Orientador: Prof. Dr. Eduardo Guéron / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional - PROFMAT, Santo André, 2018. / Calculadoras são aparelhos comuns no cotidiano do homem moderno, contudo, os conceitos matemáticos envolvidos em sua concepção ainda são conhecidos por poucos. Durante séculos, a obstinação da humanidade em construir máquinas capazes de computar de forma autônoma resultou tanto no surgimento dos atuais computadores, como também em um magnífico legado de conhecimentos matemáticos agregados a tal conquista. Conteúdos tais como congruências e álgebra booleana suscitaram a revolução dos sistemas informatizados e tem sido amplamente explorados por meio de inúmeras aplicações, nossa trajetória perpassou pela aritmética modular, o teorema de Euler-Fermat e as classes residuais, além de bases numéricas, tópicos de eletrônica digital e funções booleanas, com foco no desenvolvimento de circuitos lógicos e o engendrar de componentes eletrônicos, que configuram a base para idealização e construção de calculadoras que efetuem as operações aritméticas em bases arbitrárias, objetivo preponderante deste trabalho. O esmiuçar das etapas de construção das calculadoras, viabiliza o aprofundamento dos conceitos matemáticos que a fomentaram. A abordagem dos temas supracitados culmina para aprimorar e evidenciar a aplicabilidade da matemática à essência da era moderna. / Calculators are common apparatuses in the everyday of modern man, however, the mathematical concepts involved in its conception are still known by few. For centuries, mankind¿s obstinacy in building machines capable of computing autonomously resulted in both the emergence of current computers and a magnificent legacy of mathematical knowledge added to such achievement. Contents such as congruences and Boolean algebra have aroused the revolution of computerized systems and it has been extensively explored through numerous applications, our trajectory ran through modular arithmetic, Euler-Fermat¿s theorem and residual classes, as well as numerical bases, topics of digital electronics and Boolean functions, focusing on the development of logic circuits and the generation of electronic components, which form the basis for the design and construction of calculators that perform arithmetic operations on arbitrary bases, a preponderant objective of this work. The to detail of the construction steps of the calculators, enables the deepening of the mathematical concepts that fomented it. The approach to the aforementioned themes culminates in improving and evidencing the applicability of mathematics to the essence of the modern era.

nÃo hà / Nesta dissertaÃÃo abordamos questÃes concernentes a MatemÃtica Financeira a partir de dois enfoques, o teÃrico metodolÃgico e o uso da tecnologia da mÃquina calculadora HP 12C. Nesse sentido, nosso objetivo foi de contribuir com o uso da calculadora HP 12C para os ensino fundamental, mÃdio e superior, proporcionando a esses alunos mais interesse e motivaÃÃo para compreender melhor um assunto tÃo importante para sua vida humana e profissional. Para tanto elaboramos um tutorial com operaÃÃes elementares sob o contexto da MatemÃtica Financeira proporcionando uma aprendizagem consistente para resolver situaÃÃes prÃticas e ter o discernimento entre comprar à vista e à prazo. Dessa forma o uso adequado do tutorial facilita um avanÃo na aprendizagem do contexto da MatemÃtica Financeira, auxiliando em uma avaliaÃÃo ou orÃamento financeiro sob o ponto de vista de prevà resultados de investimentos em um negÃcio. Abordamos tambÃm nesse contexto os sistemas de amortizaÃÃes de financiamentos atualmente em uso, capitalizaÃÃo simples e composta, fluxo de caixa, valor presente lÃquido, taxa interna de retorno e fundo de pensÃo. / The Financial Mathematics treated in this issue presents two points of view, the methodological theoretical and the use of the machine technology. Its purpose is to contribute with the use of the calculator HP 12C in the elementary, secondary and higher education, providing for the students more interest and motivation to learn subject like this in their professional lives. So, we elaborate a tutorial with elementary operations about the structure of Financial Mathematics that help to solve practice situations and obtain the discernment between buying the spot or forward. The adequate use of this tutorial, help to solve practice situations and understand how to work the Financial Mathematics and allowing to foresee the results of investments in business. We also treat in this tutorial the amortization of financing systems currently in use, simple and compound capitalization, cash flow, net present value, internal rate of return and pension fund.

