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Microeconomics --- Quantitative methods (economics) --- Duality theory (Mathematics) --- Econometric models. --- Production functions (Economic theory) --- Duality theory (Mathematics). --- Production functions (Economic theory).

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Numerical approximation theory --- Numerical methods of optimisation --- Mathematical optimization --- Duality theory (Mathematics)

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These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required, dealing with the subject in an elementary fashion. With about a hundred exercises for the student, it is a suitable text for first-year graduate courses.

Locally compact Abelian groups. --- Duality theory (Mathematics) --- Algebra --- Mathematical analysis --- Topology --- Compact Abelian groups --- Locally compact groups --- Topological groups --- Groupes abéliens localement compacts --- Locally compact Abelian groups --- Pontrjagin duality --- 517.986.6 --- Pontryagin duality --- 517.986.6 Harmonic analysis of functions of groups and homogeneous spaces --- Harmonic analysis of functions of groups and homogeneous spaces --- Pontrjagin duality. --- Topological groups. Lie groups --- Duality theory (Mathematics). --- Groupes abéliens localement compacts. --- Groupes topologiques --- Groupes localement compacts

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This undergraduate text takes the reader along the trail of light from Newton's particles to Einstein's relativity. Like the best detective stories, it presents clues and encourages the reader to draw conclusions before the answers are revealed. The first seven chapters describe how light behaves, develop Newton's particle theory, introduce waves and an electromagnetic wave theory of light, discover the photon, and culminate in the wave-particle duality. The book then goes on to develop the special theory of relativity, showing how time dilation and length contraction are consequences of the two simple principles on which the theory is founded. An extensive chapter derives the equation E = mc2 clearly from first principles and then explores its consequences and the misconceptions surrounding it. That most famous of issues arising from special relativity - the aging of the twins - is treated simply but compellingly.

Theory of relativity. Unified field theory --- Newton, Isaac --- Einstein, Albert --- Special relativity (Physics) --- Wave-particle duality. --- Special relativity (Physics).

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Harmonic analysis. Fourier analysis --- 512 --- Algebra --- 512 Algebra --- Semilattices --- Semigroups --- Duality theory (Mathematics) --- Topological semigroups --- Semigroupes topologiques --- Ensembles ordonnés --- Demi-treillis --- Ordered sets