Calculus I Essentials: v. 1 (Essentials Study Guides)

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  1. Distance Learning | Manitoba Education and Training
  2. Differential calculus
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Distance Learning | Manitoba Education and Training

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. 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.


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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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Differential calculus

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. 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.

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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.


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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.

Calculus - Introduction to Calculus

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. Additionally a quick review quiz for further verification and cultivation of skills is also included with each chapter.

Review : Author Tristan Needham reveals the often unrealized beauty of complex analysis through a graphical perspective. He takes an elegant approach to complex analysis that will cause the reader to turn each page in awe of the insightful prose and intricate visuals. Readers will understand solutions through their own intuition, not memorization.

Rich in math history and lively from the start, this book would make excellent study and recreational reading for the serious student. Review : Just as the title implies, the author has submitted an unequivocal and palpable exposition on statistics. Statistics in Plain English is regarded by many as the most appropriate statistics primer for undergraduates. The text is general enough to be used in a variety of mathematical areas yet retains its comprehensiveness and accuracy. Urdan masterfully moves through essential concepts without losing the reader the way many professors would.

Students harboring apprehension towards statistics will tremendously enjoy this book. Weiss has structured the subject matter carefully and formulates his writing in a lucid and enjoyable style. He thoughtfully steers away from advanced topics as they would only serve to confuse readers who are in this elementary stage. The focus is kept on detailed explanations of the basics in a clear language that will appeal to many beginners. Review : This is an excellent, non-technical and simple introduction to statistics.

The book is intended for lower-level students who wish to know the standard topics and methods that are included in most first statistics courses.

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Math students will find it easy to understand the ideas presented, while teachers and tutors will discover an engaging and highly effective way to teach statistics material. The authors provide real-life examples such as clinical trials and observational studies to help readers grasp the subject matter even better.

All that is needed to learn from this book is a basic understanding of numbers and simple algebra. Review : The author of this book has divided it into three sections: topology, operators, and algebras of operators. He contrives a fantastic and classical introduction to topology that targets continuity and linearity, the dominating themes. Self-study students will find Simmons to be a phenomenal communicator and will have no problem at all going through chapter after chapter of his writings. He clarifies deep concepts in a manner that boasts his mathematical capacity and skill while never leaving the reader behind.

Review : Undergraduates will enjoy this introduction to the fundamentals of topology. Despite its relatively short length, this book thoroughly encompasses the basic material students are required to know.

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In the first chapter, Mendelson explains set theory in an unmitigated manner which primes readers for the following chapters. Self-study enthusiasts will fall in love with the clarity and simple progress of the writing. However, despite its simplicity this book holds much contextual depth and gravity. Feel free to get in touch if you think the list is really missing out by not listing a specific book.


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