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  • Modular Representation Theory of Finite Groups
    Modular Representation Theory of Finite Groups

    Representation theory studies maps from groups into the general linear group of a finite-dimensional vector space.For finite groups the theory comes in two distinct flavours.In the 'semisimple case' (for example over the field of complex numbers) one can use character theory to completely understand the representations.This by far is not sufficient when the characteristic of the field divides the order of the group. Modular Representation Theory of finite Groups comprises this second situation.Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as well as Green's direct analysis of indecomposable representations.There is also the strategy of writing the category of all representations as the direct product of certain subcategories, the so-called 'blocks' of the group.Brauer's work then establishes correspondences between the blocksof the original group and blocks of certain subgroups the philosophy being that one is thereby reduced to a simpler situation.In particular, one can measure how nonsemisimple a category a block is by the size and structure of its so-called 'defect group'.All these concepts are made explicit for the example of the special linear group of two-by-two matrices over a finite prime field. Although the presentation is strongly biased towards the module theoretic point of view an attempt is made to strike a certain balance by also showing the reader the group theoretic approach.In particular, in the case of defect groups a detailed proof of the equivalence of the two approaches is given.This book aims to familiarize students at the masters level with the basic results, tools, and techniques of a beautiful and important algebraic theory.Some basic algebra together with the semisimple case are assumed to be known, although all facts to be used are restated (without proofs) inthe text.Otherwise the book is entirely self-contained.

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  • Deflating Mental Representation
    Deflating Mental Representation


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  • Multiple Representation Dice
    Multiple Representation Dice

    Young learners will be on a roll with numbers and number sense with these Multiple Representation Dice. This set of 16 dice feature 4 different ways to represent a number, to support childrens learning of number sense. Includes 10 frames, base 10,

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  • The Concept of Representation
    The Concept of Representation

    Being concerned with representation, this book is about an idea, a concept, a word.It is primarily a conceptual analysis, not a historical study of the way in which representative government has evolved, nor yet an empirical investigation of the behavior of contemporary representatives or the expectations voters have about them.Yet, although the book is about a word, it is not about mere words, not merely about words.For the social philosopher, for the social scientist, words are not "mere"; they are the tools of his trade and a vital part of his subject matter.Since human beings are not merely political animals but also language-using animals, their behavior is shaped by their ideas.What they do and how they do it depends upon how they see themselves and their world, and this in turn depends upon the concepts through which they see.Learning what "representation" means and learning how to represent are intimately connected.But even beyond this, the social theorist sees the world through a network of concepts.Our words define and delimit our world in important ways, and this is particularly true of the world of human and social things. For a zoologist may capture a rare specimen and simply observe it; but who can capture an instance of representation (or of power, or of interest)?Such things, too, can be observed, but the observation always presupposes at least a rudimentary conception of what representation (or power, or interest) is, what counts as representation, where it leaves off and some other phenomenon begins.Questions about what representation is, or is like, are not fully separable from the question of what "representation" means.This book approaches the former questions by way of the latter.

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  • What is the polar representation of a Cartesian representation?

    The polar representation of a Cartesian representation is a way of expressing a point in the Cartesian plane using polar coordinates. In the polar representation, a point is described by its distance from the origin (r) and the angle it makes with the positive x-axis (θ). This is in contrast to the Cartesian representation, which describes a point using its x and y coordinates. The polar representation provides a different way of understanding and visualizing points in the plane, and it can be useful in certain mathematical and scientific contexts.

  • Which representation method?

    The representation method that should be used depends on the specific data being analyzed and the goals of the analysis. For categorical data, bar graphs or pie charts are commonly used to show the distribution of different categories. For numerical data, histograms or box plots can be used to visualize the distribution and central tendency of the data. Scatter plots are useful for showing the relationship between two numerical variables. Ultimately, the best representation method is one that effectively communicates the key insights from the data in a clear and concise manner.

  • What is the linear factor representation and the polynomial representation?

    The linear factor representation of a polynomial is a way of expressing the polynomial as a product of linear factors. For example, the linear factor representation of the polynomial x^2 - 4 is (x-2)(x+2). This representation helps in finding the roots of the polynomial. The polynomial representation is the standard way of expressing a polynomial as a sum of terms, each containing a variable raised to a power. For example, the polynomial representation of x^2 - 4 is x^2 - 4. This representation helps in performing operations like addition, subtraction, multiplication, and division of polynomials.

  • Is the standard representation the same as the exponential representation?

