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Algebra: Gruppen – Ringe – Körper
by Christian KarpfingerDieses Lehrbuch zur Algebra bietet eine Einführung in die grundlegenden Begriffe und Methoden der modernen Algebra. Es werden die Themen eines Grundkurses zur Algebra ausführlich und motivierend behandelt.Die Algebra wird von vielen Studierenden als sehr abstrakt empfunden. Daher hat sich der Autor bemüht, die Ergebnisse und Begriffe mit zahlreichen Beispielen zu unterlegen. Die Beweisführungen sind ausführlich, gelegentlich werden sogar verschiedene Beweise aufgezeigt. Die Kapitel sind in kleine Lerneinheiten unterteilt. Diese Lerneinheiten führen Schritt für Schritt an die Ergebnisse heran und können durch diese Darstellung vom Leser besser nachvollzogen werden. Der Autor hat stets darauf geachtet, dass erst dann neue Begriffe und Konzepte eingeführt werden, wenn ein gewisses Vertrauen im Umgang mit den bis dahin entwickelten Begriffen und Konzepten besteht. Das Vorgehen wird stets motiviert, schwierige Sachverhalte werden ausführlich erklärt und an Beispielen erprobt. DieLeser erhalten dadurch einen einfachen Zugang zu dem nicht ganz leichten Thema der Algebra.Die zahlreichen Aufgaben unterschiedlicher Schwierigkeitsgrade zum Ende der Kapitel überprüfen das Gelernte und fördern das tiefere Verständnis der Theorie. Das Buch wurde für die 6. Auflage vollständig durchgesehen und um zwei Beweise des quadratischen Reziprozitätsgesetzes ergänzt. Zudem erhalten Sie Zugang auf 300 Flashcards (Springer-Nature-Flashcards-App), mit denen Sie Ihr Verständnis der Theorie auf spielerische Weise testen und einüben können.
Algebra: Gruppen - Ringe - Körper
by Christian Karpfinger Kurt MeybergDieses vierfarbige Lehrbuch wendet sich an Studierende der Mathematik in Bachelor- und Lehramts-Studieng#65533;ngen. Es bietet in einem Band ein lebendiges Bild der mathematischen Inhalte, die #65533;blicherweise im ersten Studienjahr behandelt werden (und etliches mehr). Mathematik-Studierende finden wichtige Begriffe, S#65533;tze und Beweise ausf#65533;hrlich und mit vielen Beispielen erkl#65533;rt und werden an grundlegende Konzepte und Methoden herangef#65533;hrt. Im Mittelpunkt stehen das Verst#65533;ndnis der mathematischen Zusammenh#65533;nge und des Aufbaus der Theorie sowie die Strukturen und Ideen wichtiger S#65533;tze und Beweise. Es wird nicht nur ein in sich geschlossenes Theoriengeb#65533;ude dargestellt, sondern auch verdeutlicht, wie es entsteht und wozu die Inhalte sp#65533;ter ben#65533;tigt werden. Herausragende Merkmale sind: durchg#65533;ngig vierfarbiges Layout mit mehr als 600 Abbildungen pr#65533;gnant formulierte Kerngedanken bilden die Abschnitts#65533;berschriften Selbsttests in kurzen Abst#65533;nden erm#65533;glichen Lernkontrollen w#65533;hrend des Lesens farbige Merkk#65533;sten heben das Wichtigste hervor ,,Unter-der-Lupe"-Boxen zoomen in Beweise hinein, motivieren und erkl#65533;ren Details ,,Hintergrund-und-Ausblick"-Boxen stellen Zusammenh#65533;nge zu anderen Gebieten und weiterf#65533;hrenden Themen her Zusammenfassungen zu jedem Kapitel sowie #65533;bersichtsboxen mehr als 400 Verst#65533;ndnisfragen, Rechenaufgaben und Aufgaben zu Beweisen deutsch-englisches Symbol- und Begriffsglossar Der inhaltliche Schwerpunkt liegt auf den Themen der Vorlesungen Analysis 1 und 2 sowie Linearer Algebra 1 und 2. Behandelt werden dar#65533;ber hinaus Inhalte und Methodenkompetenzen, die vielerorts im ersten Studienjahr der Mathematikausbildung vermittelt werden. Auf der Website zum Buch www. matheweb. de finden Sie Hinweise, L#65533;sungswege und Ergebnisse zu allen Aufgaben Zusatzmaterialien wie Maple-Worksheets zu verschiedenen Themen des Buchs die M#65533;glichkeit, zu den Kapiteln Fragen zu stellen Das Buch wird allen Studierenden der Mathematik vom Beginn des Studiums bis in h#65533;here Semester hinein ein verl#65533;sslicher Begleiter sein.
