LEADER 03390nam 2200553 450 001 996418203603316 005 20220321133839.0 010 $a3-030-60806-9 024 7 $a10.1007/978-3-030-60806-4 035 $a(CKB)5590000000002295 035 $a(MiAaPQ)EBC6361021 035 $a(DE-He213)978-3-030-60806-4 035 $a(MiAaPQ)EBC6647501 035 $a(Au-PeEL)EBL6361021 035 $a(OCoLC)1198559148 035 $a(Au-PeEL)EBL6647501 035 $a(PPN)250220962 035 $a(EXLCZ)995590000000002295 100 $a20220321d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTopics in Galois fields /$fDirk Hachenberger and Dieter Jungnickel 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$dİ2020 215 $a1 online resource (XIV, 785 p. 11 illus.) 225 1 $aAlgorithms and Computation in Mathematics,$x1431-1550 ;$v29 311 $a3-030-60804-2 320 $aIncludes bibliographical references and index. 327 $aBasic Algebraic Structures and Elementary Number Theory -- Basics on Polynomials- Field Extensions and the Basic Theory of Galois Fields -- The Algebraic Closure of a Galois Field -- Irreducible Polynomials over Finite Fields -- Factorization of Univariate Polynomials over Finite Fields -- Matrices over Finite Fields -- Basis Representations and Arithmetics -- Shift Register Sequences -- Characters, Gauss Sums, and the DFT -- Normal Bases and Cyclotomic Modules -- Complete Normal Bases and Generalized Cyclotomic Modules -- Primitive Normal Bases -- Primitive Elements in Affin Hyperplanes -- List of Symbols -- References -- Index. 330 $aThis monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm. The book provides a thorough grounding in finite field theory for graduate students and researchers in mathematics. In view of its emphasis on applicable and computational aspects, it is also useful for readers working in information and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science. 410 0$aAlgorithms and Computation in Mathematics,$x1431-1550 ;$v29 606 $aFinite fields (Algebra) 606 $aGalois theory 615 0$aFinite fields (Algebra) 615 0$aGalois theory. 676 $a512.3 700 $aHachenberger$b Dirk$0845494 702 $aJungnickel$b D.$f1952- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418203603316 996 $aTopics in Galois Fields$91887565 997 $aUNISA LEADER 04219nam 22005775 450 001 9911035158603321 005 20251026120357.0 010 $a9789819690053$b(electronic bk.) 010 $z9789819690046 024 7 $a10.1007/978-981-96-9005-3 035 $a(MiAaPQ)EBC32376178 035 $a(Au-PeEL)EBL32376178 035 $a(CKB)41738225900041 035 $a(DE-He213)978-981-96-9005-3 035 $a(EXLCZ)9941738225900041 100 $a20251026d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Global Development of AI-Empowered Higher Education: Beyond the Horizon /$fedited by Wen Wen, Yu Zhang 205 $a1st ed. 2025. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2025. 215 $a1 online resource (243 pages) 225 1 $aResearch in Chinese Education,$x2524-4779 311 08$aPrint version: Wen, Wen The Global Development of AI-Empowered Higher Education: Beyond the Horizon Singapore : Springer,c2025 9789819690046 327 $aPreface -- Executive Summary -- Chapter 1. The Evolution and Latest Trends of AI Technology -- Chapter 2. Learning and Teaching in AI-Empowered Higher Education -- Chapter 3. Ethical Challenges of AI-Empowered Higher Education -- Chapter 4. Applications and Student Perceptions of GenAI in Higher Education: Findings from International Pilot Studies -- Chapter 5. Nurturing AI Talent in Higher Education -- Chapter 6. Policy Directions with Alternative Frameworks for AI in Higher Education Institutions -- Acknowledgement. 330 $aThis book provides a forward-looking and comprehensive examination of AI?s transformative impact on higher education. It explores the integration of AI in teaching, learning, and assessment with fresh insights into generative AI, artificial general intelligence (AGI), and their emerging roles in reshaping universities globally. Supported by case studies from 30 leading universities and empirical data from international surveys and interviews, the book stands apart by combining AI development trends with practical applications and ethical considerations. This book includes detailed discussions on AI's ethical challenges, including privacy, academic integrity, and the widening digital divide, all paired with real-world examples. A unique feature of the book is its in-depth exploration of AI talent development, outlining national strategies and institutional approaches that equip students with both AI literacy and advanced skills, establishing a new standard for cultivating future leaders in the AI era. With strategic policy recommendations, this book provides a roadmap for higher education institutions to navigate the rapidly evolving AI landscape. It highlights actionable frameworks for ensuring equitable access to technology, strengthening data security, and addressing biases in AI systems. Academics, policymakers, and education leaders will benefit from its forward-thinking approach to integrating AI while maintaining humanistic and ethical values in education. Designed for professionals in education and education policy, this book also serves as an essential guide for other readers looking to harness the power of AI in shaping the future of learning and teaching. 410 0$aResearch in Chinese Education,$x2524-4779 606 $aEducational technology 606 $aEducation$xData processing 606 $aEducation, Higher 606 $aDigital Education and Educational Technology 606 $aComputers and Education 606 $aHigher Education 615 0$aEducational technology. 615 0$aEducation$xData processing. 615 0$aEducation, Higher. 615 14$aDigital Education and Educational Technology. 615 24$aComputers and Education. 615 24$aHigher Education. 676 $a371.33 700 $aWen$b Wen$01853730 701 $aZhang$b Yu$0675177 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9911035158603321 996 $aThe Global Development of AI-Empowered Higher Education: Beyond the Horizon$94450359 997 $aUNINA