Browsing by Title

Tutkimuksessa tarkasteltiin louhittujen tunnelitilojen vaikutusta sitä ympäröivän kallioperän vedenjohtavuuteen sekä pohjaveteen. Tutkimuskohteena oli Espoon Soukan alueelle louhitut, Länsimetron jatkeen tunnelitilat. Tutkimuksessa tarkasteltiin paaluvälikohtaisesti, yhtenäiseltä linjaltaan 1998 metriä pitkän ratalinjan sekä siihen liittyvien huolto- ja teknisten tilojen pohja-, vuotovesi- ja mittapatomittauksista, injektointi- ja porauspöytäkirjoista sekä Lugeon-vesimenekkimittauksista saatuja tuloksia. Tutkimuksessa todettiin, että alueelle rakennetut tunnelitilat eivät ole vaikuttaneet merkittävästi tutkimusalueen pohjaveden päävirtaussuuntaan. Muutosta ei havaittu, vaikka kalliotilat ovat kokonaisuudessaan suhteellisen laajat ja tehdyn vertailun mukaan injektointityöt ovat vähentäneet tunnelia ympäröivän kallioperän vedenjohtavuutta. Kallioperän vesimenekkimittausten sekä tunnelin vuotovesimittausten tuloksille tehty korrelaatiotarkastelu osoitti, että tutkimusalueella kallioperän vedenjohtavuuden laskiessa myös tunneliin suotautuneen vuotoveden määrä on laskenut. Vesimenekkimittaustulosten keskiarvot, jotka muunnettiin kallion vedenjohtavuutta kuvaaviksi k-arvoiksi, korreloivat parhaiten vuotovesimäärien (l/min/100m) maksimiarvojen kanssa. Injektointityön onnistuneesta toteutuksesta huolimatta yksittäisten, kallioperältään rikkonaisten vyöhykkeiden osuuksilla on edelleen vesivuotoja, jotka nostavat tunnelitiloista mitatun kokonaisvuotovesimäärän keskiarvoa. Pääsääntöisesti tutkimusalueen tunnelitilojen vuotovesimäärät ovat vähäisiä ja tiloille asetetut tiiveysvaatimukset on saavutettu. Tutkimusalueen pohjaveden pinnan tasot laskivat louhintatöiden aikana, eikä tuloksia voida selittää ainoastaan luonnollisella vaihtelulla. Alenema oli noin -0,5– -25 metriä, kun tunnelitilat sijaitsivat 18-142 metrin etäisyydellä havaintopisteistä. Pohjaveden pinnan tasoissa ei ole tapahtunut louhintatöiden loppumisen jälkeen merkittävää muutosta. Koko hankkeen ajan tarkastelussa olleiden havaintoputkien mittaustuloksille tehtiin korrelaatiotarkastelu, jossa verrattiin pohjaveden pinnan tason laskun suuruutta havaintopisteen etäisyyden suhteen. Tarkastelussa todettiin, että tutkimusalueella pohjaveden pinnan tason aleneman suuruus korreloi tunnelin etäisyyden kanssa. Tutkimuksen tuloksia tarkasteltiin matemaattisen virtausmallinnuksen avulla. Tulosten perusteella voidaan arvioida, että tutkimusalueen pohjaveden pinnan tasot eivät pääsääntöisesti tule nousemaan ennen louhintatöitä vallinneelle tasolle. Tutkimuksen mukaan laadultaan heikkoon kallioperään rakennettaessa tulee varautua pysyvään pohjavesipinnan tason laskuun, vaikka tunnelin tiiveysvaatimukset saavutetaan. Tunnelin vuotovesien laadussa havaituilla pH- ja kiintoainespitoisuuksien muutoksilla on yhteys käynnissä olleisiin työvaiheisiin eikä tunnelin rakentamisesta ole aiheutunut haittaa ympäristön pohjaveden laadulle.

