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"The discovery-based Constructing Numbers: An Inquiry-Based Capstone Mathematics Course helps students synthesize material from elementary analysis, linear algebra, algebraic structures, and geometry while providing perspective on how mathematical thought has developed.
The book opens with the history of numbers. It moves on to cover axiomatic systems, real, complex, and constructible numbers, and an algebraic formulation of field construction. The final chapters are devoted to finite fields, probability, and permutation groups.
By actively participating in the exercises and...

When discussing the mathematical knowledge of elementary school teachers, the National Council of Teachers of Mathematics concludes that teachers must have a deep understanding of mathematics and be able to easily draw on that knowledge with flexibility in their teaching tasks. Mathematics teachers must understand the big ideas of mathematics and be able to represent mathematics as a coherent and connected endeavor.
This inquiry and exploration-based workbook has been designed as a tool for pre-service and in-service mathematics teachers to use as a guidebook for doing mathematics and...