Some unexpected examples in Calculus and Mathematics

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272 pages

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English

Some mathematicians including the author of this book believe that counterexamples will guide the reader towards a better understanding of the underlying theory.

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*Leif Mejlbro* was educated as a mathematician at the *University of Copenhagen*, where he wrote his thesis on *Linear Partial Differential Operators and Distributions*. Shortly after he obtained a position at the *Technical University of Denmark*, where he remained until h...

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It has been a general trend in the teaching of mathematics that one should not show the students what could go wrong, if some necessary assumption was missing, ”because the students would be bewildered”! However, not all mathematicians agreed in this viewpoint, including the author of this book. To their philosophy counterexamples should guide the reader towards a better understanding of the underlying theory.

Some mathematicians including the author of this book believe that counterexamples will guide the reader towards a better understanding of the underlying theory.

- Elementary theory of functions
- Integrals
- Measurable sets
- Fourier series
- Continuous curves
- Nonmeasurable sets
- Miscellaneous
- Measures in Rn and in infinite dimensional Hilbert space