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Luenberger forms the structure of his book around 5 main parts: entropy, economics, encryption, extraction, and emission, otherwise known as the 5 Es.

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He encompasses several points of view and thereby creates a well-rounded text that readers will admire. He details how each of the above parts provide function for modern info products and services. Luenberger is a talented teacher that readers will enjoy learning from. Readers will gain a profound understanding of the types of codes and their efficiency. Roman starts his exposition off with an introductory section containing brief preliminaries and an introduction to codes that preps the reader and makes it easier for them to process the remaining material. He follows that with two chapters containing a precise teaching on information theory, and a final section containing four chapters devoted to coding theory.

He finishes this pleasing journey into information and coding theory with a brief introduction to cyclic codes. Review : This is an exemplary book requiring a small level of mathematical maturity. Axler takes a thoughtful and theoretical approach to the work. This makes his proofs elegant, simple, and pleasing. He leaves the reader with unsolved exercises which many will find to be thought-provoking and stimulating. An understanding of working with matrices is required. This book works great as a supplementary or second course introduction to linear algebra.

Review : This is a beautifully written book that will help students connect the dots between four differing viewpoints in geometry. This book will help the reader develop a stronger appreciation for geometry and its unique ability to be approached at different angles — an exciting trait which ultimately enables students to strengthen their overall knowledge of the subject.

It is recommended that only those with some existing knowledge of linear and complex algebra, differential equations, and even complex analysis and algebra only use this book. Physics and engineering students beyond their introductory courses are the intended audience and will benefit the most. The material can be used as both refresher reading and as a primary study guide. Hassani is well-versed and his presentation is expertly organized.

He also effectively begins each chapter with a short preamble that helps further instill understanding of the main concepts. Review : Boas continues her tradition of conciseness and wholly satisfies physical science students with her third edition of Mathematical Methods in the Physical Sciences. She even makes a point to stress this in the preface. Boas has done students a tremendous service by combining essential math concepts into one easy to use reference guide. It contains vital pieces and bits of all the major topics including Complex numbers, linear algebra, PDEs, ODEs, calculus, analysis and probability and statistics.

Every physics student should certainly own this one. Review : Undergraduate math majors will find this book to be easily approachable but containing much depth.

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Jones and Jones form a powerful duo and expertly take students through a painless and surprisingly enjoyable learning experience. They seem aware that many readers prefer readability over a more pedantic style. This book rightfully puts emphasis on the beauty of number theory and the authors accompany each exercise with complete solutions — something students will certainly enjoy.

This book can work excellently as both introductory course literature or supplementary study and reference material. Review : Advanced undergrads interested in information on modern number theory will find it hard to put this book down. The authors have created an exposition that is innovative and keeps the readers mind focused on its current occupation. The subject of modern number theory is complex and therefore this book is intended for the more experienced student.

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However, the authors tackle the subject in a well-paced yet rigorous style that is more than commendable. Each page exudes brilliance, birthing an underlying deeper awareness of the topic. As described in the title this book really is an invitation — and curious readers would be wise to accept it. Review : This is a book that is commonly used in number theory courses and has become a classic staple of the subject. Beautifully written, An Introduction to the Theory of Numbers gives elementary number theory students one of the greatest introductions they could wish for. Led by mathematical giant G.

H Hardy, readers will journey through numerous number theoretic ideas and exercises. This book will not only guide number theory students through their current studies but will also prepare them for more advanced courses should they pursue them in the future. An absolute classic that belongs to the bookshelf on any math lover. Review : Sauer has created a book that is more than suitable for first course studies in numerical analysis.

He highlights the five critical areas of the subject which are: Convergence, Complexity, Conditioning, Compression, and Orthogonality, and makes well-planned connections to each throughout the book. The proofs are exacting but not too intricate and will firmly satisfy students. Each chapter is laden with insight, and not just analysis.

Sauer attentively infuses his book with numerous problems, some to be completed by hand and others through the use of the Matlab numerical computing package. Review : This third edition of a widely esteemed favorite has been upgraded to include the latest modern scientific computing methods as well as two completely new chapters. The book is still written and presented in the same practical an easy to read style that the previous versions were known for.

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The authors diligently treat the old familiar methods with passion while tactfully intertwining them with newer and equally important more contemporary ones. However there are strict licensing rules to pay attention to. Review : George Simmons takes newbies and out of practice scholars alike, through a refreshing crash course in three basic mathematical practices Geometry, Algebra and Trigonometry in their simple but often hated form.

High school graduates and others on the way to their first college calculus course will be thoroughly prepared to take on the intimidating realm of college level mathematics. Simmons shows readers just how uncomplicated and enjoyable mathematics can be — all in a transparent and fluid tone. He goes into adequate depth while still maintaining enough brevity to encourage the reader to think on their own.

He cuts to the chase and afterwards leaves readers feeling capable and well-equipped. Each section offers numerous exercises for readers to practice and fine-tune their abilities on.

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Lang carefully uses his grounded expertise to construct a sturdy foundation for the reader to build their future mathematical knowledge on. Basic math concepts are his sole focus and he comfortably takes readers through the material with an advanced but stress free tone.

The principles Lang brings to the forefront are absolutely vital for anyone wishing to move forward in calculus, college algebra, and other areas of mathematics. Review : Introduction to Probability Models differs from many probability books in that it covers a variety of disciplines.

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  6. It has been widely used by a number of professors as the main text for many first courses. This elementary introduction provides ample instruction on probability theory and stochastic processes, and insight into its application in a broad range of fields. Ross has filled each chapter with loads of exercises and clear examples. He also takes his time in explaining the thinking and intuition behind many of the theorems and proofs. Review : In this first volume, William Feller paints a clear picture of probability theory and several of its interesting applications from the discrete viewpoint.

    The material is a bit advanced and is only recommended for students going into their third or fourth years. His writing brims with examples that help establish an accurate conception of discrete probability, and it includes sound insight into the history and development of probability theory.

    Readers will walk away with an intuitive understanding and sharper awareness of the subject.

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    It is a must read item for any intermediate to advanced student who is working in the field of probability theory. Review : Jaynes writes a fantastic prose that views probability theory beyond the usual context. The ideas found within this book are innovative and the author takes a welcomed path away from the conventional. It is strangely akin to receiving a one-on-one lesson from the author himself.