    No, the standard representation and the exponential representation are not the same. The standard representation of a number is typically in the form of a decimal or fraction, while the exponential representation is in the form of a number raised to a power. For example, the standard representation of 100 is simply "100," while the exponential representation is "10^2." These two representations convey the same value but are written in different forms.

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  • Picturebooks: Representation and Narration
    Picturebooks: Representation and Narration

    This volume discusses the aesthetic and cognitive challenges of modern picturebooks from different countries, such as Denmark, France, Germany, Norway, Spain, Sweden, United Kingdom, and USA.The overarching issue concerns the mutual relationship between representation and narration by means of the picturebooks’ multimodal character.Moreover, this volume includes the main lines of debate and approaches to picturebooks by international leading researchers in the field.Topics covered are the impact of paratexts and interpictorial allusions, the relationship between artists’ books, crossover picturebooks, and picturebooks for adults, the narrative defiance of wordless picturebooks, the representation of emotions in images and text, and the depiction of hybrid characters in picturebooks.The enlargement of the picturebook corpus beyond an Anglo-American picturebook canon opens up new horizons and highlights the diverging styles and genre shifts in modern picturebooks.This tendency also demonstrates the influence of specific authors and illustrators on the appreciation of the picturebook genre, as in the case of Astrid Lindgren’s picturebooks and the picturebooks created by renowned illustrators, such as Anthony Browne, Wolf Erlbruch, Stian Hole, and Bruno Munari.This book will be the definite contribution to contemporary picturebook research for many years to come.

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  • Shakespeare and Queer Representation
    Shakespeare and Queer Representation

    In this engaging and accessible guidebook, Stephen Guy-Bray uses queer theory to argue that in many of Shakespeare’s works representation itself becomes queer. Shakespeare often uses representation, not just as a lens through which to tell a story, but as a textual tool in itself.Shakespeare and Queer Representation includes a thorough introduction that discusses how we can define queer representation, with each chapter developing these theories to examine works that span the entire career of Shakespeare, including his sonnets, Venus and Adonis, The Rape of Lucrece, King John, Macbeth, and Cymbeline.The book highlights the extent to which Shakespeare’s works can be seen to anticipate, and even to extend, many of the insights of the latest developments in queer theory. This thought-provoking and evocative book is an essential guide for students studying Shakespeare and Renaissance literature, gender studies, and queer literary theory.

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  • Representation Theory : A First Course
    Representation Theory : A First Course

    The primary goal of these lectures is to introduce a beginner to the finite­ dimensional representations of Lie groups and Lie algebras.Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book.Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces.It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians.This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways.It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference.This idea essentially determines the choice of material covered here.As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific.

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  • Representation Theory : A First Course
    Representation Theory : A First Course

    The primary goal of these lectures is to introduce a beginner to the finite­ dimensional representations of Lie groups and Lie algebras.Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book.Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces.It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians.This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways.It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference.This idea essentially determines the choice of material covered here.As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific.

    Price: 79.99 £ | Shipping*: 0.00 £
  • What is interest representation?

    Interest representation refers to the process of advocating for the interests and concerns of a particular group or organization to policymakers, government officials, or other decision-makers. This can involve lobbying, public relations, and other forms of communication to influence policy decisions in favor of the represented group. Interest representation is a key component of democratic societies, as it allows for diverse voices and perspectives to be heard in the policymaking process. It is often carried out by professional lobbyists, advocacy groups, trade associations, and other organizations that work on behalf of their members or constituents.

  • What are representation matrices?

    Representation matrices are matrices that represent linear transformations or operators. They are used to represent the action of a linear transformation on a vector space. The elements of the representation matrix correspond to the coefficients of the linear combination of the basis vectors of the vector space. By using representation matrices, we can easily perform operations such as composition of linear transformations and finding the inverse of a linear transformation.

  • What is the correct grammatical representation of the term fixed-point representation?

    The correct grammatical representation of the term fixed-point representation is a compound noun. In this term, "fixed-point" acts as an adjective describing the type of representation being discussed. The hyphen between "fixed" and "point" indicates that these two words are functioning together as a single unit modifying the noun "representation." This grammatical structure helps clarify that the representation being referred to is specifically of the fixed-point type.

  • Can you calculate the decimal representation of the following number in Q44 representation?

    No, I cannot calculate the decimal representation of a number in Q44 representation without knowing the specific number. In order to convert a number from Q44 representation to decimal, you would need to know the value of each digit in the Q44 representation and then perform the necessary calculations to convert it to decimal.

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