Algebra: Gruppen - Ringe - Körper
by Christian Karpfinger Kurt MeybergDieses Lehrbuch zur Algebra bietet eine Einführung in die grundlegenden Begriffe und Methoden der modernen Algebra. Es werden die Themen eines Grundkurses zur Algebra ausführlich und motivierend behandelt. Die Algebra wird von vielen Studierenden als sehr abstrakt empfunden. Daher haben sich die Autoren bemüht, die Ergebnisse und Begriffe mit zahlreichen Beispielen zu unterlegen. Die Beweisführungen sind ausführlich, die Kapitel sind in kleine Lerneinheiten unterteilt. Diese Lerneinheiten führen Schritt für Schritt an die Ergebnisse heran und können durch diese Darstellung vom Leser besser nachvollzogen werden. Die zahlreichen Aufgaben unterschiedlicher Schwierigkeitsgrade zum Ende der Kapitel überprüfen das Gelernte und fördern das tiefere Verständnis der Theorie. Das Buch wurde für die 5. Auflage vollständig durchgesehen und um einen ausführlichen Abschnitt zum semidirekten Produkt von Gruppen erweitert. Zudem wurden Lösungsmethoden inklusive Beispiele für manche typischen Aufgabenstellungen übersichtlich zusammengestellt, z.B. zum Nachweis der Reduzibilität bzw. Irreduzibilität von Polynomen.
Algebra: Form and Function (Second Edition)
by William G. Mccallum Elliot J. Marks Aysegul Sahin Ellen Schmierer Pat Shure Adam H. Spiegler Carl Swenson Eric Connally Deborah Hughes-Hallett Philip Cheifetz Ann Davidian Selin Kalaycýoðlu Brigitte Lahme Patti Frazer Lock David LovelockAlgebra: Form and Function offers a fresh approach to algebra that focuses on teaching readers how to truly understand the principles, rather than viewing them merely as tools for other forms of mathematics. Meant for a College Algebra course, Algebra: Form and Function is an introduction to one of the fundamental aspects of modern society. Algebraic equations describe the laws of science, the principles of engineering, and the rules of business. The power of algebra lies in the efficient symbolic representation of complex ideas, which also presents the main difficulty in learning it. It is easy to forget the underlying structure of algebra and rely instead on a surface knowledge of algebraic manipulations. Most students rely on surface knowledge of algebraic manipulations without understanding the underlying structure of algebra that allows them to see patterns and apply it to multiple situations: McCallum focuses on the structure from the start.
