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What exactly is analysis? What are infinitely small or infinitely large quantities? What are indivisibles and infinitesimals? What are real numbers, continuity, the continuum, differentials, and integrals? You’ll find the answers to these and other questions in this unique book! It explains in detail the origins and evolution of this important branch of mathematics, which Euler dubbed the “analysis of the infinite.” A wealth of diagrams, tables, color images and figures serve to illustrate the fascinating history of analysis from Antiquity to the present. Further, the content is presented in connection with the historical and cultural events of the respective epochs, the lives of the scholars seeking knowledge, and insights into the subfields of analysis they created and shaped, as well as the applications in virtually every aspect of modern life that were made possible by analysis. From the reviews of the German edition: Three wishes granted at once: the book “3000 Jahre Analysis” is anything but a dry mixture of mathematical facts and formulae. Instead, it is a skillful blend of textbook, nonfiction, and history book rolled into one, which has been very vibrantly written. The author Thomas Sonar has managed to present the history of Analysis vividly, thrillingly, and full of intriguing details. Florian Modler, Spektrum der Wissenschaft The book [...] is simply wonderful. Everybody [...] picks up this book with a certain expectation, of course, and they won’t be disappointed! ... It is truly fun browsing the book. Peter Littelmann, Mitteilungen der DMV.

Mathematics. --- History. --- History of Mathematical Sciences. --- Annals --- Auxiliary sciences of history --- Math --- Science --- Mathematical analysis --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis - History

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This paper proposes an approach to guide statistical capacity building in developing countries using an analysis based on components of the World Bank's Statistical Performance Indicator on a sample of 215 countries. The approach demonstrates the importance of expanding traditional capacity-building activities to include programs to strengthen and better monitor user demand for data. Based on this analysis, the paper recommends a two-step strategy for building and enhancing the sustainable statistical capacity of national statistical systems in developing countries. The strategy creates a sustainable trajectory for developing national statistical systems that meet the growing demands of local and global data users. The paper emphasizes the importance of donor coordination and South-South learning initiatives for international capacity-building efforts.

Donor Coordination --- ICT Policy and Strategies --- Information and Communication Technologies --- National Statistical System --- Official Statistics --- Science and Technology Development --- Statistical and Mathematical Sciences --- Statistical Capacity Building

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Although she was famous as the "mother of modern algebra," Emmy Noether’s life and work have never been the subject of an authoritative scientific biography. Emmy Noether – Mathematician Extraordinaire represents the most comprehensive study of this singularly important mathematician to date. Focusing on key turning points, it aims to provide an overall interpretation of Noether’s intellectual development while offering a new assessment of her role in transforming the mathematics of the twentieth century. Hermann Weyl, her colleague before both fled to the United States in 1933, fully recognized that Noether’s dynamic school was the very heart and soul of the famous Göttingen community. Beyond her immediate circle of students, Emmy Noether’s lectures and seminars drew talented mathematicians from all over the world. Four of the most important were B.L. van der Waerden, Pavel Alexandrov, Helmut Hasse, and Olga Taussky. Noether’s classic papers on ideal theory inspired van der Waerden to recast his research in algebraic geometry. Her lectures on group theory motivated Alexandrov to develop links between point set topology and combinatorial methods. Noether’s vision for a new approach to algebraic number theory gave Hasse the impetus to pursue a line of research that led to the Brauer–Hasse–Noether Theorem, whereas her abstract style clashed with Taussky’s approach to classical class field theory during a difficult time when both were trying to find their footing in a foreign country. Although similar to Proving It Her Way: Emmy Noether, a Life in Mathematics, this lengthier study addresses mathematically minded readers. Thus, it presents a detailed analysis of Emmy Noether’s work with Hilbert and Klein on mathematical problems connected with Einstein’s theory of relativity. These efforts culminated with her famous paper "Invariant Variational Problems," published one year before she joined the Göttingen faculty in 1919.

Mathematics. --- History. --- History of Mathematical Sciences. --- Annals --- Auxiliary sciences of history --- Math --- Science --- Women mathematicians --- Noether, Emmy, --- Women as mathematicians --- Mathematicians --- Women in mathematics --- Noether, Amalie Emmy, --- Noether, E.

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The COVID-19 pandemic has created urgent demand for timely data, leading to a surge in mobile phone surveys for tracking the impacts of and responses to the pandemic. This paper assesses, and attempts to mitigate, selection biases in individual-level analyses based on phone survey data. The research uses data from (i) national phone surveys that have been implemented in Ethiopia, Malawi, Nigeria, and Uganda during the pandemic, and (ii) the pre-COVID-19 national face-to-face surveys that served as the sampling frames for the phone surveys. The availability of pre-COVID-19 face-to-face survey data permits comparisons of phone survey respondents with the general adult population. Phone survey respondents are more likely to be household heads or their spouses and non-farm enterprise owners, and on average, are older and better educated vis-a-vis the general adult population. To improve the representativeness of individual-level phone survey data, the household-level phone survey sampling weights are calibrated based on propensity score adjustments that are derived from a model of an individual's likelihood of being interviewed as a function of individual- and household-level attributes. Reweighting improves the representativeness of the estimates for the phone survey respondents, moving them closer to those of the general adult population. This holds for women and men and a range of demographic, education, and labor market outcomes. However, reweighting increases the variance of the estimates and fails to overcome selection biases. Obtaining reliable data on men and women through phone surveys requires random selection of adult interviewees within sampled households.

Coronavirus --- COVID-19 --- Disease Control and Prevention --- Education --- Gender --- Gender and Development --- Health, Nutrition and Population --- Household Survey --- Phone Survey --- Primary Education --- Statistical and Mathematical Sciences --- Survey Methodology --- Survey Sampling --- Weighting Methods

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Several developing countries are currently implementing phone surveys in response to immediate data needs to monitor the socioeconomic impact of COVID-19. However, phone surveys are often subject to coverage and non-response bias that can compromise the representativeness of the sample and the external validity of the estimates obtained from the survey. Using data from high-frequency phone surveys in Ethiopia, Malawi, Nigeria, and Uganda, this study investigates the magnitude and source of biases present in these four surveys and explores the effectiveness of techniques applied to reduce bias. Varying levels of coverage and non-response bias are found in all four countries. The successfully contacted samples in these four countries were biased toward wealthier households with higher living standards. Left unaddressed, this bias would result in biased estimates from the interviewed sample that do not fully reflect the situation of poorer households in the country. However, phone survey biases can be substantially reduced by applying survey weight adjustments using information from the representative survey from which the sample is drawn. Applying these methods to the four surveys resulted in a substantial reduction in bias, although the bias was not fully eradicated. This highlights one of the potential advantages of drawing phone survey samples from existing face-to-face, representative surveys over random digit dialing or using lists from telecom providers where such adjustment methods can be more limited.

Business Cycles and Stabilization Policies --- Coronavirus --- Coverage Bias --- COVID-19 --- Disease Control and Prevention --- Health, Nutrition and Population --- Inequality --- Living Standards --- Macroeconomics and Economic Growth --- Nonresponse Bias --- Pandemic Impact --- Poverty Reduction --- Sample Representativeness --- Statistical and Mathematical Sciences --- Survey Methodology --- Weighting Methods