Search results for ""Author Hugo D. Junghenn""

Book SynopsisThis book, for a first undergraduate course in Discrete Mathematics, systematically exploits the relationship between discrete mathematics and computer programming. Unlike most discrete mathematics texts focusing on one of the other, the book explores the rich and important connection between these two disciplines and shows how each discipline reinforces and enhances the other.The mathematics in the book is self-contained, requiring only a good background in precalculus and some mathematical maturity. New mathematical topics are introduced as needed.The coding language used is VBA Excel. The language is easy to learn, has intuitive commands, and the reader can develop interesting programs from the outset. Additionally, the spreadsheet platform in Excel makes for convenient and transparent data input and output and provides a powerful venue for complex data manipulation. Manipulating data is greatly simpli?ed using spreadsheet features and visualizing the data can make Table of Contents1. Introduction. 2. VBA Operators. 3. Conditional Statements. 4. Loops, 5. Arrays. 6. String Functions. 7. Grids. 8. Recursion. 9. Charts and Graphs, 10. Random Numbers. 11. Linear Equations. 12. Linear Programming. 13. Matrix Algebra. 14. Determinants. 15. Propositional Logic. 16. Switching Circuits. 17. Gates and Logic Circuits. 18. Sets. 19. Counting. 20. Probability. 21. Random Variables. 22. Markov Chains. 23. Divisibility and Prime Numbers. 24. Congruence. 25. The Enigma Machine. 26. Large Numbers.

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Book SynopsisPython Essentials.- Number Theory.- Rational Arithmetic.- Matrix Algebra.- Polynomial Algebra.- Polynomial Applications.- Multivariate Rational Algebra.- Differentiation.- Integration.

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Book SynopsisPrinciples of Analysis: Measure, Integration, Functional Analysis, and Applications prepares readers for advanced courses in analysis, probability, harmonic analysis, and applied mathematics at the doctoral level. The book also helps them prepare for qualifying exams in real analysis. It is designed so that the reader or instructor may select topics suitable to their needs. The author presents the text in a clear and straightforward manner for the readers' benefit. At the same time, the text is a thorough and rigorous examination of the essentials of measure, integration and functional analysis.The book includes a wide variety of detailed topics and serves as a valuable reference and as an efficient and streamlined examination of advanced real analysis. The text is divided into four distinct sections: Part I develops the general theory of Lebesgue integration; Part II is organized as a course in functional analysis; Part IITrade Review"The author's aim for the book under review is to provide a rigorous and detailed treatment of the essentials of measure and integration, as well as other topics in functional analysis at the graduate level. Although he assumes readers to have an undergraduate background, such as real analysis (including some experience in dealing with limits, continuity, di erentiation, Riemann integration, and uniform convergence, including elementary set theory), a standard course of complex analysis (function theory, Cauchy's integral equation), and a knowledge of basic linear algebra, this book could also be very useful for a reader with a weaker mathematical background. This is possible since the excellently constructed introduction in Chapter 0 is a very good base for systematizing and developing the mathematical background for a broad group of readers. The book is divided into four parts.In Part I, which consists of Chapters 1{7, the author develops a detailed course concerning the general theory of Lebesgue integration as well as Fourier analysis on Rd (Chapter 6) and measures on locally compact spaces (Chapter 7). A short course on the general theory of Lebesgue integration could be based on Chapters 1{5 only but the full variant looks more attractive. It must be noted that the author's exposition is on a very high level as well as very clear and easily understandable.Part II is presented as a course in functional analysis. The author considers Chapters 8{12 to be the core of such a course. Chapter 13 could be an optional choice, but can be also included in the course. Chapter 14 plays an important role concerning Part I and Part II. This chapter includes not only deeper theorems in functional analysis but also several well-chosen applications. Note that some of them are related to the measure and integration developed in Part I and the others with the applications in the remainder of the book.Part III (Chapters 15{17) is a key part in the book since it includes many topics and applications that depend on, and indeed are meant to illustrate, the power of topics developed in the first two parts. It must be noted that these chapters are almost independent. Their goal is to provide a relatively quick overview of the subjects treated therein. The detailed exposition that this approach allows means that the reader can follow the development with relative ease. In addition to allowing the reader to consult the themes considered, some specialized sources are listed in the bibliography.Part IV consists of two appendices with proofs of the change of variables theorem and a theorem on separate and joint continuity. A reader may choose to safely omit the proofs without disturbing the flow of the text, as the author notes. An advantage for the readers is that the book contains a lot of exercises (nearly 700). It is very convenient that hints and/or a framework of intermediate steps are given for the more di□cult exercises. Many of these are extensions of material in the text or are of special independent interest. Additionally, the exercises related in a critical way to material elsewhere in the text are marked with either an upward arrow, referring to earlier results, or a downward arrow, referring to later material. Instructors may obtain complete solutions to theexercises from the publisher.In conclusion, I strongly recommend the book because it will be helpful for every level of reader. I only regret that it was not written when I was a student."- Andrey I. Zahariev - Mathematical Reviews Clippings February 2019Table of ContentsMeasurable Sets. Measurable Functions. Integration. Further Topics in Measure Theory. Banach Spaces. Hilbert Spaces. Locally Convex Spaces. Banach Algebras. Harmonic Analysis on Locally Compact Groups. Probability Theory. Operator Theory. Appendices.

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