**Author**: Yvette Kosmann-Schwarzbach

**Publisher:** Springer Science & Business Media

**ISBN:** 0387788662

**Category : **Mathematics

**Languages : **en

**Pages : **196

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**Book Description**
- Combines material from many areas of mathematics, including algebra, geometry, and analysis, so students see connections between these areas - Applies material to physics so students appreciate the applications of abstract mathematics - Assumes only linear algebra and calculus, making an advanced subject accessible to undergraduates - Includes 142 exercises, many with hints or complete solutions, so text may be used in the classroom or for self study

**Author**: Yvette Kosmann-Schwarzbach

**Publisher:** Springer Science & Business Media

**ISBN:** 0387788662

**Category : **Mathematics

**Languages : **en

**Pages : **196

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**Book Description**
- Combines material from many areas of mathematics, including algebra, geometry, and analysis, so students see connections between these areas - Applies material to physics so students appreciate the applications of abstract mathematics - Assumes only linear algebra and calculus, making an advanced subject accessible to undergraduates - Includes 142 exercises, many with hints or complete solutions, so text may be used in the classroom or for self study

**Author**: Bernard L. Johnston

**Publisher:** CRC Press

**ISBN:** 9780849303012

**Category : **Mathematics

**Languages : **en

**Pages : **276

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**Book Description**
This textbook presents modern algebra from the ground up using numbers and symmetry. The idea of a ring and of a field are introduced in the context of concrete number systems. Groups arise from considering transformations of simple geometric objects. The analysis of symmetry provides the student with a visual introduction to the central algebraic notion of isomorphism. Designed for a typical one-semester undergraduate course in modern algebra, it provides a gentle introduction to the subject by allowing students to see the ideas at work in accessible examples, rather than plunging them immediately into a sea of formalism. The student is involved at once with interesting algebraic structures, such as the Gaussian integers and the various rings of integers modulo n, and is encouraged to take the time to explore and become familiar with those structures. In terms of classical algebraic structures, the text divides roughly into three parts:

**Author**: Alexey P. Isaev

**Publisher:** World Scientific Publishing Company

**ISBN:** 9789811217401

**Category : **Science

**Languages : **en

**Pages : **500

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**Book Description**
This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras. The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed. Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C[Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed. Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO↑(p, q) are studied. For this purpose, Clifford algebras in spaces Rp, q are introduced and representations of these algebras are discussed.

**Author**: P C Argyres

**Publisher:** World Scientific

**ISBN:** 9814481602

**Category : **Science

**Languages : **en

**Pages : **804

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**Book Description**
The book contains the text of lectures given at the third of a series of biennial symposia in mathematical physics held in odd-numbered years. The subject of the symposium is the frontiers of mathematical physics. It deals with quantum phenomena and includes topics such as string theory and quantum gravity, particle physics and field theory, non-communative geometry, integrable models and infinite dimensional symmetry groups, quantum computing and information processing, and quantum chaos. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings) • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents:Freydoon Mansouri Memorial LecturesAlgebras and RepresentationsQuantization and Quantum GravityD<4 Field TheoriesString and Brane WorldvolumesD>3 Field Theories and GravityString TheoryLoop Quantum GravityLorentz ViolationApplications Readership: Researchers, academics and postgraduates in high energy physics, mathematical physics and atomic physics. Keywords:Mathematical Physics;Strings;Quantum Gravity;Noncommutative Geometry

**Author**: David W. Farmer

**Publisher:** American Mathematical Soc.

**ISBN:** 0821804502

**Category : **Mathematics

**Languages : **en

**Pages : **102

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**Book Description**
This nicely produced volume focuses on the informal analysis of geometrical patterns. By means of a series of carefully selected tasks, the book leads readers to discover some real mathematics. There are no formulas to memorize and no procedures to follow. It is a guide to start you in the right direction and bring you back if you stray too far. Discovery is left to you.

**Author**: Paul B. Yale

**Publisher:** Courier Corporation

**ISBN:** 0486169324

**Category : **Mathematics

**Languages : **en

**Pages : **288

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**Book Description**
DIVIntroduction to the geometry of euclidean, affine and projective spaces with special emphasis on the important groups of symmetries of these spaces. Many exercises, extensive bibliography. Advanced undergraduate level. /div

**Author**: Yvette Kosmann-Schwarzbach

**Publisher:** Springer Nature

**ISBN:** 3030943607

**Category : **Mathematics

**Languages : **en

**Pages : **251

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**Book Description**
- Combines material from many areas of mathematics, including algebra, geometry, and analysis, so students see connections between these areas - Applies material to physics so students appreciate the applications of abstract mathematics - Assumes only linear algebra and calculus, making an advanced subject accessible to undergraduates - Includes 142 exercises, many with hints or complete solutions, so text may be used in the classroom or for self study

**Author**: I. Hargittai

**Publisher:** Elsevier

**ISBN:** 148329949X

**Category : **Science

**Languages : **en

**Pages : **1084

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**Book Description**
Symmetry 2 aims to present an overview of the contemporary status of symmetry studies, particularly in the arts and sciences, emphasizing both its role and importance. Symmetry is not only one of the fundamental concepts in science, but is also possibly the best unifying concept between various branches of science, the arts and other human activities. Whereas symmetry has been considered important for centuries primarily for its aesthetic appeal, this century has witnessed a dramatic enhancement of its status as a cornerstone in the sciences. In addition to traditionally symmetry-oriented fields such as crystallography and spectroscopy, the concept has made headway in fields as varied as reaction chemistry, nuclear physics, and the study of the origin of the universe. The book was initiated in response to the success of the first volume, which not only received good reviews, but received the award for "The Best Single Issue of a Journal" by the Association of American Publishers for 1986. The second volume extends the application of symmetry to new fields, such as medical sciences and economics, as well as investigating further certain topics introduced in Symmetry. The book is extensively illustrated and with over 64 contributions from 16 countries presents an international overview of the nature and diversity of symmetry studies today.

**Author**: Mark A. Armstrong

**Publisher:** Springer Science & Business Media

**ISBN:** 9780387966755

**Category : **Mathematics

**Languages : **en

**Pages : **204

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**Book Description**
This is a gentle introduction to the vocabulary and many of the highlights of elementary group theory. Written in an informal style, the material is divided into short sections, each of which deals with an important result or a new idea. Includes more than 300 exercises and approximately 60 illustrations.

**Author**:

**Publisher:** Academic Press

**ISBN:** 9780080873657

**Category : **Mathematics

**Languages : **en

**Pages : **431

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**Book Description**
Symmetry Groups and Their Applications