Elementary Analysis: The Theory of Calculus (2nd Edition) (Undergraduate Texts in Mathematics)


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These topics run the gamut from classical algorithms to computational geometry. Review : This 3 volume box set does a marvelous job of covering subjects in the vast field of computer science. The writing is intact and brimming with mathematical rigor. Readers whose sole focus is learning can easily skim over areas that are excessively detailed without losing grasp of the core concepts. All three volumes are equally definitive and provide a clean theoretical explanation of fundamentals of computer science.

Additionally, each chapter section comes with questions students can use to gain better hands on experience. This is book is akin to the bible for computer scientists.

A fourth volume is also available. Review : Lengthy yet vital, this resource book is jam packed with straight-forward explanations and loads of solved problems for students to easily learn from. Excelling many of its contemporaries by leaps and bounds, The Calculus Lifesaver truly lives up to its title. Students who are tired of dreary calculus textbooks that provide no motivation behind the concepts will be gladly surprised by the detailed and informal approach Banner uses to capture their attention.

He fills all gaps and leaves readers feeling satisfied and enlightened. This book dually holds the characteristics of both an instructive primary aid as well as that of a supplementary read. Review : Even those who are not particularly gifted or even proficient in mathematics will enjoy sitting down and studying from Calculus Made Easy. Thompson creates a warm, inviting environment where students will learn and grasp the true essence of calculus without any added fluff or overt technicality.

Frustrated students who have sought after a compatible calculus aid to no avail will agree that this is a professional tool that is presented to the reader on the same wavelength. Thompson knows that math is hard. Rather than taking the standard approach that many use to confound and further bewilder students, he breaks calculus down into a form that is a lot less threatening.

He wanders off the standard presentational path for a calculus course and thereby creates a more historically accurate and useful book. But this is a book that was written for the curious student with the intention of being read and understood, not practiced and blindly memorized. The result is that students will be ready to tackle calculus subjects and courses with a newfound clarity. Review : Tenacious students in favor of stimulating study will love this book. He forces them to rely on their own perspicacity and reason instead of a collection of random techniques and mechanics.

This fourth edition includes additional problems and other minor changes not included in the third. Review : In this follow-up to Volume I of his series, Apostol continues to lay the groundwork for calculus students with precision and ease. Unlike other calculus books, this one is replete with substance. The author takes time to build and prove each theorem the way it ought to be done.


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Unlike many follow-up math books, this one never mindlessly repeats the same material. Instead, it vigorously moves ahead into new territory involving the use of multi-variables and advanced applications. Review : This short and concise book only focuses on what is essential and nothing else. Spivak makes his writing on the main objective of the book — Stokes Theorem — painless and easy to grasp.

Readers are encouraged to keep a pen and paper on hand to rewrite the proofs on their own. Review : In this uniquely interesting book, photographer Mariana Cook offers readers high quality black and white photographs of 92 noteworthy mathematicians.

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However it provides a much needed break from the rather austere climate that the math world is usually comprised of. Her selected mathematicians come from diverse backgrounds and have all reached their authoritative status in equally different ways. Each photograph is accompanied by a quick, informative and often enlightening essay by the mathematician at hand, frequently revealing the passion and deep love for their discipline that each mathematician possesses.

Cook does a wonderful job of capturing her subjects in an honest and purely human light. As such, this title is the ideal coffee table book for math geeks. Review : In Sacred Mathematics, Hidetoshi and Rothman present a tantalizing and detailed history of Sangaku puzzles that will keep the reader engaged for many hours.

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For those who are unfamiliar with the subject, sangakus are Japanese geometrical puzzles that were created on wooden tablets and hung in sacred temples and shrines. Readers will discover how the Japanese cleverly intertwined the mathematical, the spiritual, and the artistic to create their own cultural brand of geometry.

Sangaku was formulated during an era before western influence had reached Japan. This makes it a unique and fascinating art that has attracted many mathematicians. This hardcover volume is rich of illustrations and would be a nice coffee table book. Review : Math undergrads will find Principles and Techniques in Combinatorics to be a detailed but easy to read book. This is a much needed textbook that can truly be classified as introductory.


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  • The authors take careful consideration not to over-elaborate key concepts and thereby confuse those readers who are not as advanced in mathematics as others. Students will enjoy walking step by step through precisely detailed combinatorial proofs as well as reading the greatly in depth chapter on Recurrence Relations Chapter 6.

