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دانلود کتاب Contemporary Abstract Algebra
دانلود کتاب جبر انتزاعی معاصر
مشخصات کتاب
Contemporary Abstract Algebra
دسته بندی: جبر ویرایش: 9 نویسندگان: Joseph A. Gallian سری: ISBN (شابک) : 0618514716, 9780618514717 ناشر: Houghton Mifflin سال نشر: 2004 تعداد صفحات: 631 زبان: English فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود) حجم فایل: 6 مگابایت
قیمت کتاب (تومان) : 47,000
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توضیحاتی در مورد کتاب جبر انتزاعی معاصر
جوزف گالیان یک محقق شناخته شده فعال و معلم برنده جایزه است. جبر انتزاعی معاصر او، 6/e، شامل موضوعات چالش برانگیز در جبر انتزاعی و همچنین شکل‌ها، جداول، عکس‌ها، نمودارها، زندگی‌نامه‌ها، تمرین‌های کامپیوتری، و خواندن‌های پیشنهادی است که به موضوع احساس فعلی می‌دهد و محتوا را جالب و مرتبط می‌کند. دانش آموزان.
توضیحاتی درمورد کتاب به خارجی
Joseph Gallian is a well-known active researcher and award-winning teacher. His Contemporary Abstract Algebra, 6/e, includes challenging topics in abstract algebra as well as numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings that give the subject a current feel and makes the content interesting and relevant for students.
فهرست مطالب
Contents Preface Part 1: Integers and Equivalence Relations Ch 0: Preliminaries Properties of Integers Modular Arithmetic Complex Numbers Mathematical Induction Equivalence Relations Functions (Mappings) Exercises Computer Exercises Suggested Readings Part 2: Groups Ch 1: Introduction to Groups Symmetries of a Square The Dihedral Groups Exercises Suggested Reading Suggested Website Ch 2: Groups Definition and Examples of Groups Elementary Properties of Groups Historical Note Exercises Computer Exercises References Suggested Readings Ch 3: Finite Groups; Subgroups Terminology and Notation Subgroup Tests Examples of Subgroups Exercises Computer Exercises Suggested Readings Ch 4: Cyclic Groups Properties of Cyclic Groups Classification of Subgroups of Cyclic Groups Exercises Computer Exercises Suggested Reading Ch 5: Permutation Groups Definition and Notation Cycle Notation Properties of Permutations A Check-Digit Scheme Based on D5 Exercises Computer Exercises References Suggested Readings Ch 6: Isomorphisms Motivation Definition and Examples Cayley\'s Theorem Properties of Isomorphisms Automorphisms Exercises Reference Computer Exercises Ch 7: Cosets and Lagrange\'s Theorem Properties of Cosets Lagrange\'s Theorem and Consequences An Application of Cosets to Permutation Groups The Rotation Group of a Cube and a Soccer Ball An Application of Cosets to the Rubik\'s Cube Exercises Computer Exercises Ch 8: External Direct Products Definition and Examples Properties of External Direct Products The Group of Units Modulo n as an External Direct Product Applications Exercises Computer Exercises References Suggested Readings Ch 9: Normal Subgroups and Factor Groups Normal Subgroups Factor Groups Applications of Factor Groups Internal Direct Products Exercises Suggested Readings Ch 10: Group Homomorphisms Definition and Examples Properties of Homomorphisms The First Isomorphism Theorem Exercises Computer Exercise Suggested Readings Ch 11: Fundamental Theorem of Finite Abelian Groups The Fundamental Theorem The Isomorphism Classes of Abelian Groups Proof of the Fundamental Theorem Exercises Computer Exercises Reference Suggested Readings Suggested Website Part 3: Rings Ch 12: Introduction to Rings Motivation and Definition Examples of Rings Properties of Rings Subrings Exercises Computer Exercises Suggested Reading Ch 13: Integral Domains Definition and Examples Fields Characteristic of a Ring Exercises Computer Exercises Suggested Readings Ch 14: Ideals and Factor Rings Ideals Factor Rings Prime Ideals and Maximal Ideals Exercises Computer Exercises Suggested Reading Ch 15: Ring Homomorphisms Definition and Examples Properties of Ring Homomorphisms The Field of Quotients Exercises Suggested Readings Ch 16: Polynomial Rings Notation and Terminology The Division Algorithm and Consequences Exercises Suggested Reading Ch 17: Factorization of Polynomials Reducibility Tests Irreducibility Tests Unique Factorization in Z[x] Weird Dice: An Application of Unique Factorization Exercises Computer Exercises Reference Suggested Readings Ch 18: Divisibility in Integral Domains Irreducibles, Primes Historical Discussion of Fermat\'s Last Theorem Unique Factorization Domains Euclidean Domains Exercises Computer Exercise References Suggested Readings Suggested Video Suggested Websites Part 4: Fields Ch 19: Vector Spaces Definition and Examples Subspaces Linear Independence Exercises Ch 20: Extension Fields The Fundamental Theorem of Field Theory Splitting Fields Zeros of an Irreducible Polynomial Exercises Ch 21: Algebraic Extensions Characterization of Extensions Finite Extensions Properties of Algebraic Extensions Exercises Suggested Readings Ch 22: Finite Fields Classification of Finite Fields Structure of Finite Fields Subfields of a Finite Field Exercises Computer Exercises Suggested Reading Ch 23: Geometric Constructions Historical Discussion of Geometric Constructions Constructible Numbers Angle-Trisectors and Circle-Squarers Exercises References Suggested Website Part 5: Special Topics Ch 24: Sylow Theorems Conjugacy Classes The Class Equation The Sylow Theorems Applications of Sylow Theorems Exercises Computer Exercises Suggested Reading Ch 25: Finite Simple Groups Historical Background Nonsimplicity Tests The Simplicity of A5 The Fields Medal The Cole Prize Exercises Computer Exercises References Suggested Readings Ch 26: Generators and Relations Motivation Definitions and Notation Free Group Generators and Relations Classification of Groups of Order Up to 15 Characterization of Dihedral Groups Realizing the Dihedral Groups with Mirrors Exercises References Suggested Readings Ch 27: Symmetry Groups Isometries Classification of Finite Plane Symmetry Groups Classification of Finite Groups of Rotations in R3 Exercises References Suggested Readings Suggested Website Ch 28: Frieze Groups and Crystallographic Groups The Frieze Groups The Crystallographic Groups Identification of Plane Periodic Patterns Exercises References Suggested Readings Suggested Websites Ch 29: Symmetry and Counting Motivation Burnside\'s Theorem Applications Group Action Exercises Suggested Readings Ch 30: Cayley Digraphs of Groups Motivation The Cayley Digraph of a Group Hamiltonian Circuits and Paths Some Applications Exercises References Suggested Readings Suggested Website Suggested DVD Suggested Software Ch 31: Introduction to Algebraic Coding Theory Motivation Linear Codes Parity-Check Matrix Decoding Coset Decoding Exercises Reference Suggested Readings Ch 32: An Introduction to Galois Theory Fundamental Theorem of Galois Theory Solvability of Polynomials by Radicals Insolvability of a Quintic Exercises Reference Suggested Readings Suggested Website Ch 33: Cyclotomic Extensions Motivation Cyclotomic Polynomials The Constructible Regular n-gons Exercises Computer Exercises Selected Answers Index of Mathematicians Index of Terms
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