In the library at Trinity College, Cambridge in 1976, George Andrews of Pennsylvania State University discovered a sheaf of pages in the handwriting of Srinivasa Ramanujan. Soon designated as "Ramanujan’s Lost Notebook," it contains considerable material on mock theta functions and undoubtedly dates from the last year of Ramanujan’s life. In this book, the notebook is presented with additional material and expert commentary.

Ramanujan's Lost Notebook: Part I

George E. Andrews

Bruce C. Berndt

Biographies & Memoirs

Springer

Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic. In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems. Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory. Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..

Number Theory (Dover Books on Mathematics)

Science & Math

Mathematics

Dover Publications

This book integrates recent developments and related applications in $q$-series with a historical development of the field, focusing on major breakthroughs and the author's own research interests. The author develops both the important analytic topics (Bailey chains, integrals, and constant terms) and applications to additive number theory. He concludes with applications to physics and computer algebra and a section on results closely related to Ramanujan's ``Lost Notebook.'' With its wide range of applications, the book will interest researchers and students in combinatorics, additive number theory, special functions, statistical mechanics, and computer algebra. It is understandable to even a beginning graduate student in mathematics who has a background in advanced calculus and some mathematical maturity.

$q$-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra (Cbms Regional Conference Series in Mathematics)

American Mathematical Society

Ramanujans Lost Notebook Part 2 [Paperback] [Jan 01, 2018] Andrews G E

SPRINGER EXCLUSIVE (REPRINT)

Ramanujan's Lost Notebook: Part I [Paperback] [Jan 01, 2018] Andrews G E

Springer India

Ramanujans Lost Notebook Part 3 [Paperback] [Jan 01, 2018] Andrews G E

Ramanujans Lost Notebook Part 4 [Paperback] [Jan 01, 2018] Andrews G E

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Books by George E. Andrews