Introduction to Algebra: Comprehensive Journey Through Modern Algebraic Structures / Paperback

Bevezetés az algebrába

UPC: 9789632791135 / 978-9632791135

MPN: 9789632791135

Brand Name: Typotex Kft.

Product Type: Book (Fóliázott karton/Laminated Paperback)

Language: Hungarian (Magyar)

Genre: Mathematics, Algebra, University Textbook

Overview

Introduction to Algebra (Bevezetés az algebrába) by Kiss Emil is a monumental 718-page comprehensive textbook that spans the entire landscape of algebra—excluding only linear algebra—from foundational concepts to cutting-edge applications. Published by Typotex Kft. in 2011, this remarkable work guides readers from complex numbers and polynomials through classical structures of groups, rings, and fields, ultimately reaching general algebras and modern applications. What distinguishes this textbook is its exceptional readability: rather than drowning students in formalism, Professor Kiss Emil emphasizes essential ideas and the internal logic of algebraic theory, making maximum comprehension his priority. The author actively engages readers as co-discoverers, revealing both visible and hidden connections within algebra's beautiful universe. Carefully curated exercises and problems are seamlessly integrated with theoretical material, serving not merely as practice but as tools for deeper conceptual understanding, illuminating crucial proof steps, demonstrating exciting applications, and revealing fascinating additional perspectives. Written by the distinguished chair of ELTE's Department of Algebra and Number Theory—a renowned researcher and celebrated educator—this textbook represents the pinnacle of Hungarian algebraic pedagogy.

Bevezetés az algebrába: Átfogó utazás a modern algebrai struktúrákon át

Kiss Emil Bevezetés az algebrába című műve egy monumentális, 718 oldalas átfogó tankönyv, amely az algebra teljes területét felöleli—kizárólag a lineáris algebrát kivéve—az alapfogalmaktól a legújabb alkalmazásokig. A Typotex Kft. által 2011-ben kiadott figyelemre méltó mű a komplex számoktól és polinomoktól vezeti az olvasót a csoportok, gyűrűk és testek klasszikus struktúráin keresztül, végül eljutva az általános algebrákig és modern alkalmazásokig. Ami megkülönbözteti ezt a tankönyvet, az a kivételes olvashatósága: ahelyett, hogy a diákokat formalizmusban fulladná, Kiss Emil professzor a lényeges gondolatokat és az algebrai elmélet belső logikáját hangsúlyozza, a maximális megértést teszi elsődleges céljává. A szerző aktívan bevonja az olvasókat mint felfedezőtársakat, feltárva az algebra gyönyörű univerzumának látható és rejtett összefüggéseit egyaránt. A gondosan összeállított gyakorlatok és feladatok zökkenőmentesen integrálódnak az elméleti anyagba, nem pusztán gyakorlásként szolgálva, hanem a mélyebb fogalmi megértés eszközeiként, megvilágítva a bizonyítások kulcsfontosságú lépéseit, bemutatva izgalmas alkalmazásokat és feltárva lenyűgöző további perspektívákat. Az ELTE Algebra és Számelmélet Tanszékének kiváló tanszékvezetője—elismert kutató és ünnepelt oktató—által írt tankönyv a magyar algebrai pedagógia csúcsát képviseli.

Product Features

• Format: Fóliázott karton (Laminated Paperback) - durable cover for intensive study use
• Pages: 718 pages - comprehensive, exhaustive coverage
• Language: Hungarian (Magyar)
• ISBN: 9789632791135 / 978-9632791135
• Publication Year: 2011
• Publication Location: Budapest, Hungary
• Publisher: Typotex Kft.
• Subject Area: Abstract Algebra, Group Theory, Ring Theory, Field Theory, General Algebras
• Scope: Complete algebra curriculum (excluding linear algebra)
• Target Audience: University mathematics students, graduate students, mathematics educators, researchers
• Educational Level: Upper undergraduate through graduate level
• Pedagogical Approach: Concept-driven, reader-engaged, problem-integrated learning
• Exercise Integration: Seamlessly embedded problems serving conceptual development
• Coverage: Complex numbers, polynomials, groups, rings, fields, general algebras, modern applications

