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Real Algebra : A First Course
This book provides an introduction to fundamental methods and techniques of algebra over ordered fields.It is a revised and updated translation of the classic textbook Einführung in die reelle Algebra.Beginning with the basics of ordered fields and their real closures, the book proceeds to discuss methods for counting the number of real roots of polynomials.Followed by a thorough introduction to Krull valuations, this culminates in Artin's solution of Hilbert's 17th Problem.Next, the fundamental concept of the real spectrum of a commutative ring is introduced with applications.The final chapter gives a brief overview of important developments in real algebra and geometry—as far as they are directly related to the contents of the earlier chapters—since the publication of the original German edition.Real Algebra is aimed at advanced undergraduate and beginning graduate students who have a good grounding in linear algebra, field theory and ring theory.It also provides a carefully written reference for specialists in real algebra, real algebraic geometry and related fields.
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A Course in Calculus and Real Analysis
Offering a unified exposition of calculus and classical real analysis, this textbook presents a meticulous introduction to single-variable calculus.Throughout, the exposition makes a distinction between the intrinsic geometric definition of a notion and its analytic characterization, establishing firm foundations for topics often encountered earlier without proof.Each chapter contains numerous examples and a large selection of exercises, as well as a “Notes and Comments” section, which highlights distinctive features of the exposition and provides additional references to relevant literature. This second edition contains substantial revisions and additions, including several simplified proofs, new sections, and new and revised figures and exercises.A new chapter discusses sequences and series of real-valued functions of a real variable, and their continuous counterpart: improper integrals depending on a parameter.Two new appendices cover a construction of the real numbers using Cauchy sequences, and a self-contained proof of the Fundamental Theorem of Algebra. In addition to the usual prerequisites for a first course in single-variable calculus, the reader should possess some mathematical maturity and an ability to understand and appreciate proofs.This textbook can be used for a rigorous undergraduate course in calculus, or as a supplement to a later course in real analysis.The authors’ A Course in Multivariable Calculus is an ideal companion volume, offering a natural extension of the approach developed here to the multivariable setting. From reviews:[The first edition is] a rigorous, well-presented and original introduction to the core of undergraduate mathematics — first-year calculus.It develops this subject carefully from a foundation of high-school algebra, with interesting improvements and insights rarely found in other books. […] This book is a tour de force, and a necessary addition to the library of anyone involved in teaching calculus, or studying it seriously.N.J. Wildberger, Aust. Math. Soc. Gaz.
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Willkommen! 2 German Intermediate course : Course Pack
Willkommen! 2 Intermediate course is a brand new multimedia German adult learning programme for classroom and home use.This listing is for the Course Pack which includes the coursebook and CD and DVD set.The activity book is available separately (see below for details). Created in consultation with teachers and learners, it's the perfect follow-up to the Willkommen!Beginner's course or any beginner German course. It can also be used as a starting point for study to review and build on existing knowledge. This series comprises 10 units, each with a short educational video that provides an engaging and current overview of German culture and language.Shot on location in Frankfurt, the videos are closely related in topic to each unit in the book, and feature carefully curated interviews (a Green Party councilor with Turkish heritage; two generations of a family running a marble quarry and furniture business; a class of foreign-language students and their teacher; a local couple who hosts travelers from all over the world; an advertising executive who works on the 'Made in Germany' brand for clients such as Lufthansa).Frankfurt's beautiful riverside and historic centre provide the backdrop to the videos.You will visit the GoetheHaus, tour the university campus and sample the delights of the local market.Through the videos, you will be able to enter family homes, cafes and offices, to get a sense of how Germans live and speak today. This Course Pack contains:-Full-colour 190-page Coursebook - the primary text for the course. -CD and DVD set - containing all the conversations and listening activities from the Coursebook plus video content, building on the real-life German used in the course. The course is full of learning features to help you progress in reading, writing, listening and speaking German.It's designed for classroom use but is also suitable for home study. -Reviews A1 and then maps from A2 to B1 of the Common European Framework of Reference (CEFR) for languages-10 learning units - plus extensive grammar sections and word glossary-Covers the topics and functions needed for the UK AS-level examination-Lively and contemporary themes - from food and fashion to travel, work, politics and the environment-Comprehensive coverage of key grammar and vocabulary - for communicating in a range of common conversational settings-Range of activities based on authentic materials - to see everyday German in context-Deutschland info sections - give practical and cultural insights into German life-CD and DVD Set - contains all the conversations and listening activities from the coursebook plus video content building on the real-life German used in the course Also available: Activity Book (ISBN 9781444165203): for extra practice and review linked to the coursebook units.
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Advanced course or basic course?
It ultimately depends on your current level of knowledge and your goals. If you already have a strong foundation in the subject and are looking to deepen your understanding, an advanced course may be more suitable. However, if you are new to the subject or looking to refresh your knowledge, a basic course would be a better starting point. Consider your learning objectives and choose the course that aligns best with your needs.
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What is the difference between honest and sincere?
Honesty refers to telling the truth and being straightforward in one's communication, while sincerity refers to being genuine and heartfelt in one's actions and expressions. In other words, honesty is about being truthful and transparent, while sincerity is about being genuine and authentic. One can be honest without being sincere, and vice versa. For example, someone can be honest about their feelings but not sincerely express them, or someone can sincerely express themselves but not be completely honest.
