{"product_id":"a-friendly-introduction-to-abstract-algebra-9781470468811","title":"A Friendly Introduction to Abstract Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eOffers a new approach to laying a foundation for abstract mathematics. Prior experience with proofs is not assumed, and the book takes time to build proof-writing skills in ways that will serve students through a lifetime of learning and creating mathematics.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003ePreliminaries: Introduction to proofs\u003c\/li\u003e\n\u003cli\u003eSets and subsets\u003c\/li\u003e\n\u003cli\u003eDivisors\u003c\/li\u003e\n\u003cli\u003eExamples of groups: Modular arithmetic\u003c\/li\u003e\n\u003cli\u003eSymmetries\u003c\/li\u003e\n\u003cli\u003ePermutations\u003c\/li\u003e\n\u003cli\u003eMatrices\u003c\/li\u003e\n\u003cli\u003eIntroduction to groups: Introduction to groups\u003c\/li\u003e\n\u003cli\u003eGroups of small size\u003c\/li\u003e\n\u003cli\u003eMatrix groups\u003c\/li\u003e\n\u003cli\u003eSubgroups\u003c\/li\u003e\n\u003cli\u003eOrder of an element\u003c\/li\u003e\n\u003cli\u003eCyclic groups, Part I\u003c\/li\u003e\n\u003cli\u003eCyclic groups, Part II\u003c\/li\u003e\n\u003cli\u003eGroup homomorphisms: Functions\u003c\/li\u003e\n\u003cli\u003eIsomorphisms\u003c\/li\u003e\n\u003cli\u003eHomomorphisms, Part I\u003c\/li\u003e\n\u003cli\u003eHomomorphisms, Part II\u003c\/li\u003e\n\u003cli\u003eQuotient groups: Introduction to cosets\u003c\/li\u003e\n\u003cli\u003eLagrange's theorem\u003c\/li\u003e\n\u003cli\u003eMultiplying\/adding cosets\u003c\/li\u003e\n\u003cli\u003eQuotient group examples\u003c\/li\u003e\n\u003cli\u003eQuotient group proofs\u003c\/li\u003e\n\u003cli\u003eNormal subgroups\u003c\/li\u003e\n\u003cli\u003eFirst isomorphism theorem\u003c\/li\u003e\n\u003cli\u003eIntroduction to rings: Introduction to rings\u003c\/li\u003e\n\u003cli\u003eIntegral domains and fields\u003c\/li\u003e\n\u003cli\u003ePolynomial rings, Part I\u003c\/li\u003e\n\u003cli\u003ePolynomial rings, Part II\u003c\/li\u003e\n\u003cli\u003eFactoring polynomials\u003c\/li\u003e\n\u003cli\u003eQuotient rings: Ring homomorphisms\u003c\/li\u003e\n\u003cli\u003eIntroduction to quotient rings\u003c\/li\u003e\n\u003cli\u003eQuotient ring $\\mathbb{Z}_7[x]\/ \\langle x^2-1\\rangle$\u003c\/li\u003e\n\u003cli\u003eQuotient ring $\\mathbb{R}[x]\/ \\langle x^2 +1\\rangle$\u003c\/li\u003e\n\u003cli\u003e$F[x]\/ \\langle g(x)\\rangle$ is\/isn't a field, Part I\u003c\/li\u003e\n\u003cli\u003eMaximal ideals\u003c\/li\u003e\n\u003cli\u003e$F[x]\/ \\langle g(x)\\rangle$ is\/isn't a field, Part II\u003c\/li\u003e\n\u003cli\u003eAppendices: Proof of the GCD theorem\u003c\/li\u003e\n\u003cli\u003eComposition table for $D_4$\u003c\/li\u003e\n\u003cli\u003eSymbols and notations\u003c\/li\u003e\n\u003cli\u003eEssential theorems\u003c\/li\u003e\n\u003cli\u003eIndex: Index of terms\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":50046682530135,"sku":"9781470468811","price":54.9,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470468811.jpg?v=1740272060","url":"https:\/\/bookcurl.com\/products\/a-friendly-introduction-to-abstract-algebra-9781470468811","provider":"Book Curl","version":"1.0","type":"link"}