{"product_id":"principles-of-mathematics-9781119131649","title":"Principles of Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003ePresents a uniquely balanced approach that bridges introductory and advanced topics in modern mathematics\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAn accessible treatment of the fundamentals of modern mathematics, \u003ci\u003ePrinciples of Mathematics: A Primer \u003c\/i\u003eprovides a unique approach to introductory andadvanced mathematical topics. The book features six main subjects, whichcan be studied independently or in conjunction with each other including: settheory; mathematical logic; proof theory; group theory; theory of functions; andlinear algebra.\u003c\/p\u003e \u003cp\u003eThe author begins with comprehensive coverage of the necessary building blocks in mathematics and emphasizes the need to think abstractly and develop an appreciation for mathematical thinking. Maintaining a useful balance of introductory coverage and mathematical rigor, \u003ci\u003ePrinciples of Mathematics: A\u003c\/i\u003e \u003ci\u003ePrimer \u003c\/i\u003efeatures:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eDetailed explanations of important theorems and their applications\u003c\/li\u003e \u003cli\u003eHundreds of completely solved problems throughout\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"Standard material is covered here such as basis, linear transformations, the general linear group, systems of linear equations, determinants and eigenvalues. The book has many examples and exercises to help the reader.\" (\u003ci\u003eZentralblatt MATH\u003c\/i\u003e, 2016)\u003c\/p\u003e \u003cp\u003e\"The author goes deep enough into group theory to cover normal subgroups and isomorphism theorems, and deep enough into linear algebra to discuss eigenvalue theory and the general linear group. There are plenty of exercises and supplementary problems... the book is certainly different from the competition.\" (\u003ci\u003eMathematical Association of America\u003c\/i\u003e, 2016)\u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface xi \u003cp\u003e\u003cb\u003e1 Set Theory 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction, 1\u003c\/p\u003e \u003cp\u003e1.2 Set Theory – Definitions, Notation, and Terminology – What is a Set?, 3\u003c\/p\u003e \u003cp\u003e1.3 Sets Given by a Defining Property, 15\u003c\/p\u003e \u003cp\u003e1.4 The Algebra of Sets, 25\u003c\/p\u003e \u003cp\u003e1.5 The Power Set, 41\u003c\/p\u003e \u003cp\u003e1.6 The Cartesian Product, 44\u003c\/p\u003e \u003cp\u003e1.7 The Sets N, Z, and Q, 46\u003c\/p\u003e \u003cp\u003e1.8 The Set R – Real Numbers I, 71\u003c\/p\u003e \u003cp\u003e1.9 A Short Musing on Transfinite Arithmetic, 80\u003c\/p\u003e \u003cp\u003e1.10 The Set R – Real Numbers II, 102\u003c\/p\u003e \u003cp\u003e1.11 Supplementary Problems, 109\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Logic 115\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction, 116\u003c\/p\u003e \u003cp\u003e2.2 Propositional Calculus, 121\u003c\/p\u003e \u003cp\u003e2.3 Arguments I, 146\u003c\/p\u003e \u003cp\u003e2.4 Arguments II, 167\u003c\/p\u003e \u003cp\u003e2.5 A Short Revisit to Set Theory, 171\u003c\/p\u003e \u003cp\u003e2.6 Boolean Algebra, 173\u003c\/p\u003e \u003cp\u003e2.7 Supplementary Problems, 177\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Proofs 183\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction, 183\u003c\/p\u003e \u003cp\u003e3.2 Direct Proof, 193\u003c\/p\u003e \u003cp\u003e3.3 Indirect Proof, 212\u003c\/p\u003e \u003cp\u003e3.4 Mathematical Induction, 218\u003c\/p\u003e \u003cp\u003e3.5 Supplementary Problems, 241\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Functions 247\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction, 247\u003c\/p\u003e \u003cp\u003e4.2 Relations, 248\u003c\/p\u003e \u003cp\u003e4.3 Functions, 274\u003c\/p\u003e \u003cp\u003e4.4 Supplementary Problems, 321\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Group Theory 327\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction, 327\u003c\/p\u003e \u003cp\u003e5.2 Fundamental Concepts of Group Theory, 328\u003c\/p\u003e \u003cp\u003e5.3 Subgroups, 356\u003c\/p\u003e \u003cp\u003e5.4 Cyclic Groups, 382\u003c\/p\u003e \u003cp\u003e5.5 Homomorphisms and Isomorphisms, 385\u003c\/p\u003e \u003cp\u003e5.6 Normal Subgroups, 404\u003c\/p\u003e \u003cp\u003e5.7 Centralizer, Normalizer, Stabilizer, 412\u003c\/p\u003e \u003cp\u003e5.8 Quotient Group, 419\u003c\/p\u003e \u003cp\u003e5.9 The Isomorphism Theorems, 427\u003c\/p\u003e \u003cp\u003e5.10 Direct Product of Groups, 437\u003c\/p\u003e \u003cp\u003e5.11 Supplementary Problems, 441\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Linear Algebra 447\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction, 447\u003c\/p\u003e \u003cp\u003e6.2 Vector Space, 449\u003c\/p\u003e \u003cp\u003e6.3 Linear Dependence and Independence, 456\u003c\/p\u003e \u003cp\u003e6.4 Basis and Dimension of a Vector Space, 461\u003c\/p\u003e \u003cp\u003e6.5 Subspaces, 469\u003c\/p\u003e \u003cp\u003e6.6 Linear Transformations – Linear Operators, 477\u003c\/p\u003e \u003cp\u003e6.7 Isomorphism of Linear Spaces, 489\u003c\/p\u003e \u003cp\u003e6.8 Linear Transformations and Matrices, 501\u003c\/p\u003e \u003cp\u003e6.9 Linear Space Mmn, 507\u003c\/p\u003e \u003cp\u003e6.10 Matrix Multiplication, 509\u003c\/p\u003e \u003cp\u003e6.11 Some More Special Matrices. General Linear Group, 514\u003c\/p\u003e \u003cp\u003e6.12 Rank of a Matrix, 525\u003c\/p\u003e \u003cp\u003e6.13 Determinants, 534\u003c\/p\u003e \u003cp\u003e6.14 The Inverse and the Rank of a Matrix Revisited, 541\u003c\/p\u003e \u003cp\u003e6.15 More on Linear Operators, 547\u003c\/p\u003e \u003cp\u003e6.16 Systems of Linear Equations I, 585\u003c\/p\u003e \u003cp\u003e6.17 Systems of Linear Equations II, 600\u003c\/p\u003e \u003cp\u003e6.18 The Basics of Eigenvalue and Eigenvector Theory, 613\u003c\/p\u003e \u003cp\u003e6.19 Supplementary Problems, 635\u003c\/p\u003e \u003cp\u003eIndex 645\u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49528847892823,"sku":"9781119131649","price":114.9,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119131649.jpg?v=1731873260","url":"https:\/\/bookcurl.com\/products\/principles-of-mathematics-9781119131649","provider":"Book Curl","version":"1.0","type":"link"}