Interesting Facts

About the Author - Distinguished Academic Leader: Kiss Emil is a professor and department chair (tanszékvezető egyetemi tanár) at ELTE's (Eötvös Loránd University) Department of Algebra and Number Theory, holding the distinguished title "Doctor of Mathematical Sciences" (matematikai tudományok doktora)—the highest academic degree in the Hungarian scientific system, equivalent to the Doctor of Sciences (D.Sc.) degree. He is recognized both as a prominent researcher in his field and as an acclaimed educator, uniquely qualified to write an authoritative textbook that balances rigorous scholarship with pedagogical excellence.

ELTE's Mathematical Prestige: Eötvös Loránd University (ELTE) in Budapest is Hungary's premier university and one of Central Europe's most distinguished institutions, with a mathematics faculty that has produced numerous world-class mathematicians including several Fields Medal winners. The Department of Algebra and Number Theory maintains exceptional research standards, making Kiss Emil's position as its chair particularly significant.

Comprehensive Scope - Almost Complete Algebra: The textbook's remarkable claim is covering "the entire field of algebra" (az algebra teljes területét) with only one exception: linear algebra, which typically receives separate treatment due to its distinct methods and applications. This means 718 pages encompassing abstract algebra's vast landscape—from elementary structures through advanced topics—representing years of accumulated teaching wisdom and careful content curation.

Readability Over Formalism: In a field notorious for dense symbolic notation and abstract formalism, Kiss Emil prioritizes "olvasmányosan" (readability) and "maximális érthetőség" (maximum comprehension). This pedagogical choice reflects deep understanding: genuine mathematical insight comes not from manipulating symbols but from grasping underlying ideas. By emphasizing "lényeges gondolatok" (essential thoughts) and "belső logika" (internal logic) over formal apparatus, Kiss makes algebra accessible without sacrificing rigor.

Reader as Co-Discoverer: The book positions students not as passive recipients but as active participants in discovery. The phrase "az Olvasóval, annak aktív közreműködésére is építve fedezi és fedezteti fel" (discovering and helping the reader discover, building on their active participation) embodies constructivist pedagogy where understanding emerges through engagement rather than transmission. This approach mirrors how mathematicians actually work—exploring, conjecturing, testing—rather than simply absorbing finished theorems.

Hidden and Visible Connections: The book promises to reveal both "látható és rejtett összefüggések" (visible and hidden connections) within algebra's universe. Mathematics' beauty often lies in unexpected connections between seemingly unrelated areas—how group theory illuminates number theory, how ring structures appear in geometry, how field extensions enable impossible constructions. Illuminating these connections transforms algebra from a collection of techniques into a coherent intellectual universe.

Exercises as Integral Pedagogy: Rather than relegating exercises to end-of-chapter afterthoughts, Kiss integrates "gondosan összeállított feladatok és gyakorlatok" (carefully compiled problems and exercises) directly with theoretical material. These problems serve multiple sophisticated purposes: deepening conceptual understanding, illuminating crucial proof steps, demonstrating applications, and revealing additional fascinating perspectives. This integration ensures students actively engage with ideas immediately, cementing understanding before moving forward.

Collaborative Thinking: The exercises serve as "együttgondolkozás" (thinking together) tools—not tests of memorization but invitations to collaborative intellectual exploration. This framing transforms problem-solving from performance anxiety into joyful discovery, reflecting mathematics as fundamentally social and conversational rather than solitary and competitive.

From Foundations to Frontiers: The textbook's trajectory—from complex numbers and polynomials through classical structures (groups, rings, fields) to general algebras and modern applications—mirrors algebra's historical development while serving pedagogical logic. Students build understanding progressively, with each concept providing foundation for the next, ultimately reaching contemporary research topics that demonstrate algebra's ongoing vitality.

Modern Applications Emphasis: By explicitly including "modern alkalmazások" (modern applications), Kiss demonstrates algebra's relevance beyond abstract theory. Algebraic structures appear throughout mathematics, physics, computer science (cryptography, coding theory, algorithms), and even social sciences, making algebra essential intellectual infrastructure for contemporary science and technology.