Bakgrund: Vi är nu för tiden vana vid att använda oss av digitala hjälpmedel vid matematiska beräkningar. Detta tycks ha trängt undan behovet av standardalgoritmerna och andra skriftliga beräkningsmetoder. Är det så att dessa traditionella beräkningsmetoder har gått ur tiden? Kan digitala hjälpmedel ersätta alla delar som dessa metoder har bidragit till om vi ser till utvecklandet av matematisk förståelse? Min uppfattning är att det inte är så, utan att algoritmer och andra skriftliga beräkningsmetoder fortfarande har en viktig roll att spela i elevers utveckling av den matematiska förståelsen.  Syfte: Att undersöka hur man presenterar och återkopplar till skriftliga beräkningsmetoder och standardalgoritmer i matematikböcker från förskoleklass till gymnasiet. Metod: Studien är konstruerad utifrån en läroboksanalys där både en kvalitativ och en kvantitativ undersökning gjorts för att inringa både de övergripande strukturer som funnits i materialet, samt för att kunna se mer svåråtkomliga inslag, överlappningar och brister i det analyserade materialet. Tidigare forskning och litteratur inom området har beskrivits och löpande analyserats för att ge en bild av vad som sticker ut respektive överlappar åsikts- och resultatmässigt i de valda studierna och texterna. Resultat: Studien visar på en brist i matematikböckernas återkoppling till tidigare kunskaper. De kunskaper som främst är i fokus är de som rör standardalgoritmer och andra skriftliga beräkningsmetoder, men liknande brister går att se även inom andra matematiska områden. Bristen på återkoppling förekommer i merparten av de analyserade matematikböckerna och ger ett intryck av att fokus har förskjutits från algoritmkunskap till att eleven skall arbeta med digitala hjälpmedel. Det blir dock tydligt att även denna kunskap, om digitala hjälpmedel, inte heller prioriteras högt. Detta kan man se genom att beskrivningar av användning av digitala hjälpmedel förekommer mycket sparsamt i de analyserade matematikböckerna. Slutsats:Slutsatsen som kan dras av denna studie är att de analyserade matematikböckerna saknar den röda tråd som fås genom återkoppling och som skulle behövas för att ge bättre förutsättningar att skapa god matematisk förståelse. / Background: Nowadays digital tools, like calculators, are what we mainly use in our mathematical calculations. This has, seemingly, pushed away our need for other methods of calculation. We appear not to be in need of standard algorithms and other written calculating processes. Does this mean that these calculating processes are a thing of the past? Can digitals tools replace all parts contributed by the traditional methods from the perspective of development ofmathematical understanding? My point of view is that this is not the case. Instead, I believe that these “out of time” methods are highly important in the development of mathematical understanding. Purpose: To examine the way books of mathematics from first year of school all the way through the Swedish gymnasium courses, presents and reconnect to knowledge of written calculating methods and standard algorithms. Method: This study is constructed through an analysis of books of mathematics where both a qualitative and a quantitative part are included to cover both the overall structures of knowledge mediation in the analysed books and to find the more subtle elements, like knowledge overlaps or knowledge faults in the analysed books. Prior research and literature on the subject have been described and continuously analysed with the purpose to find opinions that stands out and also to find overlapping opinions or results, when comparing the chosen studies and texts. Result: The study points to a lack of reconnection to earlier knowledge in the analysed books. Foremost this concerns knowledge of standard algorithms and other types of written calculating methods, but a similar lack of reconnection is also seen within other areas of mathematics in the analysed books. The lack of reconnection occurs in most of the analysed books which gives an impression of focus being shifted from knowledge of algorithms and other written calculating methods to the advantage of digital tools. It does, however, also become clear that knowledge of how to use digital tools is equally not prioritized, since such information is sparsely presented in the analysed books. Conclusion: The conclusion that can be drawn from this study is that the analysed books of mathematicslack the common thread of knowledge that we get from reconnecting to earlier knowledge, and which would be needed to give better chances to create good mathematical understanding.