Ketterissä ohjelmistokehitysprosesseissa projektin hallinnan tehtävät on jaettu koko kehitystiimille. Asiakkaan edustaja eli tuoteomistaja vastaa budjetista, resursoinnista ja tuotteen tavoitteista. Kehittäjät ovat vastuussa tehtävien toteutustavan määrittelystä ja toteutuksen keston arvioinnista. Tuoteomistajan tärkeimmät tehtävät liittyvät tuotteen vision muodostamiseen, sen onnistuneeseen viestintään ja toteutuksen ohjaamiseen käytännössä. Näiden tehtävien puutteellinen suoritus voi johtaa projektin epäonnistumiseen joko teknisesti tai liiketoiminnallisesti. Tutkielmassa havainnoidaan tuoteomistajuuden ongelmakohtia ja niiden laiminlyönnin seurauksia tapaustutkimuksessa kolmessa ohjelmistoprojektissa. Mitä ongelmakohtia kirjallisuudessa määritellyssä tuoteomistajuudessa on? Miten tuoteomistajuutta voitaisiin kehittää käytettävyyssuunnittelun menetelmillä? Tapaustutkimuksessa kerättyjen havaintojen pohjalta esitetään kehitysehdotuksia tuoteomistajuuteen ja kehitysprosessin piirteisiin. Tuoteomistajan keskeisin tehtävä tulisi olla tuotteen vision muodostaminen. Muun kehitystiimin tehtävänä on muodostaa visioon perustuva tuote. Sekä tuotteen vision että visioon perustuvan tuotteen muodostamisen menetelmät ovat ketterän kehityksen ulkopuolella. Suunnittelulähtöisen käytettävyyssuunnittelun menetelmät ovat osin ristiriidassa ketterän kehityksen pääperiaatteiden kanssa. Tuotteen visio tulisi kartoittaa huolellisesti ennen toteutusprosessin aloittamista. Tuoteomistaja on vastuussa vision oikeellisuudesta, mutta vision muodostamisessa käytetään apuna käytettävyyssuunnittelun menetelmiä. Tuotteen muodostamiseksi kehitystiimin tulee kattaa tarvittava käytettävyyssuunnitteluosaamisen. Johtopäätöksistä muodostuu ehdotus prosessista, jossa muodostetaan tuotteen visio, ehdotetaan siihen perustuvia toteutusratkaisuja, valitaan ratkaisuille testaustapa, toteutetaan testausaineisto, suoritetaan testit, tarkistetaan hypoteesi ja päätetään jatkotoimenpiteet. Kun muutostarpeita ei enää ilmene, toteutettu ratkaisu hyväksytään sellaisenaan. Ehdotettua prosessia ei olla testattu empiirisesti.

Lakes in the boreal region hold a significant importance in the global carbon cycle. They transport and store carbon and exchange it with the atmosphere. As turbulent transport is the most important process in transporting substances in water and air, special weight has been laid on studying turbulent processes in lakes. This work concentrates on turbulence in the surface boundary layer of Lake Kuivajärvi in Western Finland. A 16-day measurement campaign was carried out in Kuivajärvi in September 2014. An acoustic Doppler velocimeter (ADV) was used for high-frequency velocity measurements. The meteorological forcing had two distinct regimes during the campaign: a relatively calm and warm period during the first 13 days and a cold and windy period during the last three days. The two regimes were visible in the measured velocity as well as in the calculated turbulence parameters. The friction velocity in water was estimated to be 3*10^-4...2*10^-2 m/s during low winds and 2*10^-3...5*10^-2 m/s during high winds. In the low-wind regime, the friction velocity in water was generally smaller than the scaled friction velocity in air. In the high-wind regime, the situation was opposite. The common practice of estimating the water-side friction velocity from above-surface measurements isn't justified in all conditions. The viscous dissipation rate was calculated using the inertial subrange method and the neutral scaling. Dissipation rate estimates were from ~10^-10 to 10^-4 W/kg during the low-wind regime. During the high-wind regime, the estimates ranged from ~10^-7 to 10^-3 W/kg. It is likely that the highest dissipation rate estimates were erroneous as such high values have not been reported elsewhere in lakes. A simplified turbulent kinetic energy equation with dissipation rate, shear production and buoyancy production was tested. There was an imbalance of turbulence production and dissipation that was also related to the two meteorological regimes. Whether the equation should also include turbulent transport terms is an open question. The most important sources for errors were noise in the velocity time series and the effect of waves. It was shown that noise removal is an essential part of the ADV data analysis, however, noise-removal methods and methods for calculating the dissipation rate should be developed further. The installment of the ADV instrument should also be improved.

