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While there are many answers on SE about Putnam{A B C D E}, nearly all of them focus only on problem solving and assume that the student already has the basic prerequisite mathematical knowledge for them. But I am actually looking for a book that will teach me the theory.

Can someone please suggest some good books, where I can self study the topics , because mostly my curriculum/teachers are not that good.... Please help.

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    $\begingroup$ Maybe "Putnam & Beyond"? $\endgroup$ – xbh Aug 25 at 4:54
  • $\begingroup$ @xbh It lacks the theory aspect mostly. It is also focused more towards problem solving.... $\endgroup$ – RandomAspirant Aug 25 at 9:27
  • $\begingroup$ Then sorry I cannot help. Maybe those classic undergrad math texts meet your requirement, such as Thomas', Apolstol's, and Spivak's Calculus. Note that Putnam itself is focusing on problem solving, so other answers would assume the basic acquaintance of those maths. $\endgroup$ – xbh Aug 25 at 9:45
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At https://www.maa.org/math-competitions/putnam-competition it says, "The Putnam Competition covers a range of material in undergraduate mathematics, including elementary concepts from group theory, set theory, graph theory, lattice theory, and number theory," so all you have to do is trundle off to the library/bookstore to find books that cover those topics. Although you also need differential and integral calculus, and linear algebra – I guess the folks who wrote that paragraph thought those topics were too obvious to need mention.

It also says, "Below are some books available for purchase that may help students prepare for this exam:

"The William Lowell Putnam Mathematical Competition Problems and Solutions 1938-1964 A. M. Gleason, R. E. Greenwood, and L. M. Kelly, Editors
"The William Lowell Putnam Mathematical Competition Problems and Solutions 1965-1984 Gerald L. Alexanderson, Leonard F. Klosinski, and Loren C. Larson, Editors
"The William Putnam Mathematical Competition 1985-2000: Problems, Solutions and Commentary Kiran S. Kedlaya, Bjorn Poonen, and Ravi Vakil"

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