Basic Modern Algebra with Applications

Fr. 89.00
ISBN: 978-81-322-3498-2
+ -
The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a way that it encourages independent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text.
 
In addition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theory to structure theory of rings and homological algebra. Algebraic aspects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraic topology, category theory, algebraic geometry, algebraic number theory, cryptography and theoretical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, with the help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, examples, exercises and historical notes represents a valuable and unique resource.                                                                                                                                  

"I want to note explicitly that his treatment of what universality means in this context is particularly well done ? It is also noteworthy that right after discussing fiber bundles in this fifth chapter, Adhikari goes on to the massively important topic of vector bundles, stressing right off the bat that "their homotopy classifications play a very important role in mathematics and physics." ? It is rather comprehensive (at around 600 pages it would be difficult to avoid this), and it shows very good taste on the author's part as far as what he's chosen to do and how he's chosen to do it?Wow! What a nice book." (Michael Berg, MAA Reviews, February, 2017)

"This fairly thick (more than 600 pages long) book covers a lot of topics that are not generally taught to American undergraduates at all. ? This book is certainly an unusual one, filled with interesting material, and there are quite a few exercises spanning a wide range of difficulty. ? have considerable value as a reference for undergraduate or graduate professors, or advanced students ? ." (Mark Hunacek, MAA Reviews, March, 2014)

"This book gives an accessible presentation on Basic Modern Algebra with Applications ? at the undergraduate level. Each chapter has interesting exercises and additional reading. ? It is an interesting book which reveals the importance of modern algebra concepts in contemporary mathematics." (Corina Mohorianu, zbMATH, Vol. 1284, 2014) 

"This is a rather unusual book. intended as a text on modern algebra for undergraduate mathematics students, the book covers a vast area including many topics which are far too advanced for an undergraduate course, yet omitting some useful and important subjects such as simple groups, cyclotomy and Galois theory? book is basic only in the sense that it starts from the beginning in many topics being covered, but the learning curve is very steep in most places."(Peter Shiu, The Mathematical Gazette, Volume 99, Issue 544, March 2015)                                   


The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a way that it encourages independent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text.
 
In addition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theory to structure theory of rings and homological algebra. Algebraic aspects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraic topology, category theory, algebraic geometry, algebraic number theory, cryptography and theoretical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, with the help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, examples, exercises and historical notes represents a valuable and unique resource.                                                                                                                                  

"I want to note explicitly that his treatment of what universality means in this context is particularly well done ? It is also noteworthy that right after discussing fiber bundles in this fifth chapter, Adhikari goes on to the massively important topic of vector bundles, stressing right off the bat that "their homotopy classifications play a very important role in mathematics and physics." ? It is rather comprehensive (at around 600 pages it would be difficult to avoid this), and it shows very good taste on the author's part as far as what he's chosen to do and how he's chosen to do it?Wow! What a nice book." (Michael Berg, MAA Reviews, February, 2017)

"This fairly thick (more than 600 pages long) book covers a lot of topics that are not generally taught to American undergraduates at all. ? This book is certainly an unusual one, filled with interesting material, and there are quite a few exercises spanning a wide range of difficulty. ? have considerable value as a reference for undergraduate or graduate professors, or advanced students ? ." (Mark Hunacek, MAA Reviews, March, 2014)

"This book gives an accessible presentation on Basic Modern Algebra with Applications ? at the undergraduate level. Each chapter has interesting exercises and additional reading. ? It is an interesting book which reveals the importance of modern algebra concepts in contemporary mathematics." (Corina Mohorianu, zbMATH, Vol. 1284, 2014) 

"This is a rather unusual book. intended as a text on modern algebra for undergraduate mathematics students, the book covers a vast area including many topics which are far too advanced for an undergraduate course, yet omitting some useful and important subjects such as simple groups, cyclotomy and Galois theory? book is basic only in the sense that it starts from the beginning in many topics being covered, but the learning curve is very steep in most places."(Peter Shiu, The Mathematical Gazette, Volume 99, Issue 544, March 2015)                                   


Autor Adhikari, Avishek / Adhikari, Mahima Ranjan
Verlag Springer India
Einband Kartonierter Einband (Kt)
Erscheinungsjahr 2016
Seitenangabe 660 S.
Lieferstatus Folgt in ca. 5 Arbeitstagen
Ausgabekennzeichen Englisch
Abbildungen Paperback
Masse H23.5 cm x B15.5 cm x D3.6 cm 984 g
Auflage Softcover reprint of the original 1st ed. 2014

Über den Autor Adhikari, Avishek

AVISHEK ADHIKARI, M.Sc. (Gold Medalist), PhD from the Indian Statistical Institute, assistant professor at the Dept of Pure Mathematics, University of Calcutta, and founder secretary of the IMBIC, India is a recipient of the President of India Medal and Young Scientist Award. He was a post-doctoral fellow at INRIA-Rocquencourt, France and a visiting scientist at Linkoping University, Sweden. He visited, on invitation, many institutions in India, Japan, Sweden, France, England, Switzerland and South Korea. His main interests are in cryptology, combinatorics, and algebra and its applications. He has published four textbooks on mathematics including Basic Modern Algebra with Applications (Springer) and edited one research monograph. He has published numerous papers in respected international journals, conference proceedings and contributed volumes. He is on the editorial board of several journals. MAHIMA RANJAN ADHIKARI, PhD, founder president of the Institute IMBIC, India and former professor of Pure Mathematics at the University of Calcutta, is a recipient of the Gold medal. He has published several research papers and eight textbooks including Basic Modern Algebra with Applications and Basic Algebraic Topology and its Applications (both with Springer). He was elected president of the Mathematical Science Section (including Statistics) of the 95th Indian Science Congress, 2008. He has successfully guided several PhD students in 9 different areas of mathematics. He has visited several institutions in India, USA, UK, China, Japan, France, Greece, Sweden, Switzerland, Italy and many other countries on invitation. YOGENDRA PRASAD CHAUBEY, PhD, is professor of Statistics at the Department of Mathematics and Statistics at Concordia University, Montreal, Canada. His research interests include sampling, linear models, distribution theory and nonparametric smoothing. His current research, funded by the Natural Sciences and Engineering Research Council of Canada's discovery grant program, is focused on the nonparametric functional estimation. He has served on the editorial board of several statistical journals and is an elected member of the International Statistical Institute. He has edited three research monographs and published over 130 research articles in several international statistical journals, conference proceedings and book chapters.

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