The main aim of this thesis was to study, choose and decribe techniques eligible for cryptography education. A pedagogically appropriate presentation for the selected techniques' principles was to be chosen. Another goal was to create an integrated modular web interface containing a calculator focused on cryptographic operations. The eligibility of techniques was assessed accordingly to the computing processes implied by these techniques and also accordingly to the ability of being presented in an illustrative way. A program simplifying calculations used in symetric and asymetric cryptography was designed and implemented. It disposes of a web interface and one of its parts is focused on steganographic techniques. On the other hand, any pedagogically appropriate presentation interconnecting this program with theoretical findings from this field was not found.

The following project has been carried out in collaboration with Abstracta AB (AAB), a company based in Lammhult with specialization in sound landscapes for indoor environments. The company manufactures different types of products with sound-absorbing properties where sustainability and design are in great focus. A new product idea of the company is based on developing an A-classified discreetly designed wall absorber that is considered more as a "wall" than a "wall with mounted absorbent on". The purpose of the project was to develop the following product on a conceptual level. A main research question with two underlying issues was developed that served as a support during the project. Question 1: How can an A-rated discreetly designed sound wall absorber be developed? 1.a: How can an A-rated sound wall absorber be developed? 1.b: How can a sound wall absorber achieve a discreetness in its design? The project followed a product development process where the mainly focus was on concept development and concept testing. The concept was developed based on data collected from a literature study and with the use of a sound absorption calculator. A sound absorption test and an examination form regarding the discrete modeling and design of the absorbent were performed for the final concept that the project resulted in. The project showed that an A-rated discreetly designed sound wall absorber can be developed through a process where design-critical specifications that affect the absorber's discrete design control how the object can be modeled. Via a sound absorption calculator, concepts can be designed that theoretically indicate an A-rate while the design-critical specifications are not exceeded. Based on the concept, a prototype is manufactured that can undergo a sound absorption test to determine the absorbent's actual sound absorption capacity. Finally, an examination is made to analyze whether the absorbent is considered a discrete alternative or not. Based on the project's results, the work process proved to be advantageous as the concept indicated a sound absorption capacity that exceeded the requirements of the A-rating and at the same time obtained a discreet design and modeling. This was achieved in connection with the manufacturing materials achieving their technical specifications and a square meter cost lower than expected. Based on the project's results, the work process proved to be advantageous as the concept indicated a sound absorption capacity that exceeded the requirements of the A-rating and at the same time obtained a discreet design and modeling. This was achieved in connection with the manufacturing materials achieving their technical specifications and a square meter cost lower than expected. In the further development of the final concept, a solution for how the absorbent is to be mounted on the wall must be developed as this was not focused on in the project based on its boundaries. To achieve a valid A-rate, an additional sound absorption test must also be performed where a larger object area of 10–12 m2 is tested. In future work, the concept's discrete modeling and design should also be examined based on physical treatment