In my master's thesis I will examine the cessation of the Turku Naantali local train service between the years 1955 1972 in relation to Finland's post-war modernization efforts, future images of the 1950's, and value goals. My main argument is that the decline of the Turku Naantali local train traffic was not deterministic, but voluntary development, and the choosing of this path can only be understood in the context of Finland s modernization policy. The post-war break in the European influences, and the corresponding rise of the American Fordist consumerist ideal, were the key factors that formed the 'Zeitgeist' of the first post-war decades. The private car was interpreted as a symbol of (the growth in) wealth and prosperity in the adopted modernization vision, and motorization was deliberately set as a goal for urban and regional planning. Urban spatial restructuring to enable (car)traffic volume growth, became the main task for scientific urban and regional planning that started in the 1950s. It did not accommodate local rail services at all into it's purist vision of hierarchic urban centres and transport system. The local importance of passenger rail and the protests of it s passengers, opposing the reduction of service levels, were also marginalized by the State Railways board of trustees (rautatiehallitus). The actions taken by the urban planning actors and The State Railways clearly manifest political choosing of the future and technocratic exercise of power. My analysis on the community structure and the development of patronage levels shows that the insufficient passenger demand may not be considered as the main cause for the decline of Turku Naantali local rail services. The traditional state-owned railway monopolies have been typically burdened with high fixed costs, so they have often been active in cutting off the less economically productive local rail services, as the competitive position with road transport has intensified. The main reason for the decline of the Turku Naantali local train service were thus the actions taken by the state railways board of trustees, that systematically weakened the competitivity of local rail services, especially the substitution of the off-peak rail service with buses in December 1955. This meant the reduction in service levels below the level of potential passenger demand, which I regard as an expression of monopoly profit-seeking. Restriction of supply is often optimal from the monopoly s transport economic point of view, especially in the case of short-distance local services. The viewpoint of my research point is qualitative and based on critical hermeneutics. I try to understand the actors decision-making processes in their relation to the specific context of the particular time and the future prospects once open for past actors. On the other hand I try to show, that the actualized future could also have been different. The perspective of learning systems , that has become prominent in the social sciences, has stressed importance of knowing the past development paths and unrealized futures, in order to consciously disengage from the undesirable pathways. Social institutions and organizational cultures are not determined by their pathways. Local rail has been widely re-interpreted since the 1970's. Experience from the Helsinki metropolitan area, as well as from elsewhere in Europe, shows that the well-functioning local rail service is an attractive mode of transport for passengers. As the benefits from local rail are mainly realized at the local level, the implementation of such a system, however, invariably requires the initiative of local actors, as well as democratic decision-making structures securing their actual implementation power. In addition, the coordination of planning between it the community structure and rail transport is essential.

