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Electronic Transactions on Numerical Analysis
its book of mathematics on numerical analysis.
One Variable Advanced Calculus
The difference between advanced calculus and calculus is that all the theorems are proved completely and the role of plane geometry is minimized. Instead, the notion of completeness is of preeminent importance. Silly gimmicks are of no significance at all. Routine skills involving elementary functions and integration techniques are supposed to be mastered and have no place in advanced calculus which deals with the fundamental issues related to existence and meaning. This is a subject which places calculus as part of mathematics and involves proofs and definitions, not algorithms and busy work.
This text contains sufficient material for a one-semester course in mathematical algorithms, for second year mathematics students. The course requires some exposure to the basic concepts of discrete mathematics, but no computing experience.
The aim of this course is twofold. Firstly, to introduce the basic algorithms for computing exactly with integers, polynomials and vector spaces. In doing so, the student is expected to learn how to think algorithmically and how to design and analyze algorithms.
Learning modern higher mathematics--discrete mathematics, in particular--requires more than ever fluency in elementary arithmetic and algebra. An alarming number of students reach university without these skills.
The Essential Mathematics pro gramme at Queen Mary is designed to address this problem. It provides training for a compulsory examination, which all first year mathematics students must pass to be admitted to the second year; the exam is to be attempted repeatedly, until passed, and is supported by the course MAS010. A similar--if a bit less demanding--programme has been introduced as the core course SEF026 within the Science and Engineering foundational year.
Basic Elements of Real Analysis (Undergraduate Texts in Mathematics)
From the author of the highly acclaimed 'A First Course in Real Analysis' comes a volume designed specifically for a short one- semester course in real analysis. Many students of mathematics and those students who intend to study any of the physical sciences and computer science need a text that presents the most important material in a brief and elementary fashion. The author has included such elementary topics as the real number system, the theory at the basis of elementary calculus, the topology of metric spaces and infinite series. There are proofs of the basic theorems on limits at a pace that is deliberate and detailed. There are illustrative examples throughout with over 45 figures.
Mathematical Illustrations - A manual of geometry and PostScript
This practical introduction to the techniques needed to produce high-quality mathematical illustrations is suitable for anyone with basic knowledge of coordinate geometry. Bill Casselman combines a completely self-contained step-by-step introduction to the graphics programming language PostScript with an analysis of the requirements of good mathematical illustrations. The many small simple graphics projects can also be used in courses in geometry, graphics, or general mathematics. Code for many of the illustrations is included, and can be downloaded from the book's web site: www.math.ubc.ca/~cass/graphics/manualMathematicians; scientists, engineers, and even graphic designers seeking help in creating technical illustrations need look no further.
Mathematics of the Rubik's cube
Groups measure symmetry. No where is this more evident than in the study of symmetry in 2- and 3-dimensional geometric figures. Symmetry, and hence groups, play a key role in the study of crystallography, elementary particle physics, coding theory, and the Rubik' s cube, to name just a few.
This is a book biased towards group theory not the 'the cube'. To paraphrase the German mathematician David Hilbert, the art of doing group theory is to pick a good example to learn from. The Rubik's cube will be our example. We motivate the study of groups by creating a group-theoretical model of Rubik's cube-like puzzles. Although some solution strategies are discussed (for the Rubik's cube - the 3 x 3 x 3 and 4 x 4 x 4 versions, the 'Rubik tetrahedron' or pyraminx, the the 'Rubik dodecahedron', or megaminx, the skewb, square 1, the masterball, and the equator puzzle), these are viewed more abstractly than most other books on the subject. We regard a solution strategy merely as a not-too-inefficient algorithm for producing all the elements in the associated group of moves.
Derivations of Applied Mathematics
This is a book of applied mathematical proofs. If you have seen a mathematical result, if you want to know why the result is so, you can look for the proof here.
The book's purpose is to convey the essential ideas underlying the derivations of a large number of mathematical results useful in the modeling of physical systems. To this end, the book emphasizes main threads of mathematical argument and the motivation underlying the main threads, deemphasizing formal mathematical rigor. It derives mathematical results from the purely applied perspective of the scientist and the engineer.
The Chaos Hypertextbook - Mathematics in the Age of the Computer
In the 1980s, strange new mathematical concepts burst forth from academic isolation to seize the attention of the public. Chaos. A fantastic notion. The study of the uncontainable, the unpredictable, the bizarre. Fractals. Curves and surfaces unlike anything ever seen in mathematics before. At first, one might think that these topics are beyond the comprehension of all but the smartest, most educated, and most specialized geniuses. It turned out that chaos, fractals, and the related topic of dimension are really not that difficult. One can devote an academic lifetime to them, of course, but the basic introduction presented in this book is no more difficult to understand than the straight line and the parabola.
Some of the topics discussed in this book have roots extending back to the close of the Nineteenth Century. But the really flashy stuff had to wait until integrated circuits integrated themselves into daily life. The real beauties of this concept are the colors, patterns, details, and motions at a level beyond line drawings on paper. This is when we need computers, lots of them, to reproduce every image, movie, and data set found in this book. This is mathematics in the age of the computer.
Unsolved Problems in Mathematical Systems and Control Theory
This book provides clear presentations of more than sixty important unsolved problems in mathematical systems and control theory. Each of the problems included here is proposed by a leading expert and set forth in an accessible manner. Covering a wide range of areas, the book will be an ideal reference for anyone interested in the latest developments in the field, including specialists in applied mathematics, engineering, and computer science.
The book consists of ten parts representing various problem areas, and each chapter sets forth a different problem presented by a researcher in the particular area and in the same way: description of the problem, motivation and history, available results, and bibliography. It aims not only to encourage work on the included problems but also to suggest new ones and generate fresh research. The reader will be able to submit solutions for possible inclusion on an online version of the book to be updated quarterly on the Princeton University Press website, and thus also be able to access solutions, updated information, and partial solutions as they are developed.
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