AlgebraA Survey of Modern Algebra. Saunders MacLane and Garrett D. Birkhoff. Hardcover: AK Peters Ltd; 5th edition, 1997. [See this book at Amazon.com] Polynomials. Edward J. Barbireau. Hardcover (hard to get): Springer, 1989. [See this book at Amazon.com] Paperback: Springer, 2003. [See this book at Amazon.com]CombinatoricsI am biased about the next book, because I took many (excellent) math coursesfrom Jack van Lint.It has very broad coverage (including Pólya's Counting Theorem):A Course in Combinatorics. J. H. van Lint and R. M. Wilson. Cambridge University Press; 2nd edition, 2001. [See this book at Amazon.com]An exceptional title for an exceptional book:Generatingfunctionology. Herbert Wilf (author of the book A=B). Academic Press; 2nd edition, 1993. [See this book at Amazon.com] Also available as downloadable PDF for non-profit/non-commercial use.An overview of theory combined with a collection of problems, hints, andsolutions incombinatorics, combinatorial number theory, and combinatorial geometry:Counting and Configurations. Jiri Herman, Radan Kucera, and Jaromir Simsa. Springer, 2003. [See this book at Amazon.com, Digital]Another collection of problems, hints, and solutions in combinatorics:102 Combinatorial Problems : From the Training of the USA IMO Team. Titu Andreescu, Zuming Feng. Birkhäuser, 2003. [See this book at Amazon.com]AnalysisA Course of Pure Mathematics. 10th ed. G.H. Hardy. Cambridge Univ. Press, 1955. [See this book at Amazon.com]
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