to review how the examination form's response results relate to this. / Följande projekt utförs i samarbete med Abstracta AB (AAB), ett företag som är stationerat i Lammhult och är specialiserade inom ljudlandskap för inomhusmiljöer. Företaget framställer olika typer av produkter med ljudabsorberande egenskaper där hållbarhet och design även är i stort fokus. En ny produktidé av företaget grundar sig i att utveckla en A-klassificerad diskret utformad väggabsorbent som betraktas mer som en ”vägg” än en ”vägg med uppmonterad absorbent på”. Syftet med projektet var att framta följande produkt på en konceptuell nivå. En huvudsaklig forskningsfråga med två underliggande frågeställningar togs fram som fungerade som ett stöd under projektets gång. Fråga 1: Hur kan en A-klassificerad diskret utformad ljudväggabsorbent utvecklas? 1.a: Hur kan en A-klassificerad ljudväggabsorbent utvecklas? 1.b: Hur kan en ljudväggabsorbent uppnå en diskrethet i sin design? Projektet följde en produktutvecklingsprocess där det största fokuset låg på konceptutvecklingen och koncepttestningen. Koncepten utvecklades utifrån insamlade data från en litteraturstudie och med användning av en ljudabsorptionskalkylator. Ett ljudabsorptionstest och ett undersökningsformulär gällande absorbentens diskreta utformning och design utfördes för det slutgiltiga konceptet som projektet resulterade i. Projektet visade att en A-klassificerad diskret utformad ljudväggabsorbent kan utvecklas genom en process där designkritiska specifikationer som berör absorbentens diskreta utformning styr hur objektet kan formges. Via en ljudabsorptionskalkylator kan koncept designas som teoretiskt indikerar en A-klassning samtidigt som de designkritiska specifikationerna ej överskrids. Utifrån konceptet tillverkas en prototyp som kan genomgå ett ljudabsorptionstest för att fastställa absorbentens verkliga ljudupptagningsförmåga. En undersökning görs slutligen för att analysera huruvida absorbenten betraktas som ett diskret alternativ eller ej. Utifrån projektets resultat visade sig arbetsprocessen vara fördelaktig då konceptet påvisade en ljudabsorptionsförmåga som överträffade A-klassningens krav och samtidigt erhöll en diskret utformning och design. Detta åstadkom i samband med att tillverkningsmaterialen uppnådde sina tekniska specifikationer och en kvadratmeterkostnad lägre än väntat. I fortsatt utveckling av det slutgiltiga konceptet måste en lösning till hur absorbenten ska monteras på väggen tas fram eftersom detta inte fokuserades på i projektet utifrån dess avgränsningar. För att en giltig A-klassificering ska nås måste även ytterligare ett ljudabsorptionstest utföras där en större objektarea på 10–12 m2 testas. I framtida arbete bör även konceptets diskreta utformning och design undersökas utifrån fysiska bemötanden för att granska hur undersökningsformulärets svarsresultat förhåller sig till detta.

Life Cycle Assessment (LCA) is a widely used method for evaluating the environmental impacts of a product throughout its entire life cycle. As a decision-making tool, LCA allows decision-makers to identify the environmental hotspots in a product or process, and to explore opportunities for improvement. However, while LCA has many potentials, it also has several limitations that need to be considered. One of the main limitations of LCA is the difficulty in obtaining accurate data, particularly for the upstream and downstream stages of a product's life cycle. Another limitation is the challenge of interpreting the results, as LCA involves complex calculations and assumptions that can be difficult for non-experts to understand. Despite these limitations, LCA remains a valuable tool for informing decision-making, and efforts are being made to address these limitations through the development of standardized methods and improved data collection and interpretation techniques. This paper provides an overview of LCA as a decision-making tool in the context of vaccine manufacturing, its potential and limitations, and the current state of research in this field.

