday life meet and make use of. The intention for this essay is to give a picture of the person behind this discoveries that changed the science and the world. Besides the purpose to bring the reader on a journey through Isaac Newton's life the main intention is to give an understanding of the way he discovered the binomial theorem, the differential- and integral calculus, the numerical methods Newton-Raphson's and Newton's interpolation-polynomial, Newtons identities and his classification of third-degree curves and elliptic curves. A derivation of Kepler's first law is also included..

Practice of mathematical proof increase the understanding of mathematics anddevelop creativity skills, problem solving, communication, logical thinking andreasoning which are all important tools not only within the subject of mathematicsbut also important tools for the society in which we are living. The aim of this projectwas to investigate whether it is accurate that proof and proving has a subordinate rolein mathematic education in the upper secondary school in Sweden. This was done byconstructing of a digital survey that was sent to approximately 100 practicingmathematics teachers in a normal size city located in the middle of Sweden. Theresults of the survey show that the teachers consider themselves comfortable withtheir own skills in teaching proof. Paradoxically, the results also show that there is alack of teaching of proof and proving in the upper secondary school, although the newcurriculum puts more focus on proof and proving..

The aim with this thesis is to study the risk management in construction projects at the Swedish Road Administration, SRA. Furthermore, the aim is to find the effects of the risk management. The theorem of this thesis is that the positive effects of the risk management in construction projects create additional value to the project. These additional values are that the project itself becomes resilient and that the project goals are achieved without any significant disturbances.This thesis shows that the risk management in construction projects do not follow the guidelines set out by the SRA. This is due to a lack of education in the method and a difficult method all together.

In this report, a case study of conditions for Swedish language development in children of immigrant origin is presented, and its results explored. The boundaries of the case study are defined as preschool pedagogues? facilitation of Swedish language development through co-learning, in children of immigrant origin in an ethnically segregated urban area. Concepts central to the report include dialogue, second language learning and perspectives on language difficulties. For the theoretical background of the report, a basic sociocultural theorem is used, which links language as well as other areas of development to verbal interaction in a social context.

The purpose of this essay is to describe and analyze experiences of how the daily rounds and a persons role is changing when you go from being a family member to being a family member as well as being a kinship carer.Essential questions at issue was:- Which feelings are associated to the roll as kinship carer?- What are the motivations for the relative/family member to become a kinship carer?- What is the change of the role like before and after the disease.Six persons have been interviewed on the subject and symbolic interactionism and role theory has been our theoretical perspective. The essay has been related to the ideas of Meads on social interaction and to Goffmans theatre theorem.The result of the essay showed that feelings and motivations as regards to the daily rounds and the role of the kinship carer were individual, where similarities and differences occurred. When ones partner, parent or child got a disease/functional disability it generated in some changes regarding their daily rounds and it led to altering of roles. To assume a role was a natural result and often happened when a relative/family member got a disease or an injury..

Myanmar?s entry in Association of South Eastern Asian Nations (ASEAN) in 1997 brought about several economic and social changes. One important change is tariff reduction through the Common Effective Preferential Tariff (CEPT-scheme), which increased Myanmar?s export to countries outside the ASEAN. The increase in exports facilitated trade creation and investment creation for Myanmar.

In a time when economic crises relieving one another, it is especially interesting to study how companies choose to finance their operations. Since there is a lack of studies that include banks, and their capital structures, with the rest of the finance market, it is uncertain whether the theories of capital structure are applicable. Therefore, this essay aims to study whether there is any correlation between the two variables debt-equity ratio and return on equity (ROE) for Swedish corporations on the finance market.In accordance with the theorems that the professors Modigliani and Miller filed, in 1958 and 1961, which describes a clear link between debts, increase corporate value through the tax shield and indirectly increased yields. Although these theorems are the foundation of the modern research they focus on perfect markets. Therefore, this paper has also chosen to place great emphasis on theories such as Trade-off and Pecking-order.

Den här C-uppsatsen, som handlar om geometri, har tre ingående delar. Den första delen berättar geometrins historiska utveckling från de första Babyloniska skrifterna via kända matematiker som Pythagoras och Euklides fram till utvecklingen av den icke-euklidiska geometrin. Den andra delen förklarar mer ingående några hållpunkter som uppmärksammades ur geometrins historia. Denna del beskriver Euklides axiomatiska framställning och bevis av Pythagoras sats, konstruktion med passare och linjal, Apollonius kägelsnitt samt en inblick i grunderna för projektiv geometri. I den avslutande delen har en jämförande studie gjorts av fyra olika läromedel för gymnasieskolan.

Earth?s resources have been exploited unsustainably. If an entire conception of exploitationof natural resources does not change now, this will entail enormous costs in the future.This insight has lead to a recently increased interest in clean technologies among privateequity capitalists. In the fourth quarter of 2006 about 10 percent of all private equityinvestments made in the US market were placed in the cleantech industry. Despite a goodinvesting climate in Sweden, Swedish capitalists have shown little interest in cleantechinvestments.