The Seven C’s of Analysis

  • Kenneth Lange
Part of the Springer Texts in Statistics book series (STS)


The current chapter explains key concepts of mathematical analysis summarized by the six adjectives convergent, complete, closed, compact, continuous, and connected. A later chapter will add to these six c’s the seventh c, convex. At first blush these concepts seem remote from practical problems of optimization. However, painful experience and exotic counterexamples have taught mathematicians to pay attention to details. Fortunately, we can benefit from the struggles of earlier generations and bypass many of the intellectual traps.


Continuous Function Euclidean Norm Cauchy Sequence Inverse Image Matrix Norm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Kenneth Lange
    • 1
  1. 1.Department of Biomathematics and Human GeneticsUCLA School of MedicineLos AngelesUSA

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