{"product_id":"theorems-corollaries-lemmas-and-methods-of-proof","title":"Theorems, Corollaries, Lemmas, and Methods of Proof","description":"\u003cp\u003e\u003cb\u003eA hands-on introduction to the tools needed for rigorous and theoretical mathematical reasoning\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSuccessfully addressing the frustration many students experience as they make the transition from computational mathematics to advanced calculus and algebraic structures, \u003ci\u003eTheorems, Corollaries, Lemmas, and Methods of Proof\u003c\/i\u003e equips students with the tools needed to succeed while providing a firm foundation in the axiomatic structure of modern mathematics.\u003c\/p\u003e \u003cp\u003eThis essential book:\u003c\/p\u003e \u003cul\u003e\n\u003cli\u003eClearly explains the relationship between definitions, conjectures, theorems, corollaries, lemmas, and proofs\u003c\/li\u003e\n\u003cli\u003eReinforces the foundations of calculus and algebra\u003c\/li\u003e\n\u003cli\u003eExplores how to use both a direct and indirect proof to prove a theorem\u003c\/li\u003e\n\u003cli\u003ePresents the basic properties of real numbers\/li\u0026gt;\u003c\/li\u003e\n\u003cli\u003eDiscusses how to use mathematical induction to prove a theorem\u003c\/li\u003e\n\u003cli\u003eIdentifies the different types of theorems\u003c\/li\u003e\n\u003cli\u003eExplains how to write a clear and understandable proof\u003c\/li\u003e\n\u003cli\u003eCovers the basic structure of modern mathematics and the key components of modern mathematics\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003eA complete chapter is dedicated to the different methods of proof such as forward direct proofs, proof by contrapositive, proof by contradiction, mathematical induction, and existence proofs. In addition, the author has supplied many clear and detailed algorithms that outline these proofs.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eTheorems, Corollaries, Lemmas, and Methods of Proof\u003c\/i\u003e uniquely introduces scratch work as an indispensable part of the proof process, encouraging students to use scratch work and creative thinking as the first steps in their attempt to prove a theorem. Once their scratch work successfully demonstrates the truth of the theorem, the proof can be written in a clear and concise fashion. The basic structure of modern mathematics is discussed, and each of the key components of modern mathematics is defined. Numerous exercises are included in each chapter, covering a wide range of topics with varied levels of difficulty.\u003c\/p\u003e \u003cp\u003eIntended as a main text for mathematics courses such as Methods of Proof, Transitions to Advanced Mathematics, and Foundations of Mathematics, the book may also be used as a supplementary textbook in junior- and senior-level courses on advanced calculus, real analysis, and modern algebra.\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Product","offer_id":54222501544280,"sku":"9780470042953","price":142.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0278\/1295\/4195\/files\/9780470042953__67730296b799c.jpg?v=1741160381","url":"https:\/\/agendabookshop.com\/products\/theorems-corollaries-lemmas-and-methods-of-proof","provider":"Agenda Bookshop","version":"1.0","type":"link"}