The Fundamental Theorem of Algebra PDF Download
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Author: Benjamin Fine
Publisher: Springer Science & Business Media
ISBN: 1461219280
Category : Mathematics
Languages : en
Pages : 220
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Book Description
The fundamental theorem of algebra states that any complex polynomial must have a complex root. This book examines three pairs of proofs of the theorem from three different areas of mathematics: abstract algebra, complex analysis and topology. The first proof in each pair is fairly straightforward and depends only on what could be considered elementary mathematics. However, each of these first proofs leads to more general results from which the fundamental theorem can be deduced as a direct consequence. These general results constitute the second proof in each pair. To arrive at each of the proofs, enough of the general theory of each relevant area is developed to understand the proof. In addition to the proofs and techniques themselves, many applications such as the insolvability of the quintic and the transcendence of e and pi are presented. Finally, a series of appendices give six additional proofs including a version of Gauss'original first proof. The book is intended for junior/senior level undergraduate mathematics students or first year graduate students, and would make an ideal "capstone" course in mathematics.
Author: Benjamin Fine
Publisher: Springer Science & Business Media
ISBN: 1461219280
Category : Mathematics
Languages : en
Pages : 220
Get Book Here
Book Description
The fundamental theorem of algebra states that any complex polynomial must have a complex root. This book examines three pairs of proofs of the theorem from three different areas of mathematics: abstract algebra, complex analysis and topology. The first proof in each pair is fairly straightforward and depends only on what could be considered elementary mathematics. However, each of these first proofs leads to more general results from which the fundamental theorem can be deduced as a direct consequence. These general results constitute the second proof in each pair. To arrive at each of the proofs, enough of the general theory of each relevant area is developed to understand the proof. In addition to the proofs and techniques themselves, many applications such as the insolvability of the quintic and the transcendence of e and pi are presented. Finally, a series of appendices give six additional proofs including a version of Gauss'original first proof. The book is intended for junior/senior level undergraduate mathematics students or first year graduate students, and would make an ideal "capstone" course in mathematics.
Author: Meixia Ding
Publisher: Routledge
ISBN: 9780367750824
Category :
Languages : en
Pages : 0
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Book Description
Drawing on rich classroom observations of educators teaching in China and the U.S., this book details an innovative and effective approach to teaching algebra at the elementary level, namely, "teaching through example-based problem solving" (TEPS). Recognizing young children's particular cognitive and developmental capabilities, this book powerfully argues for the importance of infusing algebraic thinking into early grade mathematics teaching and illustrates how this has been achieved by teachers in U.S. and Chinese contexts. Documenting best practice and students' responses to example-based instruction, the text demonstrates that this TEPS approach - which involves the use of worked examples, representations, and deep questions - helps students learn and master fundamental mathematical ideas, making it highly effective in developing algebraic readiness and mathematical understanding. This text will benefit post-graduate students, researchers, and academics in the fields of mathematics, STEM, and elementary education, as well as algebra research more broadly. Those interested in teacher education, classroom practice, and developmental and cognitive psychology will also find this volume of interest.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Dan Saracino
Publisher: Waveland Press
ISBN: 1478610131
Category : Mathematics
Languages : en
Pages : 320
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Book Description
The Second Edition of this classic text maintains the clear exposition, logical organization, and accessible breadth of coverage that have been its hallmarks. It plunges directly into algebraic structures and incorporates an unusually large number of examples to clarify abstract concepts as they arise. Proofs of theorems do more than just prove the stated results; Saracino examines them so readers gain a better impression of where the proofs come from and why they proceed as they do. Most of the exercises range from easy to moderately difficult and ask for understanding of ideas rather than flashes of insight. The new edition introduces five new sections on field extensions and Galois theory, increasing its versatility by making it appropriate for a two-semester as well as a one-semester course.
Author: Isaac Todhunter
Publisher:
ISBN:
Category : Algebra
Languages : en
Pages : 302
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Book Description
Author: Justin Hill
Publisher: Lulu.com
ISBN: 0359042112
Category : Education
Languages : en
Pages : 402
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Book Description
This textbook introduces the basic notions of group theory by a thorough treatment of important examples, including complex numbers, modular arithmetic, symmetries, and permutations. Practical examples to cryptography and coding theory are also included.
Author: Alain M Robert
Publisher: World Scientific Publishing Company
ISBN: 9813101962
Category : Mathematics
Languages : en
Pages : 387
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Book Description
This short but rigorous book approaches the main ideas of linear algebra through carefully selected examples and relevant applications. It is intended for students with various interests in mathematics, as well as established scientists seeking to refresh their basic mathematical culture.The book is also a good introduction to functional analysis and quantum theory since it discusses the general principles of linear algebra without finiteness assumptions.
Author: Anthony W. Knapp
Publisher: Springer Science & Business Media
ISBN: 0817645292
Category : Mathematics
Languages : en
Pages : 762
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Book Description
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.
Author: Jay Abramson
Publisher:
ISBN: 9789888407439
Category : Mathematics
Languages : en
Pages : 892
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Book Description
College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they've learned. Coverage and Scope In determining the concepts, skills, and topics to cover, we engaged dozens of highly experienced instructors with a range of student audiences. The resulting scope and sequence proceeds logically while allowing for a significant amount of flexibility in instruction. Chapters 1 and 2 provide both a review and foundation for study of Functions that begins in Chapter 3. The authors recognize that while some institutions may find this material a prerequisite, other institutions have told us that they have a cohort that need the prerequisite skills built into the course. Chapter 1: Prerequisites Chapter 2: Equations and Inequalities Chapters 3-6: The Algebraic Functions Chapter 3: Functions Chapter 4: Linear Functions Chapter 5: Polynomial and Rational Functions Chapter 6: Exponential and Logarithm Functions Chapters 7-9: Further Study in College Algebra Chapter 7: Systems of Equations and Inequalities Chapter 8: Analytic Geometry Chapter 9: Sequences, Probability and Counting Theory
Author: Seong R. Kim
Publisher: Createspace Independent Pub
ISBN: 9781466396135
Category : Mathematics
Languages : en
Pages : 346
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Book Description
Students need the best teacher, so you need examples, because examples are the best teacher. All the examples in this book are fully worked, and help you do math better. And this book is for your skill of algebra, and you will grow the skill through examples. Some examples may look too easy or too hard. It all depends on your skill of algebra. Whatever your skill may be though, you can grow yours if you follow the steps in each example. Each is detailed so that you can learn those tools fast, and increase your caliber quickly as well as properly. And this book covers functions, and explains what a function is about, how it gets made, what it does or how it behaves, and what we can do with it or how to use it. What then, is it for? A function is an idea in math, so it's a math idea, and is a tool in math. So it's a math tool. And we use it, solving problems, of course. So students need to get the idea. And thus, this book helps you get the idea of a function, that is, the concept of a math object called a function, and you will get to see how to work with it properly, because the book explains many basic functions, how they get made, and how they work, along with their nature so that you can develop your own idea, to solve problems, of course. And this book is particularly for those students who want to study calculus later or now in university level, and want to be science or engineering majors. And you can look at some preview, which is at http://www.lulu.com/spotlight/runmath All the books shown there are in electronic version in PDF for Adobe Digital Editions. You can see though, the preview with no download, and see it in you web browser. There are two options. One is Algebra Examples Basic Functions 1, which is the first half the whole book, which is this book. And the other is Algebra Examples Basic Functions 2, which is the last half. If either is found, click 'More Detail' underneath the cover image, and then, click 'Preview' below the cover image. Then, the preview will show up.
