Fundamental Theorem of Algebra: Papers

EBook Description: The Fundamental Theorem of Algebra states that any complex polynomial must have a complex root. This basic result, whose first accepted proof was given by Gauss, lies really at the intersection of the theory of numbers and the theory of equations, and arises also in many other areas of mathematics. The purpose of his book is to examine 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 lends itself to generalizations, which in turn, lead 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. In addition to the proofs and techniques themselves, many applications such as the insolvability of the quintic and the trascendence of e and pi are presented. For a linear algebra course, the Fundamental Theorem of Algebra is needed, so it is the refore desireable to have a proof of it interms of linear algebra

Elementary & Intermediate Algebra, 4/e by Baratto/Bergman is part of the latest offerings in the successful Streeter-Hutchison Series in Mathematics. The fourth edition continues the hallmark approach of encouraging the learning of mathematics by focusing its coverage on mastering math through practice. This worktext seeks to provide carefully detailed explanations and accessible pedagogy to introduce beginning and intermediate algebra concepts and put the content in context. The authors use a three-pronged approach (I. Communication, II. Pattern Recognition, and III. Problem Solving) to present the material and stimulate critical thinking skills. Items such as Math Anxiety boxes, Check Yourself exercises, and Activities represent this approach and the underlying philosophy of mastering math through practice. The exercise sets have been expanded, organized, and clearly labeled. Vocational and professional-technical exercises have been added throughout. Repeated exposure to this consistent structure should help advance the student�s skills in relating to mathematics. The book is designed for a combined beginning and intermediate algebra course, or it can be used across two courses, and is appropriate for lecture, learning center, laboratory, or self-paced courses. It is accompanied by numerous useful supplements, including McGraw-Hill�s online homework management system, MathZone.

Beginning and Intermediate Algebra: An Integrated Approach

Get a good grade in algebra with Gustafson and Frisk's BEGINNING AND INTERMEDIATE ALGEBRA! Written with you in mind, the authors provide clear, no-nonsense explanations that will help you learn difficult concepts with ease. Prepare for exams with numerous resources located online and throughout the text such as online tutoring, chapter summaries, self-checks, getting ready exercises, and vocabulary and concept problems. Use this text, and you'll learn solid mathematical skills that will help you both in future mathematical courses and in real-life!

"Numerical Linear Algebra in Signals, Systems and Control"

The purpose of Numerical Linear Algebra in Signals, Systems and Control is to present an interdisciplinary book, blending linear and numerical linear algebra with three major areas of electrical engineering: Signal and Image Processing, and Control Systems and Circuit Theory. Numerical Linear Algebra in Signals, Systems and Control will contain articles, both the state-of-the-art surveys and technical papers, on theory, computations, and applications addressing significant new developments in these areas. The goal of the volume is to provide authoritative and accessible accounts of the fast-paced developments in computational mathematics, scientific computing, and computational engineering methods, applications, and algorithms. The state-of-the-art surveys will benefit, in particular, beginning researchers, graduate students, and those contemplating to start a new direction of research in these areas. A more general goal is to foster effective communications and exchange of information between various scientific and engineering communities with mutual interests in concepts, computations, and workable, reliable practices.

Algebra: A Complete Course

The reason that we named our program "Algebra: A Complete Course," is that we believe the best way to learn Algebra is to start at the beginning and end at the end! In this program you will find a complete study of the essential material covered in a traditional Algebra 1 and Algebra 2 course.

However, we need to continue a little further with this answer because Algebra 1 and Algebra 2 are terms that refer mostly to the traditional way that Algebra has been taught. Traditional Algebra 1 classes attempt to cover most of Algebra in the first year, but the methods that are used, and the speed with which the material is covered, hinders student understanding of the material. Instead, the student is just exposed to memorizing rules, formulas, tricks, and shortcuts. By the time they get to what is called an Algebra 2 course, (sometimes after they take a Geometry course), they have forgotten almost all of the Algebra that they memorized. So, that Algebra 2 course (which is by definition, a rehash of whatever has been called ?Algebra 1?), must repeat practically all of the Algebra 1 course. In fact, it usually repeats a lot of the Pre-Algebra material as well. This is usually referred to as the "spiral method" of learning, and it is not very effective in helping students to excel, especially at this level of mathematics.

We think that this huge overlap is generally unproductive, and largely unnecessary if the concepts are taught analytically. Therefore we call our program "Algebra: A Complete Course," because we employ a mastery-learning approach, sometimes moving at a slower pace, but without the overlap. As a result, students often complete the course even more quickly.

Elementary Algebra with Applications

This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation.

"The Linear Algebra a Beginning Graduate Student Ought to Know"

Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as computer science, the physical and social sciences, and engineering. It entails an extensive corpus of theoretical results as well as a large body of computational techniques. Unfortunately, in recent years the content of the linear algebra courses required to complete an undergraduate degree in mathematics has been depleted to the extent that they fail to provide a sufficient theoretical or computational background. Students are not only less able to formulate or even follow mathematical proofs, they are also less able to understand the mathematics of the numerical algorithms they need for applications. Certainly, the material presented in the average undergraduate linear algebra course is insufficient for graduate study. This book is intended to fill this gap by providing enough material "theoretical and computational" to allow the student to work independently or in advanced courses.

Calculus: A Complete Course

For the three-semester calculus course. Proven in North America and abroad, this classic text has earned a reputation for excellent accuracy and mathematical rigour. Previous editions have been praised for providing complete and precise statements of theorems, using geometric reasoning in applied problems, and for offering a range of applications across the sciences. Written in a clear, coherent, and readable form, Calculus: A Complete Course makes student comprehension a clear priority. This seventh edition features a new co-author, Dr. Christopher Essex, who has been invited to contribute his unique style and approach to the subject material. Instructors and students will appreciate revised exercises, greater emphasis on differential equations, new pedagogical features, and an enhanced MyLab.

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