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    ANALYTIC NUMBER THEORY FOR UNDERGRADUATES

    by Heng Huat Chan (National University of Singapore, Singapore)

    This book is written for undergraduates who wish to learn some basic results in analytic number theory. It covers topics such as Bertrand's Postulate, the Prime Number Theorem and Dirichlet's Theorem of primes in arithmetic progression.

    The materials in this book are based on A Hildebrand's 1991 lectures delivered at the University of Illinois at Urbana-Champaign and the author's course conducted at the National University of Singapore from 2001 to 2008.

     
    Contents:
    • Facts about Integers
    • Arithmetical Functions
    • Averages of Arithmetical Functions
    • Elementary Results on the Distribution of Primes
    • The Prime Number Theorem
    • Dirichlet Series
    • Primes in Arithmetic Progression
     
    Readership: Final-year undergraduates and first-year graduates with basic knowledge of complex analysis and abstract algebra; academics.
     
    “This book aims at bringing to the students the basic techniques in analytic number theory. This serves as a good starting point for advanced undergraduate students to embark onto research in this area of number theory … Without much modification, this book fits very well into a one-semester course in number theory. The text is well written with topics organized in a logical and coherent manner. All the difficult estimates are explained in detail so that students would have no difficulties in studying them in private.”
    Professor Kai-Man Tsang

    University of Hong Kong
     
    “This is a true textbook, i.e., a book of texts that the instructor can expand on … The book is well-produced, pleasing to the eye, and has almost no typographical errors … I know of nowhere else that so many important results can be found so clearly presented in so small a space … I hope that it will be adopted, or used as a supplement, by instructors of graduate-level courses.”
    See Full Review
    MAA Reviews
     
    128pp    Pub. date: Apr 2009  
    ISBN:   978-981-4271-35-6
    981-4271-35-7
       US$58 / £47

     


    128pp    Pub. date: Apr 2009  
    ISBN:   978-981-4271-36-3(pbk)
    981-4271-36-5(pbk)
       US$30 / £24

     


     

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    Updated on 6 November 2009