Foundations of Advanced Mathematics
Author: William E. Kline
Publisher:
Published: 1975
Total Pages: 583
ISBN-13: 9780278469198
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Fundamentals of Advanced Mathematics 1
Author: Henri Bourles
Publisher: Elsevier
Published: 2017-07-10
Total Pages: 270
ISBN-13: 0081021127
DOWNLOAD EBOOK →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
Foundations for Advanced Mathematics
Author: Carol Avelsgaard
Publisher: Scott Foresman & Company
Published: 1990
Total Pages: 325
ISBN-13: 9780673381521
DOWNLOAD EBOOK →Practical Foundations of Mathematics
Author: Paul Taylor
Publisher: Cambridge University Press
Published: 1999-05-13
Total Pages: 590
ISBN-13: 9780521631075
DOWNLOAD EBOOK →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.
Advanced Mathematics
Author: Martin Perkins
Publisher:
Published: 1982
Total Pages: 580
ISBN-13: 9780713512724
DOWNLOAD EBOOK →A Bridge to Advanced Mathematics
Author: Dennis Sentilles
Publisher: Courier Corporation
Published: 2013-05-20
Total Pages: 418
ISBN-13: 0486277585
DOWNLOAD EBOOK →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.
Foundations for Advanced Mathematics
Author: Ann Xavier
Publisher:
Published: 1993-06-30
Total Pages:
ISBN-13: 9780877202844
DOWNLOAD EBOOK →A Transition to Advanced Mathematics
Author: Douglas Smith
Publisher: Cengage Learning
Published: 2010-06-01
Total Pages: 416
ISBN-13: 9780495562023
DOWNLOAD EBOOK →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.
A Transition to Advanced Mathematics
Author: William Johnston
Publisher: Oxford University Press
Published: 2009-07-27
Total Pages: 766
ISBN-13: 0199718660
DOWNLOAD EBOOK →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.
New Foundations in Mathematics
Author: Garret Sobczyk
Publisher: Springer Science & Business Media
Published: 2012-10-26
Total Pages: 373
ISBN-13: 0817683852
DOWNLOAD EBOOK →The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.