Dagsljus i byggnader är viktigt för både den fysiska och psykiska hälsan. Dagsljusinsläpp i byggnader sker genom fönster, men fönster är även den byggnadskomponent som medför störst energiförluster i en byggnad. Därför finns det problem i att skapa en god balans mellan utformning, energieffektivisering och termisk komfort samtidigt som ett tillfredsställande dagsljus ska tillämpas i byggnader där människor vistas. Detta examensarbete som omfattar 15 hp syftar till att effektivisera samt förenkla bedömningen av ett tillfredsställande dagsljus, för att uppnå kraven i miljöcertifieringsmetoden Miljöbyggnad, där även intilliggande faktorer som energi och termiskt klimat studeras. Målet var att upprätta ett förprojekteringsverktyg för indikatorn Dagsljus som i framtiden kan användas av konsulter, arkitekter och andra inom byggbranschen när en byggnad ska miljöcertifieras enligt metoden Miljöbyggnad. För att skapa verktyget gjordes datamodeller av testrum med olika förutsättningar, där dagsljusfaktorn, DF, kontrollerades. Under arbetets gång har datorprogrammen Velux, ParaSol och Thermal Comfort Calculator använts. Parameterstudier utfördes för att åskådliggöra samband mellan dagsljusfaktor, fönsterarea samt rummets form och storlek, vilket resulterade i att två diagram upprättades. För att kontrollera att parameterstudiens resultat kan tillämpas för verkliga objekt och rum utfördes en fallstudie på byggnaden Ängsbacken i Sandviken. Denna fallstudie validerade att diagrammen som upprättats kan uppskatta en dagsljusfaktor, DF, för ett rum som sedan kan erhålla ett preliminärt betyg för indikatorn Dagsljus inom Miljöbyggnad. Diagrammen som upprättats kan användas som ett grovt förprojekteringsverktyg som kan tillämpas när konsult, arkitekt m.fl känner till rumsdjup samt fasadväggens area (bredden och höjden i rummet) men vill veta hur stort fönster som krävs för att uppnå BRONS eller SILVER för indikatorn Dagsljus inom Miljöbyggnad. Vidare kan vara intressant att studera om det även finns ett samband mellan de tre indikatorerna Dagsljus, Solvärmelast och Termiskt klimat och vilken påverkan fönsterglas, solavskärmningar m.m kan ha på dagsljusfaktorn. För samtliga testrum som modellerats och tillämpats i studien har betyget GULD erhållits för Solvärmelasten. För det Termiska klimatet fick samtliga testrum betyget SILVER. Dessa indikatorer verkar inte påverkas av rummets geometri i lika stor utsträckning som dagsljusfaktorn, som tar mer hänsyn till både rummets och fönstrets storlek samt utformning. Därför bör vid bedömning enligt Miljöbyggnad största vikt ligga på att uppfylla ett tillfredsställande dagsljusinsläpp genom att kontrollera att dagsljusfaktorn uppfylls i rummet, vilket enkelt kan utföras med hjälp av studiens förprojekteringsverktyg. Det effektiva förprojekteringsverktyget kan användas för att förenkla och påskynda bedömningsprocessen samt uppskatta ett betyg för indikatorn Dagsljus inom Miljöbyggnad. Genom att använda sig av verktyget i ett tidigt projekteringsskede, där användningen av tidskrävande datorprogram undviks, kan både kostnader och tid minimeras. / Daylight in buildings is important for both physical and mental health. Daylighting in buildings is transferred through windows, but the windows are also the building component that causes the greatest energy loss in a building. Therefore, there is a problem in creating a good balance between design, energy efficiency and thermal comfort while maintaining a sufficient daylight to be applied in buildings where people are staying. This thesis comprising 15 hp aims to efficiency and simplify the assessment of satisfying daylight, to achieve the requirements of the environmental certification method Miljöbyggnad, where neighboring factors such as energy and the thermal environment is studied. The goal was to establish a pre-planning tool for the indicator Daylight that can be used in the future by consultants and similar when a building is assessed by environmental certification according to the method Miljöbyggnad. The tool is based on computer models of experimental room with different conditions where the daylight factor, DF, was controlled. The computer programs Velux, ParaSol and Thermal Comfort Calculator where applied during the study. Parametric studies were performed to illustrate the connection between daylight factor, window area and the shape and size of the room, resulting in the establishment of two charts. To check that the parameter results of the study can be applied to real-world objects and rooms a case study was performed on the building Ängsbacken in Sandviken. This case study validated that the diagrams drawn can appreciate a daylight factor, DF, for a room that can then obtain a preliminary rating for the indicator Daylight in Miljöbyggnad. The diagrams can be used as a rough pre-planning tool that can be applied when the consultant, architect or similar knows the room depth and facadewall area (width and height of the room) but want to know how big window needed to achieve BRONZE or SILVER for indicator Daylight in Miljöbyggnad. In the future it might be interesting to study if there is also a correlation between the three indicators Daylight, Solar Thermal Load and Thermal environment and the impact of windows, sun screens etc. which can affect the daylight factor. For all test room modeled and applied in the study, grade GOLD were obtained for the Solarheating. For the Thermal environment all the test room obtained the grade SILVER. These indicators seem unaffected by the geometry just as much as the daylight factor, which takes more into account both the room and the window size and design. Therefore the assessment according to Miljöbyggnad paramount lie on meeting a satisfying daylight by checking that the daylight factor is fulfilled in the room, which can easily be performed with the help of this studies pre-planning tool. The effective pre-planning tool can be used to simplify and speed up the evaluation process and appreciate a score for indicator Daylight in Miljöbyggnad. By making use of the tool in an early planning stage, where the use of time-consuming computer programs is avoided, both the cost and time can be minimized.

