Set Theory and Foundations of Mathematics: An Introduction to Mathematical Logic Volume II: Foundations of Mathematics

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This book provides an introduction to mathematical logic and the foundations of mathematics. It will help prepare students for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra. The presentation of finite state and Turing machines leads to the Halting Problem and Gödel's Incompleteness Theorem, which have broad academic interest, particularly in computer science and philosophy. Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Introduction Contents: Preface About the Authors Introduction Propositional Logic Predicate Logic Models of Predicate Logic Boolean Algebras Computability Decidable and Undecidable Theories Algorithmic Randomness Nonstandard Numbers Foundations of Geometry Bibliography Index Readership: Advanced undergraduate or beginning graduate students interested in mathematical logic, mathematics, computer science, and philosophy.

INTRODUCTION TO MATHEMATICAL STATISTICS (8版)

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Introduction to Mathematical Statistics, Global Edition ISBN13：9781292264769 出版社：Pearson Education Limited 作者：Robert V. Hogg;Joeseph McKean;Allen T. Craig 裝訂／頁數：平裝／760頁 規格：20.7cm*25.5cm*2.1cm (高/寬/厚) 版次：8 出版日：2019/11/05 內容簡介 　　Comprehensive coverage of mathematical statistics – with a proven approach 　　Introduction to Mathematical Statistics by Hogg, McKean, and Craig enhances student comprehension and retention with numerous, illustrative examples and exercises. Classical statistical inference procedures in estimation and testing are explored extensively, and the text’s flexible organization makes it ideal for a range of mathematical statistics courses. 　　Substantial changes to the 8th Edition – many based on user feedback – help students appreciate the connection between statistical theory and statistical practice, while other changes enhance the development and discussion of the statistical theory presented. 　　1. Many additional real data sets to illustrate statistical methods or compare methods. 　　2. Expanded use of the statistical software R, a powerful statistical language which is free and can run on all three main platforms. However, instructors can choose another statistical package if desired. 　　3. Downloadable, supplemented mathematical review material in Appendix A: reviews sequences, infinite series, differentiation, and integration (univariate and bivariate). 　　4. Expanded discussion of iterated integrals, with added figures to clarify discussion. 　　5. A new subsection on the bivariate normal distribution begins the section on the multivariate normal distribution in Chapter 3 (Some Special Distributions). 　　6. Several important topics have been added, including Tukey’s multiple comparison procedure in Chapter 9 (Inferences About Normal Models)and confidence intervals for the correlation coefficients found in Chapters 9 and 10 (Nonparametric and Robust Statistics). 　　7. Discussion on standard errors for estimates obtained by bootstrapping the sample is now offered in Chapter 7 (Sufficiency). 　　Several topics that were discussed in the Exercises are now discussed in the text, including quantiles in Section 1.7.1 and hazard functions in Section 3.3. 目錄 Ch 1 Probability and Distributions Ch 2 Multivariate Distributions Ch 3 Some Special Distributions Ch 4 Some Elementary Statistical Inferences Ch 5 Consistency and Limiting Distributions Ch 6 Maximum Likelihood Methods Ch 7 Sufficiency Ch 8 Optimal Tests of Hypotheses Ch 9 Inferences About Normal Models Ch10 Nonparametric and Robust Statistics Ch11 Bayesian Statistics