Kaksiosaisessa tutkielmassa käsitellään tutkielmien arvosanoja Helsingin yliopistossa. Tutkielman osassa I tarkastellaan, onko miesten ja naisten välillä eroa pro gradu -tutkielmien arvosanoissa ja millaisia eroja tiedekuntien välillä on. Tutkielmassa selvitetään, ovatko nuorena valmistuminen ja nopeasti tutkinnon suorittaminen yhteydessä hyviin pro gradu -tutkielmien arvosanoihin, sekä onko opinto-oikeuden perusteella yhteyttä pro gradu -tutkielmien arvosanoihin. Osan I aineisto on vuosina 2000-2012 suoritettujen tutkintojen pro gradu -tutkielmien arvosanat. Tutkielmassa selvitetään, onko tuona aikana pro gradu -tutkielmien arvosanoissa tapahtunut muutoksia, ja onko vuoden 2005 tutkinnonuudistus yhteydessä arvosanoihin. Koska pro gradu -tutkielman arvosana on tutkielmassa järjestysasteikollinen, malliksi valitaan kumulatiivinen logit-malli. Tutkielmassa käytettävä kumulatiivinen logit-malli on osittainen suhteellisten vastamittojen malli (partial proportional odds model). Tällä mallilla selitetään pro gradu -tukielmien arvosanoja sukupuolella, tiedekunnalla, valmistumisiällä, opintojen kestolla, opinto-oikeuden perusteella ja tutkinnon suoritusvuodella. Miehet saavat naisia parempia arvosanoja pro gradu -tutkielmista Helsingin yliopiston tasolla. Miehet eivät saa naisia parempia pro gradu -tutkielmien arvosanoja kaikissa tarkasteltavissa tiedekunnissa. Nuorempina valmistuneet, nopeammin opiskelleet ja ylioppilastutkinnon perusteella opinto-oikeuden saaneet opiskelijat saavat muita todennäköisemmin parhaimpia arvosanoja pro gradu -tutkielmista. Tiedekuntien välillä on suuria eroja pro gradu -tutkielmien arvosanoissa. Pro gradu -tutkielmien arvosanoissa ei ole tapahtunut suuria muutoksia vuosina 2000-2012. Osassa II tutkimusaihe on, onko kandidaatin ja pro gradu -tutkielmien arvosanojen ja opiskelijan sukupuolen välillä yhteys. Tätä tutkitaan tarkastelemalla molempien tutkintojen arvosanojen riippuvuutta sukupuolesta koko valtiotieteellisen tiedekunnan tasolla χ2-riippumattomuustestillä ja sen kaikkien viidentoista oppiaineen tasolla Fisherin eksaktilla ja Fisherin yhdistettyjen todennäköisyyksien testeillä. Myös arvosanojen riippuvuutta oppiaineesta tarkastellaan, jotta saadaan selville jakautuvatko arvosanat samoin kaikissa oppiaineissa. Miehet saavat valtiotieteellisessä tiedekunnassa parempia arvosanoja tutkielmista kuin naiset. Tämä johtuu siitä, että oppiaineiden välillä on suuria eroja niin arvosana- kuin sukupuolijakaumissa. Miesten paremmat arvosanat kandidaatin tutkielmissa ja erityisesti pro gradu -tutkielmissa selittyvät oppiaineiden välisillä eroilla. Miesvaltaisissa oppiaineissa saadaan muita oppiaineita parempia arvosanoja etenkin pro gradu -tutkielmista.

Through food it is possible to teach several things. Especially, it is important to teach about the environmental effects of food since many Finns have erroneous beliefs about them. This study's themes are central in the Finnish curriculums in the general sections as well as in geography's contents. The aim for this study is to create a teaching material about origin of food and environmental effects of food using inquiry-based learning (IBL). The teaching material is tested in upper secondary schools. Through this study is gathered information about students' awareness about the environmental effects of food and about IBL in some Finnish schools. Food research has increased during the last decades but it is fragmented to different fields of social studies. In the food system, grocery stores have increased their power in the expense of other actors. Consumers have great responsibility in taking into account the environment even though they do not have realistic opportunities to make a difference compared to other actors. Many factors have an effect to which products people buy and it is usually unconscious. The origin of food is rarely most important factor. In geography food issues are usually taught as one of the resources. IBL is a student directed learning method in which students find an answer to a question through inquiry. Advantages for this method are that students are engaged and motivated to solve the problem and they learn more effectively. Challenges for IBL are that it takes a lot of time, it is harder to control, classes are big and its definition is unclear. In geography IBL could be used much more than it is nowadays. IBL can also be used in environmental education since it develops critical thinking and through it students get meaningful experiences that promote environmental responsibility. This study is combination of action and case study. Study was implemented by holding three teaching experiment on geography classes in upper secondary schools. In