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Calculus II (Undergraduate Texts in Mathematics)
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See terms - opens in a new window or tab. The writing is classic and elucidating, accompanied by many engaging illustrations and side notes. Review : This book contains a treasure chest of priceless history and deep facts that even established pros will find themselves learning from. John Stillwell foregoes the encyclopedic route and makes it his goal to help the reader understand the beauty behind mathematics instead.
He brilliantly unifies mathematics into a clear depiction that urges readers to rethink what they thought they knew already.
He effectively travels all pertinent ground in this relatively short text, striking a clever balance between brevity and comprehensiveness. Review : Gilbert Strang has a reputation for writing ample, pragmatic, and insightful books. During the course of reading this one, it will become blatantly clear to the reader that the author has created this work out of passion and a genuine love for the subject.
Every engineer can benefit deeply from reading this. He covers all aspects of computational science and engineering with experience and authority. The topics discussed include applied linear algebra and fast solvers, differential equations with finite differences and finite elements, and Fourier analysis and optimization. Strang has taught this material to thousands of students.
With this book many more will be added to that number. The book contains interesting historical facts and insightful examples. Luenberger forms the structure of his book around 5 main parts: entropy, economics, encryption, extraction, and emission, otherwise known as the 5 Es. 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. 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. 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. 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.
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. 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.
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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.
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. Jaynes should be praised for taking a huge step away from mainstream probability theory and into this fresher approach. The only disappointment to this masterpiece is that, sadly, Jaynes died before completely finishing it, causing the editor to step in and thinly inject the missing pieces. Review : This small entertaining book presents a remarkable assortment of probability problems and puzzles that will keep readers stimulated for hours.
Monsteller narrates parts of his book with a sense of humor which creates an easy-going and comfortable learning environment.
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The problems the author has selected put emphasis on, and will help readers learn, invaluable techniques. Detailed solutions to each problem are also included so as not to leave the reader bewildered or uncertain. The book ranges in scope from basic probability puzzlers to very difficult and intricate ones for the highly advanced student. This book easily doubles as supplementary study material or as a source of recreational math enjoyment. Review : Rudin has written an exquisite book on analysis.
Before approaching, students should have a modest understanding of mapping, set theory, linear algebra and other basic topics. Buskes, Gerard; Rooij, Arnoud Van Topological Spaces: From Distance to Neighborhood. Fine, Benjamin; Rosenberger, Gerhard The Fundamental Theorem of Algebra. Beardon, Alan F. Gordon, Hugh Discrete Probability. Roman, Steven Introduction to Coding and Information Theory.
Sethuraman, Bharath Undergraduate Analysis 2nd ed. Geometric Constructions. Protter, Murray H. Basic Elements of Real Analysis. Priestley, W. Calculus: A Liberal Art 2nd ed. Singer, David A. Geometry: Plane and Fancy. Smith, Larry Applied Abstract Algebra 2nd ed. Numbers and Geometry. Laubenbacher, Reinhard; Pengelley, David Mathematical Expeditions: Chronicles by the Explorers. Frazier, Michael W. Schiff, Joel L. The Laplace Transform: Theory and Applications.
Brunt, B. Inside Calculus. Hartshorne, Robin Geometry: Euclid and Beyond. Callahan, James J. Cederberg, Judith N. A Course in Modern Geometries 2nd ed. Gamelin, Theodore W. Complex Analysis. Vector Analysis. Counting: The Art of Enumerative Combinatorics. Saxe, Karen Beginning Functional Analysis.
Estep, Donald Practical Analysis in One Variable. Toth, Gabor Glimpses of Algebra and Geometry 2nd ed. Aitsahlia, Farid; Chung, Kai Lai Topics in the Theory of Numbers. Discrete Mathematics: Elementary and Beyond. Elements of Number Theory. Buchmann, Johannes Introduction to Cryptography 2nd ed. Irving, Ronald S. Ross, Clay C. Differential Equations: An Introduction with Mathematica 2nd ed. Difference Equations: From Rabbits to Chaos. Chambert-Loir, Antoine A Field Guide to Algebra. Elaydi, Saber An Introduction to Difference Equations 3rd ed.
Undergraduate Algebra 3rd ed. Singer, Stephanie Frank Linearity, Symmetry, and Prediction in the Hydrogen Atom. The Four Pillars of Geometry. Bix, Robert Moschovakis, Yiannis Notes on Set Theory 2nd ed. Mathematical Masterpieces: Further Chronicles by the Explorers.
Harris, John M. Combinatorics and Graph Theory 2nd ed. Naive Lie Theory. Hairer, Ernst; Wanner, Gerhard . Analysis by its History. Edgar, Gerald Measure, Topology, and Fractal Geometry 2nd ed. Herod, James; Shonkwiler, Ronald W. Mendivil, Frank; Shonkwiler, Ronald W. Explorations in Monte Carlo Methods. Stein, William Childs, Lindsay N. A Concrete Introduction to Higher Algebra 3rd ed. Introduction to Boolean Algebras. Bak, Joseph; Newman, Donald J. Complex Analysis 3rd ed. Beck, Matthias; Geoghegan, Ross Advanced Calculus: A Geometric View.
Hurlbert, Glenn Linear Optimization: The Simplex Workbook. Mathematics and Its History 3rd ed. Ghorpade, Sudhir R. A Course in Multivariable Calculus and Analysis. Davidson, Kenneth R.
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