Algebra: A Combined Course: Concepts With Applications
by Charles P. McKeagueA Combined Course: Concepts With Applications
Algebra: The Easy Way to Learn Algebra
by Hugh NeillAlgebra: A Complete Introduction is the most comprehensive yet easy-to-use introduction to using Algebra.Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all the key areas of algebra including elementary operations, linear equations, formulae, simultaneous equations, quadratic equations, logarithms, variation, laws and sequences.Everything you will need is here in this one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions.Chapter 1: The meaning of algebraChapter 2: Elementary operations in algebraChapter 3: Brackets and operations with themChapter 4: Positive and negative numbersChapter 5: Equations and expressionsChapter 6: Linear equationsChapter 7: FormulaeChapter 8: Simultaneous equationsChapter 9: Linear inequalitiesChapter 10: Straight-line graphs; coordinatesChapter 11: Using inequalities to define regionsChapter 12: Multiplying algebraical expressions Chapter 13: FactorsChapter 14: FractionsChapter 15: Graphs of quadratic functionsChapter 16: Quadratic equationsChapter 17: IndicesChapter 18: LogarithmsChapter 19: Ratio and proportionChapter 20: VariationChapter 21: The determination of lawsChapter 22: Rational and irrational numbers and surdsChapter 23: Arithmetical and geometric sequences
Algebra: A Complete Introduction (Teach Yourself)
by Hugh Neill P. AbbottAlgebra: A Complete Introduction is the most comprehensive yet easy-to-use introduction to using Algebra. Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. <P><P>The book covers all the key areas of algebra including elementary operations, linear equations, formulae, simultaneous equations, quadratic equations, logarithms, variation, laws and sequences.<P>Everything you will need is here in this one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions.
Algebra: A Complete Introduction (Teach Yourself)
by Hugh Neill P. AbbottAlgebra: A Complete Introduction is the most comprehensive yet easy-to-use introduction to using Algebra.<P><P>Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all the key areas of algebra including elementary operations, linear equations, formulae, simultaneous equations, quadratic equations, logarithms, variation, laws and sequences.Everything you will need is here in this one book. <P>Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions.Chapter 1: The meaning of algebra; Chapter 2: Elementary operations in algebra; Chapter 3: Brackets and operations with them; Chapter 4: Positive and negative numbers; Chapter 5: Equations and expressions; Chapter 6: Linear equations;Chapter 7: Formulae; Chapter 8: Simultaneous equations;Chapter 9: Linear inequalities;Chapter 10: Straight-line graphs; coordinates;Chapter 11: Using inequalities to define regions;Chapter 12: Multiplying algebraical expressions Chapter 13: Factors;Chapter 14: Fractions;Chapter 15: Graphs of quadratic functions;Chapter 16: Quadratic equations;Chapter 17: Indices;Chapter 18: Logarithms;Chapter 19: Ratio and proportion;Chapter 20: Variation;Chapter 21: The determination of laws;Chapter 22: Rational and irrational numbers and surds; Chapter 23: Arithmetical and geometric sequences
Algebra: Essentials and Applications
by Holt Rinehart WinstonAlgebra Essentials and Applications is focused, organized, and easy to follow. The program shows your students how to read, write, and understand the unique language of mathematics, so that they are prepared for every type of problem-solving and assessment situation.
Algebra: Groups, Rings, and Fields (Textbooks in Mathematics)
by Louis RowenThis text presents the concepts of higher algebra in a comprehensive and modern way for self-study and as a basis for a high-level undergraduate course. The author is one of the preeminent researchers in this field and brings the reader up to the recent frontiers of research including never-before-published material. From the table of contents: - Groups: Monoids and Groups - Cauchyís Theorem - Normal Subgroups - Classifying Groups - Finite Abelian Groups - Generators and Relations - When Is a Group a Group? (Cayley's Theorem) - Sylow Subgroups - Solvable Groups - Rings and Polynomials: An Introduction to Rings - The Structure Theory of Rings - The Field of Fractions - Polynomials and Euclidean Domains - Principal Ideal Domains - Famous Results from Number Theory - I Fields: Field Extensions - Finite Fields - The Galois Correspondence - Applications of the Galois Correspondence - Solving Equations by Radicals - Transcendental Numbers: e and p - Skew Field Theory - Each chapter includes a set of exercises
Algebra: Groups, Rings, and Fields (Textbooks in Mathematics)
by Louis Halle Rowen Uzi VishneAlgebra is a subject we have become acquainted with during most of our mathematical education, often in connection with the solution of equations. Algebra: Groups, Rings, and Fields, Second Edition deals with developments related to their solutions.The principle at the heart of abstract algebra, a subject that enables one to deduce sweeping conclusions from elementary premises, is that the process of abstraction enables us to solve a variety of such problems with economy of effort. This leads to the glorious world of mathematical discovery.This second edition follows the original three-pronged approach: the theory of finite groups, number theory, and Galois’ amazing theory of field extensions tying solvability of equations to group theory.As algebra has branched out in many directions, the authors strive to keep the text manageable while at the same time introducing the student to exciting new paths. In order to support this approach, the authors broadened the first edition, giving monoids a greater role, and relying more on matrices. Hundreds of new exercises were added.A course in abstract algebra, properly presented, could treat mathematics as an art as well as a science. In this exposition, we try to present underlying ideas, as well as the results they yield.