    Elementary Analysis The Theory of Calculus Undergraduate Texts in Mathematics

    An abundance of combinatorial problems that are perfect for math competition trainers and participants can be found at the end of each chapter, adding even more value to this already low-priced gem. Review : This second edition of Combinatorics and Graph Theory presents all relevant concepts in a clear and straight to-the-point manner that students will undoubtedly favor.

    The authors waste no time and quickly set out to teach readers in a brilliantly written and warmly engaging manner.


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    The second edition also contains new material not previously included in the first, such as extended information on Polya theory, stable marriage problems, and Eulerian trails. Review : This high-level text is clearly understandable and widely engaging. Braun runs through the pages of his book in a light, expertly written manner that will keep readers hooked for hours. Review : This is an extraordinary book that every student and mathematician should absolutely have. The PCM carries the true signature of a math encyclopedia in that it is versatile and capable of being all things to all learners in every field of mathematics, and on all levels also.

    In light of its broad spectrum of topics, the editors have managed to keep this book cohesive and well knit together. The PCM includes specialized articles from contributors on a variety of math topics that even the most advanced pros can learn from. Non-mathematicians who are curious about the trade can also learn a great deal of information from the PCM due to its overall accessible nature. This is the kind of book that will still be read a hundred years from now, and it truly is the nicest book I own. Review : This awesome reference gives math lovers exactly what they want from a math encyclopedia.

    This book is formatted in an A- Z structure. Tanton makes no diversions in outlining or trying to draw connections other than what is necessary. He essentially gives readers the needed facts and resources, and then keeps it moving. This will prove to be wonderful for some while disappointing for others. The book contains more than entries as well as relevant timelines following the entries.

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    Real analysis

    Review : This is one of the finest introductory texts on logic that any student can read. While not a mandatory requirement, it is highly recommended that the reader has a slight understanding of math logic. This will make it easier to complete the many exercises found throughout. Review : This is a clearly written and expertly arranged independent study guide designed to make the topic of set theory comprehensible and easy to grasp for self-study students. Without a doubt, this books more than delivers. Readers can expect a smooth ride devoid of complexity and assumed pre-exposure to the subject.

    Ideas, commentaries and recommendations that are resourcefully placed alongside the main text delightfully height the learning experience. This is one of those unfortunately rare but wonderfully rigorous independent study math books that many students stumble across and never seem to put down. Review : The author of this work, Sunders Mac Lane, has concisely spread out all the vital category theory information that students will probably ever need to know.

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    Category theory is a tough topic for many and is not effortlessly explained. Those with limited experience with graduate-level mathematics are cautioned to start with a more basic text before delving into this one. The astounding part about all of it is that Jan Gullberg is a doctor and not a mathematician. The enthusiasm he exhibits throughout will spread onto readers like wildfire.

    Elementary Analysis

    This work is clearly a labor of love, not self-exaltation. Readers will appreciate that Gullberg is simply a man who has fallen in love with and holds an immense adoration for one of the most important components of human civilization. Review : Math aficionados will profit greatly from this book. That is because this book does more than just skim the surface.

    The authors prompt readers to actually think about the ideas and methods mentioned rather than blindly swallow them down for later use. They present captivating discussions on many topics instead of dull facts and easy answers. The end result of reading this book is an appreciation that will develop from the thought processes readers are required to use. 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.

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    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.

    Elementary Analysis: The Theory of Calculus (2nd Edition) (Undergraduate Texts in Mathematics) Elementary Analysis: The Theory of Calculus (2nd Edition) (Undergraduate Texts in Mathematics)
    Elementary Analysis: The Theory of Calculus (2nd Edition) (Undergraduate Texts in Mathematics) Elementary Analysis: The Theory of Calculus (2nd Edition) (Undergraduate Texts in Mathematics)
    Elementary Analysis: The Theory of Calculus (2nd Edition) (Undergraduate Texts in Mathematics) Elementary Analysis: The Theory of Calculus (2nd Edition) (Undergraduate Texts in Mathematics)
    Elementary Analysis: The Theory of Calculus (2nd Edition) (Undergraduate Texts in Mathematics) Elementary Analysis: The Theory of Calculus (2nd Edition) (Undergraduate Texts in Mathematics)
    Elementary Analysis: The Theory of Calculus (2nd Edition) (Undergraduate Texts in Mathematics) Elementary Analysis: The Theory of Calculus (2nd Edition) (Undergraduate Texts in Mathematics)

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