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From Numbers to Analysis
"This book is recommended to students and instructors looking for a very well-organized introduction to the foundations of analysis".Acta Sci. Math., 1999
A Modern Theory of Integration
The theory of integration is one of the twin pillars on which analysis is built. The first version of integration that students see is the Riemann integral. Later, graduate students learn that the Lebesgue integral is ?better? because it removes some restrictions on the integrands and the domains over which we integrate. However, there are still drawbacks to Lebesgue integration, for instance, dealing with the Fundamental Theorem of Calculus, or with ?improper? integrals. This book is an introduction to a relatively new theory of the integral (called the ?generalized Riemann integral? or the ?Henstock-Kurzweil integral?) that corrects the defects in the classical Riemann theory and both simp...
Measure Theory and Integration
This text approaches integration via measure theory as opposed to measure theory via integration, an approach which makes it easier to grasp the subject. Apart from its central importance to pure mathematics, the material is also relevant to applied mathematics and probability, with proof of the mathematics set out clearly and in considerable detail. Numerous worked examples necessary for teaching and learning at undergraduate level constitute a strong feature of the book, and after studying statements of results of the theorems, students should be able to attempt the 300 problem exercises which test comprehension and for which detailed solutions are provided. - Approaches integration via measure theory, as opposed to measure theory via integration, making it easier to understand the subject - Includes numerous worked examples necessary for teaching and learning at undergraduate level - Detailed solutions are provided for the 300 problem exercises which test comprehension of the theorems provided
Introduction to Numerical Analysis
On the occasion of this new edition, the text was enlarged by several new sections. Two sections on B-splines and their computation were added to the chapter on spline functions: Due to their special properties, their flexibility, and the availability of well-tested programs for their computation, B-splines play an important role in many applications. Also, the authors followed suggestions by many readers to supplement the chapter on elimination methods with a section dealing with the solution of large sparse systems of linear equations. Even though such systems are usually solved by iterative methods, the realm of elimination methods has been widely extended due to powerful techniques for h...
Measures, Integrals and Martingales
This is a concise and elementary introduction to contemporary measure and integration theory as it is needed in many parts of analysis and probability theory. Undergraduate calculus and an introductory course on rigorous analysis in R are the only essential prerequisites, making the text suitable for both lecture courses and for self-study. Numerous illustrations and exercises are included to consolidate what has already been learned and to discover variants and extensions to the main material. Hints and solutions can be found on the authors website, which can be reached at http: //www.motapa.de/measures_integrals_and_martingales/index.htm
Measure Theory
Discusses all aspects of measure theory, including countability, outer measure and measurability, measureable functions, the Lebesgue integral of a function, convergance of sequences of measurable functions, absolutely continuous functions, differentials and integration, the Lebesgue LP-spaces, product measures, and Lebesgue-Stieltjes integrals.
Professional Development of Mathematics Teachers
This book offers a counterpart to the extensive corpus of literature available on the same topic from a Western perspective. It showcases innovative approaches to professional development of mathematics teachers in Asian countries, and reports on both empirical and expository studies of teachers’ professional development in these counties. It provides scholars from non-English-speaking and under-represented Asian countries the opportunity to engage in discourse with other scholars in the field, and is the first book to present substantial contributions from scholars in Asia on the professional development of mathematics teachers in their respective countries. It includes perspectives that shed valuable light on how the approaches pursued in Asian countries resemble or differ from those in the West.
Foundations of Functional Analysis
Provides fundamental concepts about the theory, application and various methods involving functional analysis for students, teachers, scientists and engineers. Divided into three parts it covers: Basic facts of linear algebra and real analysis. Normed spaces, contraction mappings, linear operators between normed spaces and fundamental results on these topics. Hilbert spaces and the representation of continuous linear function with applications. In this self-contained book, all the concepts, results and their consequences are motivated and illustrated by numerous examples in each chapter with carefully chosen exercises.
