این برنامه به زبان متلب نوشته شده و قابلیت محاسبه تجزیه LU هر نوع ماتریس متقارن را به صورت سه ماتریس L D Lt دارد که در آن، D یک ماتریس قطری و Lt ترانهاده ماتریس L است.
Numerical Linear Algebra: A Concise Introduction with MATLAB and Julia
Title: Numerical Linear Algebra: A Concise Introduction with MATLAB and Julia | Author(s): Folkmar Bornemann, Walter Simson | Publisher: Springer | Year: 2018 | Edition: 1st | Language: English | Pages : 153 |ISBN: 3319742213, 9783319742212 | Size: 3 MB | Extension: pdf
This book offers an introduction to the algorithmic-numerical thinking using basic problems of linear algebra. By focusing on linear algebra, it ensures a stronger thematic coherence than is otherwise found in introductory lectures on numerics. The book highlights the usefulness of matrix partitioning compared to a component view, leading not only to a clearer notation and shorter algorithms, but also to significant runtime gains in modern computer architectures. The algorithms and accompanying numerical examples are given in the programming environment MATLAB, and additionally – in an appendix – in the future-oriented, freely accessible programming language Julia. This book is suitable for a two-hour lecture on numerical linear algebra from the second semester of a bachelors degree in mathematics.
Mathematics Rebooted: A Fresh Approach to Understanding
Title: Mathematics Rebooted: A Fresh Approach to Understanding | Author(s): Lara Alcock | Publisher: Oxford University Press | Year: 2017| Edition: 1 | Language: English | Pages : 256 | ISBN: 0198803796, 9780198803799 | Size: 8 MB | Extension: pdf
Would you like to understand more mathematics? Many people would. Perhaps at school you liked mathematics for a while but were then put off because you missed a key idea and kept getting stuck. Perhaps you always liked mathematics but gave it up because your main interest was music or languages or science or philosophy. Or perhaps you studied mathematics to advanced levels, but have now forgotten most of what you once knew. Whichever is the case, this book is for you. It aims to build on what you know, revisiting basic ideas with a focus on meaning. Each chapter starts with an idea from school mathematics - often primary school mathematics - and gradually builds up a network of links to more advanced material. It explores fundamental ideas in depth, using insights from research in mathematics education and psychology to explain why people often get confused, and how to overcome that confusion. For nervous readers, it will build confidence by clarifying basic ideas. For more experienced readers, it will highlight new connections to more advanced material. Throughout, the book explains how mathematicians think, and how ordinary people can understand and enjoy mathematical ideas and arguments. If you would like to be better informed about the intrinsic elegance of mathematics, this engaging guide is the place to start.
Title: Crossing Numbers of Graphs | Author(s): Marcus Schaefer |Publisher: CRC Press | Year: 2018 | Language: english | Pages : 353 |ISBN: 9781498750493 | Size: 4 MB | Extension: pdf
Features
Aimed at graduate students and professionals in both mathematics and computer science
The first book of its kind devoted to the topic
Authored by a noted authority in crossing numbers
Summary
Crossing Numbers of Graphs is the first book devoted to the crossing number, an increasingly popular object of study with surprising connections. The field has matured into a large body of work, which includes identifiable core results and techniques. The book presents a wide variety of ideas and techniques in topological graph theory, discrete geometry, and computer science.
ابو عبدالله محمدبن موسي خوارزمي در حدود سال 135هجري در شهر خوارزم متولد شد.وي يكي از مفاخر علمي ايران وجهان و از بزرگ ترين دانشمندان مسلمان در قرنهاي گذشته است.
يكي از آثار خوارزمي كتاب جبر و مقابله است.اين كتاب نخستين كتابي است كه نام جبر را بر خود دارد و نام جبر به عنوان بخشي از رياضي ،از نام اين كتاب گرفته شده است.از اين نظر ،خوارزمي را مي توان يكي از بنيان گذاران علم جبر دانست.امروز جبر به شاخه اي مهم از رياضي گفته مي شود.
كتاب حساب خوارزمي در قرن دوازدهم هجري به زبان هاي اروپايي ترجمه شد و به «الخوريسمي»يا «الگوريسمي»كه از نام «الخوارزمي»گرفته شده بود شهرت يافت.بعدها الگوريسم يا الگوريتم به معناي فن محاسبه(يعني حساب)به كار رفت.امروزه الگوريتم به روشي از محاسبه گفته مي شود كه در آن محاسبه مرحله به مرحله انجام مي گيرد و محاسبه هر مرحله به مراحل قبلي بستگي دارد.
Title: Cohomology and Differential Forms | Author(s): Izu Vaisman |Publisher: Dover Publications | Year: 2016 | Language: English | Pages : 293 | ISBN: 0486804836, 9780486804835 | Size: 21 MB | Extension: pdf
This monograph explores the cohomological theory of manifolds with various sheaves and its application to differential geometry. Based on lectures given by author Izu Vaisman at Romanias University of Iasi, the treatment is suitable for advanced undergraduates and graduate students of mathematics as well as mathematical researchers in differential geometry, global analysis, and topology.
A self-contained development of cohomological theory constitutes the central part of the book. Topics include categories and functors, the Čech cohomology with coefficients in sheaves, the theory of fiber bundles, and differentiable, foliated, and complex analytic manifolds. The final chapter covers the theorems of de Rham and Dolbeault-Serre and examines the theorem of Allendoerfer and Eells, with applications of these theorems to characteristic classes and the general theory of harmonic forms.
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