The major aims of this paper are to present how we can improve the students understanding and involvement in mathematics by using a programming/graphic calculator. I will use differentials as examples such as differentiation ,integrals and differential equations, creating lines of slopes for differential equation of the type y’= f(x,y) . Find the solution of some differential equations by using regression and create the graph connected to the differential equation. As we have different approaches to solving a problem, it is a hope the students interest in mathematics will improve. The tools used will be programming, graphic commands as plot, f-line, etc. One goal is also to show how we can create small programs solving problems in mathematics. For many students this will be a stepping stone for further work with programming. The programs used can be copied using the program FA 124 that can be downloaded from Casios homepages. On request I can send you the programs.

The major aims of this paper are to present how we can improve the students understanding and involvement in mathematics by using a programming/graphic calculator. I will use differentials as examples such as differentiation ,integrals and differential equations, creating lines of slopes for differential equation of the type y’= f(x,y) . Find the solution of some differential equations by using regression and create the graph connected to the differential equation. As we have different approaches to solving a problem, it is a hope the students interest in mathematics will improve. The tools used will be programming, graphic commands as plot, f-line, etc. One goal is also to show how we can create small programs solving problems in mathematics. For many students this will be a stepping stone for further work with programming. The programs used can be copied using the program FA 124 that can be downloaded from Casios homepages. On request I can send you the programs.

Made available in DSpace on 2016-04-27T16:57:23Z (GMT). No. of bitstreams: 1 Natalia Coelho Soares.pdf: 1911222 bytes, checksum: 49a1ece22c9ff2a82a16d9ff71201d25 (MD5) Previous issue date: 2012-12-10 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This research aimed to investigate whether and how eighth-grade middle school students who have difficulty in solving mathematical operations with natural numbers deepen their knowledge in this field when they have the opportunity to work with technological tools that are not frequently used in classroom. Data collection was based on twelve semi-structured interviews, which were done according to André (2008) concept of study of case. The students conceptions about solving mathematical operations with natural numbers were analyzed based mainly on the APOS theory. It was concluded that by introducing technological tools that are not frequently used in classroom, such as abacus and printing calculator, the students were allowed to deepen their knowledge about natural numbers and, consequently, reframe their conceptions about it / Este trabalho apresenta uma pesquisa de mestrado que teve o objetivo de investigar se e como, alunos do 8º ano do ensino fundamental, que apresentam dificuldades na resolução de atividades matemáticas que envolvem operações com os números naturais, aprofundam seus conhecimentos, quando lhes é dada a oportunidade do uso de tecnologias não usuais em sala de aula. Para a coleta de dados, foram realizadas doze entrevistas semiestruturadas que caracterizaram o estudo de caso, conforme definido por André (2008). As análises das concepções construídas pelos sujeitos basearam-se sobretudo na teoria APOS. Concluiu-se que a introdução das tecnologias não usuais, como o ábaco e, principalmente, a calculadora com impressora possibilitaram o aprofundamento e a consequente ressignificação das concepções dos sujeitos sobre as operações dos números naturais