The Art Of Problem Solving Volume 2

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Also, would anyone be able to recommend a complementary full algebra 1 textbook to buy for my AOPS introduction to algebra book? [Disclosure/context: I teach online classes for Ao PS which use their books as the textbooks.

However, the opinions expressed here are my own and I am not speaking for Ao PS.] The Ao PS subject books (Prealgebra, Introduction to Algebra, etc) are meant to be stand-alone textbooks which you can learn from without using another textbook.

A weaker student may prefer a more traditional textbook, to use either instead of or in conjunction with an Ao PS book.

Ao PS books also tend to be less useful as definitive references than traditional textbooks: you will find fewer well-organized statements of important facts and identities and theorems in them (though I think this is more relevant to the more advanced books than it is to Prealgebra). Spend a good chunk of time trying all the problems at the beginning of each section, before you move on to read their solutions.

Montgomery, An Introduction to the Theory of Numbers, 5th ed. Harold Davenport, The Higher Arithmetic: An Introduction to the Theory of Numbers, 7th ed. Lecture notes and assignments for the course 18.781, Theory of Numbers, by Prof. Miklos Bona, A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory, 2nd ed.

Colin Adams, The Knot Book (American Mathematical Society, 2004).

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A Decade of the Berkeley Math Circle: The American Experience, edited by Zvezdelina Stankova and Tom Rike (American Mathematical Society, 2008). More advanced reading (abstract linear algebra): Sheldon Axler, Linear Algebra Done Right, 3rd ed. Isaiah Lankham, Bruno Nachtergaele and Anne Schilling, Linear Algebra - As an Introduction to Abstract Mathematics (Lecture Notes for MAT67, UC Davis, 2007). Joseph Gallian, Contemporary Abstract Algebra, 7th ed.

Paul Zeitz, The Art and Craft of Problem Solving, 2nd ed. Sandor Lehoczky and Richard Rusczyk, The Art of Problem Solving, Vol.