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This book originates as an essential underlying component of a modern, imaginative three-semester honors program (six undergraduate courses) in Mathematical Studies. In its entirety, it covers Algebra, Geometry and Analysis in One Variable. The book is intended to provide a comprehensive and rigorous account of the concepts of set, mapping, family, order, number (both natural and real), as well as such distinct procedures as proof by induction and recursive definition, and the interaction between these ideas; with attempts at including insightful notes on historic and cultural settings and...

In the spirit of the author’s Basic Language of Mathematics, this companion volume is a careful exposition of the concepts and processes of Linear Algebra. It stresses cautious and clear explanations, avoiding reliance on co-ordinates as much as possible, and with special, but not exclusive, attention to the finite-dimensional situation. It is intended to also serve as a conceptual and technical background for use in geometry and analysis as well as other applications.