| Description |
1 online resource : illustrations |
| Series |
Textbooks in mathematics |
| Contents |
Cover; Half Title; Title Page; Copyright Page; Contents; Preface; 1. Proof; 1.1 The Need for Proof; 1.2 Proving by Contradiction; 1.3 If, and Only If; 1.4 Definitions; 1.5 Proving That Something Is False; 1.6 Conclusion; What You Should Know; Exercise 1; 2. Sets; 2.1 What Is a Set?; 2.2 Examples of Sets: Notation; 2.3 Describing a Set; 2.4 Subsets; 2.5 Venn Diagrams; 2.6 Intersection and Union; 2.7 Proving That Two Sets Are Equal; What You Should Know; Exercise 2; 3. Binary Operations; 3.1 Introduction; 3.2 Binary Operations; 3.3 Examples of Binary Operations; 3.4 Tables |
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3.5 Testing for Binary OperationsWhat You Should Know; Exercise 3; 4. Integers; 4.1 Introduction; 4.2 The Division Algorithm; 4.3 Relatively Prime Pairs of Numbers; 4.4 Prime Numbers; 4.5 Residue Classes of Integers; 4.6 Some Remarks; What You Should Know; Exercise 4; 5. Groups; 5.1 Introduction; 5.2 Two Examples of Groups; 5.3 Definition of a Group; 5.4 A Diversion on Notation; 5.5 Some Examples of Groups; 5.6 Some Useful Properties of Groups; 5.7 The Powers of an Element; 5.8 The Order of an Element; What You Should Know; Exercise 5; 6. Subgroups; 6.1 Subgroups; 6.2 Examples of Subgroups |
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6.3 Testing for a Subgroup6.4 The Subgroup Generated by an Element; What You Should Know; Exercise 6; 7. Cyclic Groups; 7.1 Introduction; 7.2 Cyclic Groups; 7.3 Some Definitions and Theorems about Cyclic Groups; What You Should Know; Exercise 7; 8. Products of Groups; 8.1 Introduction; 8.2 The Cartesian Product; 8.3 Direct Product Groups; What You Should Know; Exercise 8; 9. Functions; 9.1 Introduction; 9.2 Functions: A Discussion; 9.3 Functions: Formalizing the Discussion; 9.4 Notation and Language; 9.5 Examples; 9.6 Injections and Surjections; 9.7 Injections and Surjections of Finite Sets |
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What You Should KnowExercise 9; 10. Composition of Functions; 10.1 Introduction; 10.2 Composite Functions; 10.3 Some Properties of Composite Functions; 10.4 Inverse Functions; 10.5 Associativity of Functions; 10.6 Inverse of a Composite Function; 10.7 The Bijections from a Set to Itself; What You Should Know; Exercise 10; 11. Isomorphisms; 11.1 Introduction; 11.2 Isomorphism; 11.3 Proving Two Groups Are Isomorphic; 11.4 Proving Two Groups Are Not Isomorphic; 11.5 Finite Abelian Groups; What You Should Know; Exercise 11; 12. Permutations; 12.1 Introduction; 12.2 Another Look at Permutations |
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12.3 Practice at Working with Permutations12.4 Even and Odd Permutations; 12.5 Cycles; 12.6 Transpositions; 12.7 The Alternating Group; What You Should Know; Exercise 12; 13. Dihedral Groups; 13.1 Introduction; 13.2 Towards a General Notation; 13.3 The General Dihedral Group D[sub(n)]; 13.4 Subgroups of Dihedral Groups; What You Should Know; Exercise 13; 14. Cosets; 14.1 Introduction; 14.2 Cosets; 14.3 Lagrange's Theorem; 14.4 Deductions from Lagrange's Theorem; 14.5 Two Number Theory Applications; 14.6 More Examples of Cosets; What You Should Know; Exercise 14; 15. Groups of Orders Up To 8 |
| Subject |
Group theory.
|
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Mathematics.
|
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applied mathematics.
|
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mathematics.
|
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MATHEMATICS -- Complex Analysis.
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MATHEMATICS -- Functional Analysis.
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Group theory
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|
Mathematics
|
| Form |
Electronic book
|
| Author |
Neill, Hugh, author
|
| ISBN |
9781315405766 |
|
1315405768 |
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