the teaching experiment students tried to find information about the origins of food products for one dish they had chosen and reflected answers for questions about them. The students (N=60) filled surveys before and after the teaching experiment and their teachers (N=3) were interviewed after the teaching experiment. Some answers were analysed statistically and some through grouping them to different themes. Students' previous experiences of inquiry were mostly structured. Students enjoyed IBL because it was independent and they could work in pairs. They also thought that the subject was interesting. Teachers liked about the concrete subject and clear structure of the lesson. Students would have needed more time to do the exercise. Teachers thought that the most important challenge to adopt IBL is that it takes a lot of time, it is harder to control and students' attitudes are challenging. They still use similar exercises as the teaching experiment every week. Teachers did not have correct conceptions about IBL. Students had erroneous beliefs about the environmental effects of food production before the teaching experiment but they were more aware of them afterwards. After the students, they learned about the environmental effects of food production, ways to find information about the origin of food and to reflect the effects of their own choices. The teachers thought that during the lesson students realized the importance of their actions and choices. Most of the results are in line with previous research. After this study using food and other subjects that connect to students' daily lives in teaching increase their motivation to learn. In order to use more student directed learning methods, we have to change both curriculums and the way that we think about learning and education. Teachers also need training and teaching materials. The results of this study cannot be generalized to whole country but they can be an example and a basis for future more exhaustive research.

Tutkielmassani kuvailen, mitä tutkiva oppiminen ja tutkiva matematiikka on ja voisi olla. Tutkielmassani pyrin selvittämään avainhenkilöiden eli matematiikan opettajien matematiikan oppimiseen ja opettamiseen liittyvien uskomusten ja tutkivan oppimisen soveltamisen välistä yhteyttä. Lisäksi selvitän, miksi tutkivalla matematiikalla tulisi olla tukevampi asema opetuksessa ja oppimisessa. Pyrin myös käsittelemään tutkivaa oppimista kriittisesti ja tiedostaen, että oppimistyylejä on monia erilaisia eikä tutkiva oppiminen välttämättä ole kaikille tai kaikissa ryhmissä ja olosuhteissa paras vaihtoehto. Tutkiva oppiminen on konstruktivistisen oppimiskäsityksen pohjalta luotu malli, jossa oppilaat tutkivat itse jotakin ongelmaa ilman, että heille on ennalta opetettu asiasta kaikkia tarvittavia tietoja. Tutkivassa oppimisessa opettajan tehtävä on ohjata työskentelyä, ei antaa suoria vastauksia. Tutkivan oppimisen mallia voidaan pitää hyödyllisenä, sillä sen on todettu kehittävän erityisesti arkielämässä tarvittavia ongelmanratkaisutaitoja. Tutkivaa matematiikkaa sovellettaessa on kuitenkin mahdollista, että opiskelun painottuessa liian voimakkaasti asioiden ymmärryksen vahvistamiseen ja keksimiseen, algebralliset taidot jäävät puutteellisiksi. Hyvin olennaista tutkivaa matematiikkaa harjoitettaessa onkin opettajan näkemys sekä aiheenvalinnassa että tasapainon löytämisessä mekaanisen laskutaidon ja algebrallisen osaamisen välillä. Osana tutkielmaani toteutimme Christian Seppäsen ja Katja Huhkan kanssa tutkimuksen, jossa selvitimme opettajien uskomuksia ja käytänteitä tutkivasta oppimisesta. Tutkimuskysymykset oli asetettu seuraavasti: 1) Millä tavalla matematiikan opettajat ymmärtävät käsitteen 'tutkiva oppiminen'? 2) Kuinka paljon ja millä tavoin matematiikan opettajat käyttävät työssään tutkivan oppimisen menetelmiä? 3) Millainen yhteys matematiikan opettajien matematiikan oppimiseen ja opettamiseen liittyvillä uskomuksilla tutkivan oppimisen menetelmien käyttämiseen opetuksessa? Tutkimuksessa havaittiin, että vastanneiden opettajien käsitys tutkivasta oppimisesta oli hyvin linjassa yleisen määritelmän kanssa. Lisäksi havaittiin, että opettajat pitivät tutkivan oppimisen mallia hyödyllisenä, mutta tästä huolimatta sovelsivat sitä käytännössä melko vähän. Tarkemmin analysoituna havaittiin kuitenkin, että opettajien uskomuksilla laajemmin oli vaikutusta siihen kuinka paljon tutkivaa oppimista käytettiin omassa opetuksessa. Myös työtavoilla ja tutkivan oppimisen käyttämisellä näyttäisi olevan yhteys, mutta tästä ei voida päätellä syy-seuraussuhdetta. Opetuksen muuttaminen enemmän tutkivan oppimisen suuntaan voisi olla mahdollista vaikuttamalla opettajien uskomuksiin.

