Equations of Lines, Parabolas and Circles. Polynomial and Rational Functions. Exponential and Logarithmic Functions. Basic Trigonometry. Trigonometric Functions. Advanced Trigonometry. Vectors and Parametric Equations. Polar Coordinates and Complex Numbers. Systems of Linear Equations and Matrices.
Topics in Discrete Math. Linear Equations and Inequalities. Introduction to Functions. 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.
Mathematics Placement Test Information
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.
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. 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.
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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.
Mathematics Course Descriptions
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.
Mathematics and Statistics Courses
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.
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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.
Mathematics (MATH) | Iowa State University Catalog
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.