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Elementary Mathematics from a Higher Standpoint
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_This three-part treatment on mathematical knowledge needed by teachers was a pathbreaking book published by the German mathematician Felix Klein between 1924 and 1928 and it is still as relevant as it was 90 years ago. The books pulse with the excitement of the actual lectures they came from and combine geometric intuition with the precision of arithmetic formulas in an inspiring way.§§The first volume begins with topics associated with arithmetic, including calculating with natural numbers, the first extension of the notion of numbers, special properties of integers, and complex numbers. Algebra-related subjects constitute the second part, which examines real equations with real unknowns as well as equations in the field of complex quantities. The final part explores elements of analysis, with discussions of logarithmic and exponential functions, geometric functions, and infinitesimal calculus.§
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