Hungarian Mathematical Pedagogy: This textbook exemplifies Hungary's exceptional mathematical education tradition, which has consistently produced world-class mathematicians despite the nation's small population. Hungarian mathematical pedagogy emphasizes deep conceptual understanding, problem-solving creativity, and elegant exposition—all evident in Kiss's approach.

Doctoral Expertise: The author's "matematikai tudományok doktora" degree signifies not just advanced knowledge but proven original research contributions. This research background ensures the textbook reflects current mathematical understanding while maintaining pedagogical accessibility—balancing frontier knowledge with teaching clarity.

718 Pages of Mathematical Journey: The substantial length allows unhurried development, giving each concept proper attention without artificial compression. This generous space permits detailed explanations, multiple examples, extensive exercises, and thorough exploration of connections—luxury often absent from shorter texts that sacrifice depth for brevity.

Publishers

Typotex Kft. is Hungary's leading academic publisher specializing in scientific, mathematical, and technical literature, headquartered in Budapest. With an exceptional reputation built over decades, Typotex serves as the premier source for high-quality Hungarian-language STEM educational materials, collaborating with Hungary's most distinguished academics from institutions like ELTE, Budapest University of Technology and Economics, and leading research institutes. The publisher's mission extends beyond commercial publishing to encompass cultural stewardship: making world-class mathematical and scientific knowledge accessible to Hungarian-speaking students, educators, and researchers while preserving Hungary's extraordinary mathematical heritage. Typotex's catalog spans pure and applied mathematics, theoretical and experimental physics, computer science, engineering disciplines, and natural sciences, serving Hungarian universities, secondary schools, and professional communities throughout Central Europe. Their commitment to mathematical publishing is particularly significant given Hungary's disproportionate contribution to world mathematics—a small nation that has produced numerous Fields Medalists, Abel Prize winners, and foundational mathematical innovators. By publishing comprehensive textbooks like Kiss Emil's Introduction to Algebra, Typotex ensures that Hungarian students can access authoritative, pedagogically sophisticated mathematical education in their native language, democratizing knowledge that might otherwise require expensive English-language imports. Typotex represents not merely a publishing house but an intellectual institution dedicated to maintaining and advancing Hungary's scientific and mathematical excellence for future generations.

We value your feedback! Share your experience with this product to help others make informed decisions. Your review is important to us!

Hashtags

#IntroductionToAlgebra #AbstractAlgebra #KissEmil #HungarianMathematics #GroupTheory #RingTheory #FieldTheory #TypetexPublishing #UniversityMathematics #AlgebraTextbook #ELTEUniversity #MathematicalStructures #AlgebraPedagogy #ModernAlgebra #BudapestPublishers #HungarianAcademic #STEMEducation #MathematicsEducation #AlgebraicStructures #GeneralAlgebras #MathematicsTextbook #AdvancedMathematics #AlgebraTheory #HungarianSTEM #MathematicalPedagogy #ConceptualLearning #ProblemSolvingAlgebra #BevezetésAlgebrába #MagyarMatematika #AlgebraTankönyv

Hashtags (Magyar)

#BevezetésAlgebrába #AbsztraktAlgebra #KissEmil #MagyarMatematika #CsoportElmélet #GyűrűElmélet #TestElmélet #TypetexKiadó #EgyetemiMatematika #AlgebraTankönyv #ELTEEgyetem #MatematikaiStruktúrák #AlgebraiPedagógia #ModernAlgebra #BudapestiKiadó #MagyarAkadémiai #STEMOktatás #MatematikaiOktatás #AlgebraiStruktúrák #ÁltalánosAlgebrák #MatematikaTankönyv #HaladóMatematika #AlgebraElmélet #MagyarSTEMOktatás #MatematikaiPedagógia #FogalmiTanulás #ProblémamegoldásAlgebra #AlgebraÉsSzámelmélet #ELTETanszék #MatematikaiTudományok