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This volume offers English translations of three early works by Ernst Schröder (1841-1902), a mathematician and logician whose philosophical ruminations and pathbreaking contributions to algebraic logic attracted the admiration and ire of figures such as Dedekind, Frege, Husserl, and C. S. Peirce. Today he still engages the sympathetic interest of logicians and philosophers. The works translated record Schröder’s journey out of algebra into algebraic logic and document his transformation of George Boole’s opaque and unwieldy logical calculus into what we now recognize as Boolean algebra. Readers interested in algebraic logic and abstract algebra can look forward to a tour of the early history of those fields with a guide who was exceptionally thorough, unfailingly honest, and deeply reflective.
Algebraic logic. --- Logic, Symbolic and mathematical --- Logic. --- Mathematical logic. --- Universal algebra. --- Mathematics. --- History. --- Mathematics—Study and teaching. --- Mathematical Logic and Foundations. --- General Algebraic Systems. --- History of Mathematical Sciences. --- Mathematics Education. --- Math --- Science --- Algebra, Multiple --- Multiple algebra --- N-way algebra --- Universal algebra --- Algebra, Abstract --- Numbers, Complex --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Metamathematics --- Set theory --- Syllogism --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Philosophy --- Psychology --- Reasoning --- Thought and thinking --- Methodology
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Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highly-acclaimed work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications. The philosophy of the earlier book is retained, i.e., presenting the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. The wealth of examples and discussion prepares the reader for the complete arguments now given in the general case. Key Features of Symmetry, Representations, and Invariants: • Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus • Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux) • Self-contained chapters, appendices, comprehensive bibliography • More than 350 exercises (most with detailed hints for solutions) further explore main concepts • Serves as an excellent main text for a one-year course in Lie group theory • Benefits physicists as well as mathematicians as a reference work.
algebra --- topologie (wiskunde) --- Mathematical physics --- Topological groups. Lie groups --- Algebra --- wiskunde --- Group theory --- fysica --- Representations of groups --- Invariants --- Symmetry (Mathematics) --- Lie groups --- Représentations de groupes --- Analyse multidimensionnelle --- Symétrie (Mathématiques) --- Groupes de Lie --- Algèbre --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Representations of groups. --- Invariants. --- Symmetry (Mathematics). --- Algebra. --- Lie groups. --- Group theory. --- Geometry. --- Mathematical physics. --- Topological Groups. --- Group Theory and Generalizations. --- Mathematical Methods in Physics. --- Topological Groups, Lie Groups. --- General Algebraic Systems. --- Groups, Topological --- Continuous groups --- Physical mathematics --- Physics --- Mathematics --- Euclid's Elements --- Mathematical analysis --- Groups, Theory of --- Substitutions (Mathematics) --- Physics. --- Topological groups. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics
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