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Number Theory And Its Applications
This book emphasizes the role of symmetry and presents as many viewpoints as possible of an important phenomenon — the functional equation of the associated zeta-function. It starts from the basics before warping into the space of new interest; from the ground state to the excited state. For example, the celebrated Gauss quadratic reciprocity law is proved in four independent ways, which are in some way or other dependent on the functional equation. The proofs rest on finite fields, representation theory of nilpotent groups, reciprocity law for the Dedekind sums, and the translation formula for the theta-series, respectively. Likewise, for example, the Euler function is treated in several different places.One of the important principles of learning is to work with the material many times. This book presents many worked-out examples and exercises to enhance the reader's comprehension on the topics covered in an in-depth manner. This is done in a different setting each time such that the reader will always be challenged. For the keen reader, even browsing the text alone, without solving the exercises, will yield some knowledge and enjoyment.
Number Theory And Its Applications Ii
The aim of the book is to give a smooth analytic continuation from basic subjects including linear algebra, group theory, Hilbert space theory, etc. to number theory. With plenty of practical examples and worked-out exercises, and the scope ranging from these basic subjects made applicable to number-theoretic settings to advanced number theory, this book can then be read without tears. It will be of immense help to the reader to acquire basic sound skills in number theory and its applications.Number theory used to be described as the queen of mathematics, that is, there is no practical use. However, with the development of computers and the security of internet communications, the importance...
The Math Encyclopedia of Smarandache type Notions
About the works of Florentin Smarandache have been written a lot of books (he himself wrote dozens of books and articles regarding math, physics, literature, philosophy). Being a globally recognized personality in both mathematics (there are countless functions and concepts that bear his name) and literature, it is natural that the volume of writings about his research is huge. What we try to do with this encyclopedia is to gather together as much as we can both from Smarandache’s mathematical work and the works of many mathematicians around the world inspired by the Smarandache notions. We structured this book using numbered Definitions, Theorems, Conjectures, Notes and Comments, in order...
Research on Smarandache Problems in Number Theory (collected papers), Vol. II
This book contains 34 papers, most of which were written by participants to the First Northwest Number Theory Conference held in Shangluo Teacher?s College, China, in March, 2005. In this Conference, several professors gave a talk on Smarandache Problems and many participants lectured on them both extensively and intensively. All these papers are original and have been refereed. The themes of these papers range from the mean value or hybrid mean value of Smarandache type functions, the mean value of some famous number theoretic functions acting on the Smarandache sequences, to the convergence property of some infinite series involving the Smarandache type sequences.
Scientia Magna, Vol. 3, No. 1, 2007.
Third International Conference on Number Theory and Smarandache Problems, 23-25 March 2007, Weinan Teacher's University, China. Papers on Smarandache multi-spaces and mathematical combinatorics, Smarandache stepped functions, cube-free integers as sums of two squares, recurrences for generalized Euler numbers, the generalization of the primitive number function, the Smarandache LCM function and its mean value, a conjecture involving the F. Smarandache LCM function, a new arithmetical function and its asymptotic formula, and other similar topics. Contributors: J. Wang, A. Muktibodh, M. Selariu, X. Zhang, Y. Zhang, M. Liu, R. Zhang, S. Ma, L. Mao, and many others.
Australia-China Relations post 1949
This book challenges the common perceptions of Australian dependence upon great-power allies in the conduct of its foreign relations through a critical examination of Australia's relations with the People's Republic of China. The author focuses on the economic and political dimensions of the policy-making process from the founding of the PRC in 1949 to the present era, against an analytical framework that takes into account both internal and external factors in the formulation and implementation of Australian foreign policy. Informed by political science and international relations, the book differs from the conventional literature on Sino-Australian relations, which has either focused on pu...
The Annotations on the Waterway Classic; Shui Jing Zhu 水经注
The Annotations on the Waterway Classic (Chinese: 水经注; pinyin: Shuǐ Jīng Zhù) is a work on the ancient geography of China, describing the traditional understanding of its waterways and ancient canals, compiled by Li Daoyuan during the Northern Wei Dynasty (386-534 AD). The book is divided into sections by river, each described with its source, course, and major tributaries, including cultural and historical notes. The work is much expanded from its source text, the older (and now lost) Waterway Classic (Shuijing 水经). The original text described 137 different rivers in China, and its authorship was attributed to Jin dynasty scholar Guo Pu. Li Daoyuan's 40-volume, 300,000-character version includes 1252 rivers.
Mathematical Reviews
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