Review of
Wandering
in the World of Smarandache Numbers, by A. A. K. Majumdar,
Proquest Information & Learning, Ann Arbor, MI, 2010. Available in PDF form
at http://fs.gallup.unm.edu/Majumdar.pdf ISBN 9781599731247.
Like all of the
really good math books, this one starts with a foundation of material that is
already known and then presents new material and poses as yet unanswered
questions. For example, chapter one covers some of the Smarandache sequences
which are generally based on concatenation rather than formulas. Chapter two
deals with the Smarandache determinant sequences, where the generation of the
elements is done by taking the determinants of matrices of specific types.
Chapter three covers the Smarandache function, four the Pseudo-Smarandache
function and chapter five Smarandache number related triangles.
After putting
forward and proving results that are known, the author extends the material
with additional theorems, proofs and conjectures. To Majumdar’s credit, there
is no skimping on proofs, when it can be proven, the complete proof is given.
If you have an
interest in these topics and are looking for an area of research exploration,
check out this book. Professor Smarandache has been an enormous source of new
ideas and problems in mathematics, some of them are put forward and examined in
this book. There are also a large number of different paths that can be
explored, like most of number theory they are easy to state and understand, but
may be very hard to prove.
http://www.amazon.com/gp/product/159973124X?keywords=9781599731247&qid=1456585505&ref_=sr_1_1&sr=8-1
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