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از ساعت 7 صبح تا 10 شب
ویرایش: [1 ed.]
نویسندگان: Joseph H. Silverman
سری: Pure and Applied Undergraduate Texts, 55
ISBN (شابک) : 1470468603, 9781470468606
ناشر: American Mathematical Society
سال نشر: 2022
تعداد صفحات: 567
[589]
زبان: English
فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود)
حجم فایل: 5 Mb
در صورت تبدیل فایل کتاب Abstract Algebra: An Integrated Approach به فرمت های PDF، EPUB، AZW3، MOBI و یا DJVU می توانید به پشتیبان اطلاع دهید تا فایل مورد نظر را تبدیل نمایند.
توجه داشته باشید کتاب جبر چکیده: یک رویکرد یکپارچه نسخه زبان اصلی می باشد و کتاب ترجمه شده به فارسی نمی باشد. وبسایت اینترنشنال لایبرری ارائه دهنده کتاب های زبان اصلی می باشد و هیچ گونه کتاب ترجمه شده یا نوشته شده به فارسی را ارائه نمی دهد.
Preface Chapter 1. A Potpourri of Preliminary Topics 1.1. What Are Definitions, Axioms, and Proofs? 1.2. Mathematical Credos to Live By! 1.3. A Smidgeon of Mathematical Logic and Some Proof Techniques 1.4. A Smidgeon of Set Theory 1.5. Functions 1.6. Equivalence Relations 1.7. Mathematical Induction 1.8. A Smidgeon of Number Theory 1.9. A Smidgeon of Combinatorics Exercises Chapter 2. Groups — Part 1 2.1. Introduction to Groups 2.2. Abstract Groups 2.3. Interesting Examples of Groups 2.4. Group Homomorphisms 2.5. Subgroups, Cosets, and Lagrange's Theorem 2.6. Products of Groups Exercises Chapter 3. Rings — Part 1 3.1. Introduction to Rings 3.2. Abstract Rings and Ring Homomorphisms 3.3. Interesting Examples of Rings 3.4. Some Important Special Types of Rings 3.5. Unit Groups and Product Rings 3.6. Ideals and Quotient Rings 3.7. Prime Ideals and Maximal Ideals Exercises Chapter 4. Vector Spaces — Part 1 4.1. Introduction to Vector Spaces 4.2. Vector Spaces and Linear Transformations 4.3. Interesting Examples of Vector Spaces 4.4. Bases and Dimension Exercises Chapter 5. Fields — Part 1 5.1. Introduction to Fields 5.2. Abstract Fields and Homomorphisms 5.3. Interesting Examples of Fields 5.4. Subfields and Extension Fields 5.5. Polynomial Rings 5.6. Building Extension Fields 5.7. Finite Fields Exercises Chapter 6. Groups — Part 2 6.1. Normal Subgroups and Quotient Groups 6.2. Groups Acting on Sets 6.3. The Orbit-Stabilizer Counting Theorem 6.4. Sylow's Theorem 6.5. Two Counting Lemmas 6.6. Double Cosets and Sylow's Theorem Exercises Chapter 7. Rings — Part 2 7.1. Irreducible Elements and Unique Factorization Domains 7.2. Euclidean Domains and Principal Ideal Domains 7.3. Factorization in Principal Ideal Domains 7.4. The Chinese Remainder Theorem 7.5. Field of Fractions 7.6. Multivariate and Symmetric Polynomials Exercises Chapter 8. Fields — Part 2 8.1. Algebraic Numbers and Transcendental Numbers 8.2. Polynomial Roots and Multiplicative Subgroups 8.3. Splitting Fields, Separability, and Irreducibility 8.4. Finite Fields Revisited 8.5. Gauss's Lemma and Eisenstein's Irreducibility Criterion 8.6. Ruler and Compass Constructions Exercises Chapter 9. Galois Theory: Fields+Groups 9.1. What Is Galois Theory? 9.2. A Quick Review of Polynomials and Field Extensions 9.3. Fields of Algebraic Numbers 9.4. Algebraically Closed Fields 9.5. Automorphisms of Fields 9.6. Splitting Fields — Part 1 9.7. Splitting Fields — Part 2 9.8. The Primitive Element Theorem 9.9. Galois Extensions 9.10. The Fundamental Theorem of Galois Theory 9.11. Application: The Fundamental Theorem of Algebra 9.12. Galois Theory of Finite Fields 9.13. A Plethora of Galois Equivalences 9.14. Cyclotomic Fields and Kummer Fields 9.15. Application: Insolubility of Polynomial Equations by Radicals 9.16. Linear Independence of Field Automorphisms Exercises Chapter 10. Vector Spaces — Part 2 10.1. Vector Space Homomorphisms (aka Linear Transformations) 10.2. Endomorphisms and Automorphisms 10.3. Linear Transformations and Matrices 10.4. Subspaces and Quotient Spaces 10.5. Eigenvalues and Eigenvectors 10.6. Determinants 10.7. Determinants, Eigenvalues, and Characteristic Polynomials 10.8. Inifinite-Dimensional Vector Spaces Exercises Chapter 11. Modules — Part 1:Rings+Vector-Like Spaces 11.1. What Is a Module? 11.2. Examples of Modules 11.3. Submodules and Quotient Modules 11.4. Free Modules and Finitely Generated Modules 11.5. Homomorphisms, Endomorphisms, Matrices 11.6. Noetherian Rings and Modules 11.7. Matrices with Entries in a Euclidean Domain 11.8. Finitely Generated Modules over Euclidean Domains 11.9. Applications of the Structure Theorem Exercises Chapter 12. Groups — Part 3 12.1. Permutation Groups 12.2. Cayley's Theorem 12.3. Simple Groups 12.4. Composition Series 12.5. Automorphism Groups 12.6. Semidirect Products of Groups 12.7. The Structure of Finite Abelian Groups Exercises Chapter 13. Modules — Part 2: Multilinear Algebra 13.1. Multilinear Maps and Multilinear Forms 13.2. Symmetric and Alternating Forms 13.3. Alternating Forms on Free Modules 13.4. The Determinant Map Exercises Chapter 14. Additional Topics in Brief 14.1. Sets Countable and Uncountable 14.2. The Axiom of Choice 14.3. Tensor Products and Multilinear Algebra 14.4. Commutative Algebra 14.5. Category Theory 14.6. Graph Theory 14.7. Representation Theory 14.8. Elliptic Curves 14.9. Algebraic Number Theory 14.10. Algebraic Geometry 14.11. Euclidean Lattices 14.12. Non-Commutative Rings 14.13. Mathematical Cryptography Exercises Sample Syllabi List of Notation List of Figures Index