The aim of this thesis is to answer which factors define the location of industrial wind power. Most important source materials are the wind power surveys of the Regional Councils of Finland, written between 2010 and 2012. The surveys enlighten which factors are taken into account in wide scale wind power planning. I compare this information with papers in scientific journals and documentation such as legislation, documents and guidelines produced by different authorities as well as environmental impact assessments. I sample wind power location defining factors and their limit values from the surveys of the Regional Councils. This makes it possible to compare the factors and their values and to answer which factors are most common and how their values differ between different surveys. I also compare information about the interest groups that have taken part in the process. This helps in naming the most important interest groups and in understanding in which ways the views of the different actors can be gathered. Techno-economic factors affect wind power location. These factors are wind speed, proximity to electricity grid, proximity to electricity substations, connectivity to electricity grid, proximity to road network and the suitability of the land use for building. The single most important factor is the wind speed. The wind power plant's proximity to grid is more important than proximity to road network. Offshore wind power has slightly differing location factors e.g. the depth in the sea area. Other factors that often affect wind power location are settlements, locally and nationally valuable landscapes, locally and nationally significant cultural-historical environments and nationally significant prehistoric conservation areas, effects to the defence force, other conservation areas and bird areas. Several other factors have also been linked to wind power location. Additionally for finding out which factors determine wind power location it is interesting to know how the values given to these factors differ between surveys. In different surveys there are different values for example for how far the settlements are from the planned area, what is the minimum wind speed of the area and what is the minimum required area in square kilometers for wind power regional planning. In some surveys, the Natura regions are excluded whereas in some it might be possible to locate wind power within them. Wind power construction is in a likely turning point in Finland. Political goals, the economic support system, numerous private wind power projects as well as nation wide regional planning undertakings create possibilities for significant increase of wind power in the future. At the same time, the regulations and the operational environment of the companies change rapidly. A couple year old wind power surveys of the Regional Councils are already partly out of date because several wind power regulations have changed. Especially the guidelines linked to traffic and aviation safety have changed. It is important that these changes are taken into account in the regional planning. In the wind power surveys the existing wind power projects haven't often been weighted in the survey process. In this case, it is possible that there are ongoing projects in the region at the same time as there is a planning process going on but these areas are disconnected and in different places. It is important to observe the existing wind power projects already early in the process. The projects should also be weighted more heavily in the comparison of the different potential areas. Otherwise, there is a threat that those areas are excluded from the regional planning even though there isn't any weighty reason for them to be excluded.

