Exercise sheet 3 pdf

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Exercise sheet 3

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MA17xexam01pdf

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Java-XSC : módulo complexo e complexo intervalar

This work aims to develop modules that will increase the computational power of the Java-XSC library, and XSC an acronym for "Language Extensions for Scientific Computation . This library is actually an extension of the Java programming language that has standard functions and routines elementary mathematics useful interval. in this study two modules were added to the library, namely, the modulus of complex numbers and complex numbers of module interval which together with the modules original numerical applications that are designed to allow, for example in the engineering field, can be used in devices running Java programs

Visualização das funções complexas e do Teorema Fundamental da Álgebra

Pós-graduação em Matemática Universitária - IGCE

Discours sur la nature des grandeurs négatives et imaginaires,

Mode of access: Internet.

A treatise on the geometrical representation of the square roots of negative quantities /

Mode of access: Internet.

GeoPlexo: um material manipulável para o ensino dos números complexos

This study aims to develop a manipulative material to assist the teaching and learning of Complex Numbers. Primarily, It tries to define the status of the current teaching of Complex Numbers, having as guide the bias of the research produced in dissertations and published on the website of Capes and the Virtual Library of Profmat from 2004 to 2014. It presents historical aspects of the theme, a mathematical foundation and a discussion of the use of manipulative materials as teaching resources for the teaching of mathematics. It introduces the manipulative material called GeoPlexo and a sequence of activities of potentiation and settling of complex numbers, explaining its use. It concludes with the importance of manipulative materials as a teaching resource for the teaching of Complex Numbers, especially regarding the geometric visualization of this mathematical object.

On the use of complex numbers in quantum models for information retrieval

Quantum-inspired models have recently attracted increasing attention in Information Retrieval. An intriguing characteristic of the mathematical framework of quantum theory is the presence of complex numbers. However, it is unclear what such numbers could or would actually represent or mean in Information Retrieval. The goal of this paper is to discuss the role of complex numbers within the context of Information Retrieval. First, we introduce how complex numbers are used in quantum probability theory. Then, we examine van Rijsbergen’s proposal of evoking complex valued representations of informations objects. We empirically show that such a representation is unlikely to be effective in practice (confuting its usefulness in Information Retrieval). We then explore alternative proposals which may be more successful at realising the power of complex numbers.

Construction of the transcomplex numbers from the complex numbers

A geometrical construction of the transcomplex numbers was given elsewhere. Here we simplify the transcomplex plane and construct the set of transcomplex numbers from the set of complex numbers. Thus transcomplex numbers and their arithmetic arise as consequences of their construction, not by an axiomatic development. This simplifes transcom- plex arithmetic, compared to the previous treatment, but retains totality so that every arithmetical operation can be applied to any transcomplex number(s) such that the result is a transcomplex number. Our proof establishes the consistency of transcomplex and transreal arithmetic and establishes the expected containment relationships amongst transcomplex, complex, transreal and real numbers. We discuss some of the advantages the transarithmetics have over their partial counterparts.

Paraconsistent Multivalued Logic and Coincidentia Oppositorum: Evaluation with Complex Numbers

Paraconsistent logic admits that the contradiction can be true. Let p be the truth values and P be a proposition. In paraconsistent logic the truth values of contradiction is . This equation has no real roots but admits complex roots . This is the result which leads to develop a multivalued logic to complex truth values. The sum of truth values being isomorphic to the vector of the plane, it is natural to relate the function V to the metric of the vector space R2. We will adopt as valuations the norms of vectors. The main objective of this paper is to establish a theory of truth-value evaluation for paraconsistent logics with the goal of using in analyzing ideological, mythical, religious and mystic belief systems.

Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.