Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

First published in 1975, this classic book gives a systematic account of transcendental number theory, that is, the theory of those numbers that cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory, which continues to see rapid progress today. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalization of the Thue-Siegel-Roth theorem, of Shidlovsky's work on Siegel's E-functions and of Sprindžuk's solution to the Mahler conjecture. This edition includes an introduction written by David Masser describing Baker's achievement, surveying the content of each chapter and explaining the main argument of Baker's method in broad strokes. A new afterword lists recent developments related to Baker's work.

Transcendental numbers.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Transcendental numbers --- Motives (Mathematics) --- Algebraic fields

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Economics --- Index numbers (Economics) --- Statistical methods. --- Numbers, Index --- Prices --- Economic indicators --- Indexation (Economics) --- Economic statistics --- Econometrics

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Poetry and mathematics might seem to be worlds apart. Nevertheless, a number of Greek and Roman poets incorporated counting and calculation within their verses. Setting the work of authors such as Callimachus, Catullus and Archimedes in dialogue with the less well-known isopsephic epigrams of Leonides of Alexandria and the anonymous arithmetical poems preserved in the Palatine Anthology, the book reveals the various roles that number played in ancient poetry. Focussing especially on counting and arithmetic, Max Leventhal demonstrates how the discussion, rejection or enacting of these two operations was bound up with wider conceptions of the nature of poetry. Practices of composing, reading, interpreting and critiquing poetry emerge in these texts as having a numerical component. The result is an illuminating new way of approaching Greek and Latin poetry – and one that reaches across modern disciplinary divisions.

Greek poetry --- Latin poetry --- Mathematics in literature. --- Numbers in literature --- History and criticism.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book focuses on multiple comparisons of proportions in multi-sample models with Bernoulli responses. First, the author explains the one-sample and two-sample methods that form the basis of multiple comparisons. Then, regularity conditions are stated in detail. Simultaneous inference for all proportions based on exact confidence limits and based on asymptotic theory is discussed. Closed testing procedures based on some one-sample statistics are introduced. For all-pairwise multiple comparisons of proportions, the author uses arcsine square root transformation of sample means. Closed testing procedures based on maximum absolute values of some two-sample test statistics and based on chi-square test statistics are introduced. It is shown that the multi-step procedures are more powerful than single-step procedures and the Ryan-Einot-Gabriel-Welsch (REGW)-type tests. Furthermore, the author discusses multiple comparisons with a control. Under simple ordered restrictions of proportions, the author also discusses closed testing procedures based on maximum values of two-sample test statistics and based on Bartholomew's statistics. Last, serial gatekeeping procedures based on the above-mentioned closed testing procedures are proposed although Bonferroni inequalities are used in serial gatekeeping procedures of many.

Statistical science --- Mathematical statistics --- Biomathematics. Biometry. Biostatistics --- biomathematica --- biostatistiek --- statistiek --- biometrie --- statistisch onderzoek --- Bernoulli numbers. --- Estadística