The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation. Instructors: If you decide to use some or all of this book with your classes, please send me an email letting me know, so I can have some idea if people are finding it useful.

This license means that you have full permission to modify the text to your liking, have it printed, and use it in your classes.

## The Best Books on the History of Mathematics | Five Books

The only requirements are that you include attribution to the original authors, and make your changes available with the same permissions. 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.

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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. 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.

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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.

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.

The challenge will train them to think intuitively and effectively. While some will find this frustrating, motivated and determined students will take it as an opportunity to probe deeper and explore real analysis further than they normally might. Review : Rudin provides a solid handling of graduate level real and complex analysis. He encompasses all basic and advanced topics such as differentiation, Banach and Hilbert Spaces, Fourier analysis, etc. Readers who are familiar with Rudin can expect to see his usual writing style — elegant and concise.

He goes through a standard but thorough teaching on measure theory in the first half of the book and then progresses onto an innovative study of complex analysis. Review : This book gives students an accessible introduction to the world of complex analysis and how its methods are used.

A First Course in Complex Analysis is reader-friendly to the newcomer and therefore is ideal for use by both undergrads as well as graduates.

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## Problems in Algebraic Number Theory

For undergrads, the authors refrain from abstractness and maintain an appreciated level of transparency. While for graduates, they effortlessly fill in the gaps that many standard course texts tend to leave wide open. Each chapter is followed by a section detailing the applications of the previously discussed topic.