Foundations of Advanced Mathematics
Author | : William E. Kline |
Publisher | : |
Total Pages | : 583 |
Release | : 1975 |
Genre | : Mathematics |
ISBN | : 9780278469198 |
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Author | : William E. Kline |
Publisher | : |
Total Pages | : 583 |
Release | : 1975 |
Genre | : Mathematics |
ISBN | : 9780278469198 |
Author | : Henri Bourles |
Publisher | : Elsevier |
Total Pages | : 270 |
Release | : 2017-07-10 |
Genre | : Mathematics |
ISBN | : 0081021127 |
This precis, comprised of three volumes, of which this book is the first, exposes the mathematical elements which make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering. This first volume focuses primarily on algebraic questions: categories and functors, groups, rings, modules and algebra. Notions are introduced in a general framework and then studied in the context of commutative and homological algebra; their application in algebraic topology and geometry is therefore developed. These notions play an essential role in algebraic analysis (analytico-algebraic systems theory of ordinary or partial linear differential equations). The book concludes with a study of modules over the main types of rings, the rational canonical form of matrices, the (commutative) theory of elemental divisors and their application in systems of linear differential equations with constant coefficients. Part of the New Mathematical Methods, Systems, and Applications series Presents the notions, results, and proofs necessary to understand and master the various topics Provides a unified notation, making the task easier for the reader. Includes several summaries of mathematics for engineers
Author | : Paul Taylor |
Publisher | : Cambridge University Press |
Total Pages | : 590 |
Release | : 1999-05-13 |
Genre | : Mathematics |
ISBN | : 9780521631075 |
This book is about the basis of mathematical reasoning both in pure mathematics itself (particularly algebra and topology) and in computer science (how and what it means to prove correctness of programs). It contains original material and original developments of standard material, so it is also for professional researchers, but as it deliberately transcends disciplinary boundaries and challenges many established attitudes to the foundations of mathematics, the reader is expected to be open minded about these things.
Author | : Carol Avelsgaard |
Publisher | : Scott Foresman & Company |
Total Pages | : 325 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : 9780673381521 |
Author | : Dennis Sentilles |
Publisher | : Courier Corporation |
Total Pages | : 418 |
Release | : 2013-05-20 |
Genre | : Mathematics |
ISBN | : 0486277585 |
This helpful "bridge" book offers students the foundations they need to understand advanced mathematics. The two-part treatment provides basic tools and covers sets, relations, functions, mathematical proofs and reasoning, more. 1975 edition.
Author | : Martin Perkins |
Publisher | : |
Total Pages | : 580 |
Release | : 1982 |
Genre | : Calculators |
ISBN | : 9780713512724 |
Author | : William Johnston |
Publisher | : Oxford University Press |
Total Pages | : 766 |
Release | : 2009-07-27 |
Genre | : Mathematics |
ISBN | : 0199718660 |
A Transition to Advanced Mathematics: A Survey Course promotes the goals of a "bridge'' course in mathematics, helping to lead students from courses in the calculus sequence (and other courses where they solve problems that involve mathematical calculations) to theoretical upper-level mathematics courses (where they will have to prove theorems and grapple with mathematical abstractions). The text simultaneously promotes the goals of a ``survey'' course, describing the intriguing questions and insights fundamental to many diverse areas of mathematics, including Logic, Abstract Algebra, Number Theory, Real Analysis, Statistics, Graph Theory, and Complex Analysis. The main objective is "to bring about a deep change in the mathematical character of students -- how they think and their fundamental perspectives on the world of mathematics." This text promotes three major mathematical traits in a meaningful, transformative way: to develop an ability to communicate with precise language, to use mathematically sound reasoning, and to ask probing questions about mathematics. In short, we hope that working through A Transition to Advanced Mathematics encourages students to become mathematicians in the fullest sense of the word. A Transition to Advanced Mathematics has a number of distinctive features that enable this transformational experience. Embedded Questions and Reading Questions illustrate and explain fundamental concepts, allowing students to test their understanding of ideas independent of the exercise sets. The text has extensive, diverse Exercises Sets; with an average of 70 exercises at the end of section, as well as almost 3,000 distinct exercises. In addition, every chapter includes a section that explores an application of the theoretical ideas being studied. We have also interwoven embedded reflections on the history, culture, and philosophy of mathematics throughout the text.
Author | : Douglas Smith |
Publisher | : Cengage Learning |
Total Pages | : 416 |
Release | : 2010-06-01 |
Genre | : Mathematics |
ISBN | : 9780495562023 |
A TRANSITION TO ADVANCED MATHEMATICS helps students make the transition from calculus to more proofs-oriented mathematical study. The most successful text of its kind, the 7th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors place continuous emphasis throughout on improving students' ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. Students will come away with a solid intuition for the types of mathematical reasoning they'll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Author | : Hugh Neill |
Publisher | : Cambridge University Press |
Total Pages | : 128 |
Release | : 2002-03-14 |
Genre | : Juvenile Nonfiction |
ISBN | : 9780521893565 |
Starting Advanced Mathematics is a self-study guide for students who will be continuing their study of Mathematics after GCSE either to AS/A level or as part of the International Baccalaureate. It will enable students to consolidate the basic algebra and trigonometry skills that they will require during their study of advanced Mathematics. Other GCSE formulae and results that they may require during their post 16 studies are included for reference. The book is also a valuable revision aid for Higher Tier GCSE students who need more practice in Algebra and Trigonometry.
Author | : Ann Xavier |
Publisher | : |
Total Pages | : |
Release | : 1993-06-30 |
Genre | : Mathematics |
ISBN | : 9780877202844 |