A Concise Introduction To Pure Mathematics by Martin W. Liebeck

A concise, student-friendly introduction to rigorous mathematical thinking that develops proof techniques and key foundational topics for undergraduates: logical reasoning and set theory, functions and relations, elementary number theory and divisibility, basic combinatorics and counting, sequences and limits, and introductory algebraic structures such as groups and rings, all reinforced with examples and exercises aimed at building facility in constructing and understanding proofs.

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