A Transition to Advanced Mathematics

A Transition to Advanced Mathematics, 8th Edition, is an academic textbook published by Cengage Learning to help students move from calculus into upper-level mathematics courses. Authored by Douglas Smith, Maurice Eggen, and Richard St. Andre, the volume prepares undergraduates for abstract mathematical reasoning by establishing formal methods of argument.

The text organizes foundational concepts around symbolic logic, set theory, and algebraic properties. Early sections introduce propositional connectives, quantifiers, and basic proof methods. The material then expands into set operations, indexed families of sets, and mathematical induction.

Across all topics, the textbook maintains a continuous emphasis on reading and writing proofs while guiding students in spotting common errors in proofs. This focused approach offers effective introductory preparation for modern algebra and analysis, supporting students as they move beyond computational calculus into higher-level abstract mathematics.