: While "Charles Zimmer" is fictional, there are real mathematicians with the name Zimmer. For example, Robert J. Zimmer Group Actions in Ergodic Theory Rudolf A. Zimmer Essential Mathematics for algebra and trigonometry review. Math 111 at Fresno State
. While the specific Zimmer text mentioned in popular culture is elusive in physical PDF form, the syllabus for such a course typically covers: Symbolic Logic and Set Theory
: Formal definitions of one-to-one, onto, and bijective functions. Standard Textbooks : Actual textbooks often used for this purpose include: A Transition to Advanced Mathematics by Douglas B. Smith, Maurice Eggen, and Richard St. Andre. A First Course in Linear Algebra
The Mystery of Charles Zimmer’s "Transitions in Advanced Algebra"
One of the subtlest yet deadliest transitions is notation. Does ( fg(x) ) mean ( f(x) \cdot g(x) ) or ( f(g(x)) )?
: Wrote authoritative texts on ergodic theory and functional analysis, such as Essential Results of Functional Analysis available on Amazon .