Lectures on Fundamental Concepts of Algebra and Geometry

An unabridged printing, with text and all figures digitally enlarged: Euclid's Elements - A Non-Euclidean World - On The History Of The Parallel Postulate - Logical Significance Of Definitions, Axioms, And Postulates - Consistency, Independence, And Categoricalness Of A Set Of Assumptions - Class, Correspondence. Number - Order, Discrete Sequences - The Sequence Of Cardinal Numbers, Denumerable Classes, Dense Classes, Continuous Classes - Group, Number System - Historical And Logical Development Of The Concept Of Real Number - Negative Numbers - Ordinary And Higher Complex Numbers - Geometry. Hilbert's Assumptions - Hilbert's Assumptions Continued - Pieri's Assumptions - The Dimensions Of A Class - Spaces Of Four Or More Dimensions - Algebra And Geometry - Variable And Function - Limit - General Conclusions - The Growth Of Algebraic Symbolism by U. G. Mitchell