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. 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. 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.

### Trigonometry Ratios-Sine, Cosine, Tangent

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. 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. 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. 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. 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. 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.

## Trigonometry

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.

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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. 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. 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.

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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.

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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. Then the angle at the tip of your forefinger is A, the tip of your thumb is B and the right angle is C. Now, use that to memorize the following definitions:. The trig cheat sheet only gives the formulas for these theorems. If you are required to use the full definition, or are unsure when to use each formula, you will need additional study material.

Pythagorean Theorem, Law of Sines, Law of Cosines, Law of Tangents are all about the relationships between the sides and angles of triangles. Using the definition of a right triangle on your hand as explained above the lengths of the sides are related by the following formula:. When the angle C is p, 0, or 2p, the law of cosines reduces to a simpler formula. If it is easier for you to memorize these too, go ahead, but usually I just solve for them. Here is a list of the most important trig formulas. Squared formulas. Sum and Difference formulas a and b are angles.

Power Reduction Formulas. Product to Sum Formulas a and b are angles. Sum to Product Formulas a and b are angles. Bright Hub Education. Skip to content. Angles Until now, you probably measured angles in degrees. Everything you need to know to get through your trig class. Whether in high school or college, the tips, tricks, formulas and methods you need can all be found here. More Info. All rights reserved.