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to students and researchers who have already seen the topics it presents, as a second source "for an alternate and powerful treatment of the topic". Alessandro Di
Bucchianico also writes that he is "not entirely positive" about the book, complaining about its "endless rows of definitions, statements,
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Each chapter concludes with a discussion of the history of the problems it covers, and pointers to the literature on these problems. Also included at the end of the book are solutions to some of the "exercises" provided at the end of each chapter, each of which could be (and often is) the basis of a
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found the book difficult going, despite the many topics of interest to her that it covered. She writes that she found herself "unsatisfied as a reader", "bogged down in technical details", and missing a unified picture of combinatorics as Rota saw it, even though a unified picture of combinatorics
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and proofs" without a connecting thread or motivation. He concludes that, although it is a good book for finding a clear description of Rota's favorite pieces of mathematics and their proofs, it is missing the enthusiasm and sense of unity that Rota himself brought to the subject.
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On the other hand, Michael Berg reviews the book more positively, calling its writing "crisp and elegant", its exercises deep, "important and fascinating", its historical asides "fun", and the overall book "simply too good to pass up".
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is too advanced for undergraduates, but could be used as the basis for one or more graduate-level mathematics courses. However, even as a practicing mathematician in combinatorics, reviewer
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in their
Cambridge Mathematical Library book series, listing Kung, Rota, and Yan as its authors (ten years posthumously in the case of Rota). The Basic Library List Committee of the
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has six chapters, densely packed with material: each could be "a basis for a course at the Ph.D. level". Chapter 1, "Sets, functions and relations", also includes material on
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was exactly what Rota often pushed for in his own research. Quinn nevertheless commends the book as "a fine reference" for some beautiful mathematics.
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Like Quinn, John Mount complains that parts of the book are unmotivated and lacking in examples and applications, "like a compressed
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treatment of discrete mathematics". He also writes that some of the exercises, such as one asking for a reproof of the
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research publication, and which connect the material from the chapters to some of its applications.
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One of the things Rota became known for, in the 1970s, was the revival of the
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has suggested its inclusion in undergraduate mathematics libraries.
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on antichains in power sets, special classes of lattices,
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and its combinatorial interpretation. Chapter 5 concerns
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as a general technique for the formal manipulation of
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584:2009 non-fiction books
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32:in his courses at the
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156:Riemann zeta function
172:roots of polynomials
164:Rota–Baxter algebras
144:generating functions
361:10.1112/blms/bdr016
160:symmetric functions
73:partitions of a set
512:Quinn, Jennifer J.
309:"Boekbesprekingen"
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396:MAA Reviews
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573:Categories
524:(6): 530,
473:MathSciNet
278:1159.05002
238:References
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553:citation
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312:(PDF)
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