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Are there still honest, genuine people?
Yes, there are still honest and genuine people in the world. While it may sometimes seem like dishonesty and insincerity are prevalent, there are still many individuals who value honesty and authenticity in their interactions with others. These people can be found in all walks of life, and their integrity and genuineness can have a positive impact on those around them. It's important to recognize and appreciate these individuals and strive to embody those qualities ourselves.
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For real robots: Which course of study is suitable?
For real robots, a suitable course of study would be robotics engineering or mechatronics. These fields of study focus on the design, construction, and operation of robots, as well as the integration of mechanical, electrical, and computer engineering principles. Additionally, courses in computer science, artificial intelligence, and control systems would also be beneficial for those interested in working with real robots. Overall, a combination of engineering, computer science, and robotics-specific courses would provide a strong foundation for a career in working with real robots.
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Collision Course
Private investigator Tess Grey feels duty bound to help when the missing girl she has been asked to find becomes involved a high-stakes case of extortion.Private investigator Tess Grey's latest case involves tracking down Hayley Cameron, a young girl who has fled after discovering that she was adopted.Tess, aided by her fiance Po Villere, traces Hayley to the apartment of Madison Toner - one of Hayley's college friends - in Bangor, Maine.Despite Tess's pleas, Hayley refuses to return to her adoptive mother.Both Tess and Po believe there's more to her running away than it seems, especially when they see Madison's father bloodied and beaten.Concerned for Hayley's well-being, they conduct a stake-out. When thugs turn up to blackmail Madison and Hayley, Tess and Po feel duty bound to get involved.But what are the girls embroiled in? Who are after them and to what lengths will they go?Tess and Po don't know it yet, but events are about to grow deadly.
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MySQL Crash Course
MySQL is one of the most popular database management systems available, powering everything from Internet powerhouses to individual corporate databases to simple end-user applications, and everything in between.This book will teach you all you need to know to be immediately productive with the latest version of MySQL.By working through 30 highly focused hands-on lessons, your MySQL Crash Course will be both easier and more effective than you'd have thought possible. Learn How To Retrieve and Sort DataFilter Data Using Comparisons, Regular Expressions, Full Text Search, and Much MoreJoin Relational DataCreate and Alter TablesInsert, Update, and Delete DataLeverage the Power of Stored Procedures and TriggersUse Views and CursorsManage Transactional ProcessingCreate User Accounts and Manage Security via Access Control
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Complete Crochet Course
A complete guide for a beginning crocheter that teaches you how to crochet from the very first stitch and explains all tools, materials and stitches needed to get started.This book is also invaluable for intermediate to advanced crocheters as the book delves into experienced stitches and techniques needed.It includes 10 patterns to get beginners started with their first projects and will clearly identify what skills and lessons need to be learned before starting each project.
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Happiness Course Package
If life is getting a bit rough then get the Happiness Course Package If you struggle with sleep, focus and feeling great, then these courses are for you With over 50 lessons, each up to and over an hour long, you'll be happy in no time Upon completion of this course you will receive a certificate For a full list of courses see Full Details Save a huge 88% off on this Happiness Course Package
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Why can't honest, sincere people be found anywhere anymore?
It is not accurate to say that honest and sincere people cannot be found anymore. While it may seem that way due to increased instances of dishonesty and insincerity in the world, there are still many individuals who uphold these values. It is important to seek out and surround oneself with people who prioritize honesty and sincerity, as they do exist in every community and society. Building strong relationships with trustworthy individuals can help counteract the perception that these qualities are lacking in today's world.
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Why can't one find honest, sincere people anywhere anymore?
It may seem challenging to find honest and sincere people nowadays due to various factors such as societal pressures, individualistic mindsets, and the prevalence of dishonesty in certain environments. In a fast-paced and competitive world, some individuals may prioritize personal gain over honesty, leading to a lack of sincerity in interactions. Additionally, the rise of technology and social media can sometimes create a facade of perfection, making it difficult to discern genuine sincerity from superficiality. Despite these challenges, there are still honest and sincere people out there, and cultivating authentic relationships based on trust and integrity can help in finding them.
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Do straightened rivers also have upper course, lower course, and middle course?
Yes, straightened rivers can still have upper, middle, and lower courses. The upper course is typically where the river originates and flows through steep, mountainous terrain. The middle course is where the river begins to meander and flow through flatter land. The lower course is where the river flows into a larger body of water, such as a lake or ocean. Even if a river has been straightened by human intervention, it will still have these distinct sections based on its natural characteristics and flow patterns.
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What are the differences between the upper course, middle course, and lower course?
The upper course of a river is typically characterized by steep gradients, fast-flowing water, and narrow valleys. It is also where the river begins, often in mountainous or hilly areas. The middle course is characterized by a gentler gradient, wider valleys, and slower-flowing water. It is also where the river begins to meander and deposit sediment. The lower course is characterized by a very gentle gradient, a wide floodplain, and slow-moving water. It is also where the river deposits the majority of its sediment and often forms a delta as it enters a larger body of water.
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