{"product_id":"advanced-mathematics-9781119563518","title":"Advanced Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eProvides a smooth and pleasant transition from first-year calculus to upper-level mathematics courses in real analysis, abstract algebra and number theory\u003c\/b\u003e\u003cb\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eMost universities require students majoring in mathematics to take a transition to higher math course that introduces mathematical proofs and more rigorous thinking. Such courses help students be prepared for higher-level mathematics course from their onset. \u003ci\u003eAdvanced Mathematics: A Transitional Reference \u003c\/i\u003eprovides a crash course in beginning pure mathematics, offering instruction on a blendof inductive and deductive reasoning. By avoiding outdated methods and countless pages of theorems and proofs, this innovative textbook prompts students to think about the ideas presented in an enjoyable, constructive setting.\u003c\/p\u003e \u003cp\u003eClear and concise chapters cover all the essential topics students need to transition from the rote-orientated courses of calculus to the more rigorous proof-orientated advanced mathematic\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003ePreface vii\u003c\/p\u003e \u003cp\u003ePossible Beneficial Audiences ix\u003c\/p\u003e \u003cp\u003eWow Factors of the Book x\u003c\/p\u003e \u003cp\u003eChapter by Chapter (the nitty-gritty) xi\u003c\/p\u003e \u003cp\u003eNote to the Reader xiii\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xiv\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1 Logic and Proofs 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Sentential Logic 3\u003c\/p\u003e \u003cp\u003e1.2 Conditional and Biconditional Connectives 24\u003c\/p\u003e \u003cp\u003e1.3 Predicate Logic 38\u003c\/p\u003e \u003cp\u003e1.4 Mathematical Proofs 51\u003c\/p\u003e \u003cp\u003e1.5 Proofs in Predicate Logic 71\u003c\/p\u003e \u003cp\u003e1.6 Proof by Mathematical Induction 83\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2 Sets and Counting 95\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Basic Operations of Sets 97\u003c\/p\u003e \u003cp\u003e2.2 Families of Sets 115\u003c\/p\u003e \u003cp\u003e2.3 Counting: The Art of Enumeration 125\u003c\/p\u003e \u003cp\u003e2.4 Cardinality of Sets 143\u003c\/p\u003e \u003cp\u003e2.5 Uncountable Sets 156\u003c\/p\u003e \u003cp\u003e2.6 Larger Infinities and the ZFC Axioms 167\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3 Relations 179\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Relations 181\u003c\/p\u003e \u003cp\u003e3.2 Order Relations 195\u003c\/p\u003e \u003cp\u003e3.3 Equivalence Relations 212\u003c\/p\u003e \u003cp\u003e3.4 The Function Relation 224\u003c\/p\u003e \u003cp\u003e3.5 Image of a Set 242\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4 The Real and Complex Number Systems 255\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Construction of the Real Numbers 257\u003c\/p\u003e \u003cp\u003e4.2\u003ci\u003e The\u003c\/i\u003e Complete Ordered Field: The Real Numbers 269\u003c\/p\u003e \u003cp\u003e4.3 Complex Numbers 281\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5 Topology 299\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction to Graph Theory 301\u003c\/p\u003e \u003cp\u003e5.2 Directed Graphs 321\u003c\/p\u003e \u003cp\u003e5.3 Geometric Topology 334\u003c\/p\u003e \u003cp\u003e5.4 Point-Set Topology on the Real Line 349\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6 Algebra 367\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Symmetries and Algebraic Systems 369\u003c\/p\u003e \u003cp\u003e6.2 Introduction to the Algebraic Group 385\u003c\/p\u003e \u003cp\u003e6.3 Permutation Groups 403\u003c\/p\u003e \u003cp\u003e6.4 Subgroups: Groups Inside a Group 419\u003c\/p\u003e \u003cp\u003e6.5 Rings and Fields 433\u003c\/p\u003e \u003cp\u003eIndex 443\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49407084757335,"sku":"9781119563518","price":89.96,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119563518.jpg?v=1730498125","url":"https:\/\/bookcurl.com\/products\/advanced-mathematics-9781119563518","provider":"Book Curl","version":"1.0","type":"link"}