Algebra: A Computational Introduction (Studies in Advanced Mathematics)
by John Scherk<p>Adequate texts that introduce the concepts of abstract algebra are plentiful. None, however, are more suited to those needing a mathematical background for careers in engineering, computer science, the physical sciences, industry, or finance than Algebra: A Computational Introduction. Along with a unique approach and presentation, the author demonstrates how software can be used as a problem-solving tool for algebra. A variety of factors set this text apart. Its clear exposition, with each chapter building upon the previous ones, provides greater clarity for the reader. The author first introduces permutation groups, then linear groups, before finally tackling abstract groups. He carefully motivates Galois theory by introducing Galois groups as symmetry groups. He includes many computations, both as examples and as exercises. All of this works to better prepare readers for understanding the more abstract concepts. <p>By carefully integrating the use of Mathematica throughout the book in examples and exercises, the author helps readers develop a deeper understanding and appreciation of the material. The numerous exercises and examples along with downloads available from the Internet help establish a valuable working knowledge of Mathematica and provide a good reference for complex problems encountered in the field.</p>
Algebra: A Teaching and Source Book
by Ernest Shult David SurowskiThis book presents a graduate-level course on modern algebra. It can be used as a teaching book - owing to the copious exercises - and as a source book for those who wish to use the major theorems of algebra. The course begins with the basic combinatorial principles of algebra: posets, chain conditions, Galois connections, and dependence theories. Here, the general Jordan-Holder Theorem becomes a theorem on interval measures of certain lower semilattices. This is followed by basic courses on groups, rings and modules; the arithmetic of integral domains; fields; the categorical point of view; and tensor products. Beginning with introductory concepts and examples, each chapter proceeds gradually towards its more complex theorems. Proofs progress step-by-step from first principles. Many interesting results reside in the exercises, for example, the proof that ideals in a Dedekind domain are generated by at most two elements. The emphasis throughout is on real understanding as opposed to memorizing a catechism and so some chapters offer curiosity-driven appendices for the self-motivated student.
Algebra
by The University of Chicago School Mathematics Project Susan A. Brown R. James BreunlinNIMAC-sourced textbook
Algebra 1
by AbekaAlgebra 1 is a practical textbook with many features to make your study of algebra interesting and successful.
Algebra 1: A Reference Guide
by K12 Summit CurriculumIn this book, students explore the tools of algebra. Students learn to identify the structure and properties of the real number system; complete operations with integers and other rational numbers; work with square roots and irrational numbers; graph linear equations; solve linear equations and inequalities in one variable; solve systems of linear equations; use ratios, proportions, and percentages to solve problems; use algebraic applications in geometry, including the Pythagorean theorem and formulas for measuring area and volume; complete an introduction to polynomials; and understand logic and reasoning.
Algebra 1: An Integrated Approach
by Robert Gerver Richard Sgroi Claudia Carter Mary HansenAlgebra 1 textbook.
Algebra 1 (Grade #9)
by Berchie Holliday Gilbert J. Cuevas Beatrice LuchinAlgebra 1 is a key program in our vertically-aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics scores on today's high-stakes assessments.