Being physically active is one of the key aspects of health. Thus, equal opportunities for exercising in different places is one important factor of environmental justice and segregation prevention. Currently, there are no openly available scientific studies about actual physical activities in different parts of the Helsinki Metropolitan Area other than sports barometers. In the lack of comprehensive official data sources, user-generated data, like social media, may be used as a proxy for measuring the levels and geographical distribution of sports activities. In this thesis, I aim to assess 1) how Twitter tweets could be used as an indicator of sports activities, 2) how the sports tweets are distributed spatially and 3) which socio-economic factors can predict the number of sports tweets. For recognizing the tweets related to sports, out of 38.5 million tweets, I used Named Entity Matching with a list of sports-related keywords in Finnish, English and Estonian. Due to the spatial nature of my study, I needed tweets that contain a geotag, meaning that the tweet is attached to coordinates that indicate a location. However, only about 1% of tweets contain a geotag, and since 2019 Twitter doesn’t support precise geotagging anymore with some exceptions. Therefore, I implemented geoparsing methods to search for location names in the text and transform them to coordinates if the mentioned place was within the study area. After that, I aggregated the posts to postal code areas and used statistical and spatial methods to measure spatial autocorrelation and correlation with different socio-economic variables to examine the spatial patterns and socio-economic factors that affect the tweeting about sports. My results show that the sports tweets are concentrated mainly in the center of Helsinki, where the population is also concentrated. The distribution of the sports tweets exhibits local clusters like Tapiola, Leppävaara, Tikkurila and Pasila besides the largest cluster in the center of Helsinki. Sports-wise mapping of the tweets reveals that for example racket sport and skiing tweets are heavily concentrated around the corresponding facilities. Statistical analyses indicate that the number of tweets per inhabitant does not correlate with the education level or the amount of average income in the postal code area. The factors that predict the number of tweets per inhabitant are number of sports facilities per inhabitant, employment, and percentage of children (0-14 years old) in the postal code area. Keys to a successful study when analyzing Twitter data are geoparsing, having enough data, and a good language model to process it. Despite the promising results of this study, Twitter as indicator of physical activity should be studied more to better understand the kind of bias it inherently has before basing real-life decisions on Twitter research.

Spectral theory is a powerful tool when applied to differential equations. The fundamental result being the spectral theorem of Jon Von Neumann, which allows us to define the exponential of an unbounded operator, provided that the operator in question is self-adjoint. The problem we are considering in this thesis, is the self-adjointness of the Schr\"odinger operator $T = -\Delta + V$, a linear second-order partial differential operator that is fundamental to non-relativistic quantum mechanics. Here, $\Delta$ is the Laplacian and $V$ is some function that acts as a multiplication operator. We will study $T$ as a map from the Hilbert space $H = L^2(\mathbb{R}^d)$ to itself. In the case of unbounded operators, we are forced to restrict them to some suitable subspace. This is a common limitation when dealing with differential operators such as $T$ and the choice of the domain will usually play an important role. Our aim is to prove two theorems on the essential self-adjointness of $T$, both originally proven by Tosio Kato. We will start with some necessary notation fixing and other preliminaries in chapter 2. In chapter 3 basic concepts and theorems on operators in Hilbert spaces are presented, most importantly we will introduce some characterisations of self-adjointness. In chapter 4 we construct the test function space $D(\Omega)$ and introduce distributions, which are continuous linear functionals on $D(\Omega).$ These are needed as the domain for the adjoint of a differential operator can often be expressed as a subspace of the space of distributions. In chapter 5 we will show that $T$ is essentially self-adjoint on compactly supported smooth functions when $d=3$ and $V$ is a sum consisting of an $L^2$ term and a bounded term. This result is an application of the Kato-Rellich theorem which pertains to operators of the form $A+B$, where $B$ is bounded by $A$ in a suitable way. Here we will also need some results from Fourier analysis that will be revised briefly. In chapter 6 we introduce some mollification methods and prove Kato's distributional inequality, which is important in the proof of the main theorem in the final chapter and other results of similar nature. The main result of this thesis, presented in chapter 7, is a theorem originally conjectured by Barry Simon which says that $T$ is essentially self-adjoint on $C^\infty_c(\mathbb{R}^d)$, when $V$ is a non-negative locally square integrable function and $d$ is an arbitrary positive integer. The proof is based around mollification methods and the distributional inequality proven in the previous chapter. This last result, although fairly unphysical, is somewhat striking in the sense that usually for $T$ to be (essentially) self-adjoint, the dimension $d$ restricts the integrability properties of $V$ significantly.