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Numbers imitate space, which is of such a di?erent nature --Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in...

Central to this thesis is the characterisation and exploitation of electromagnetic properties of light in imaging and measurement systems. To this end an information theoretic approach is used to formulate a hitherto lacking, quantitative definition of polarisation resolution, and to establish fundamental precision limits in electromagnetic systems. Furthermore rigorous modelling tools are developed for propagation of arbitrary electromagnetic fields, including for example stochastic fields exhibiting properties such as partial polarisation, through high numerical aperture optics. Finally...

Central to this thesis is the characterisation and exploitation of electromagnetic properties of light in imaging and measurement systems. To this end an information theoretic approach is used to formulate a hitherto lacking, quantitative definition of polarisation resolution, and to establish fundamental precision limits in electromagnetic systems. Furthermore rigorous modelling tools are developed for propagation of arbitrary electromagnetic fields, including for example stochastic fields exhibiting properties such as partial polarisation, through high numerical aperture optics. Finally...

Matthew D. Hirschberg's extraordinary journey serves as proof that any obstacle in life can be overcome. Matt's story is one of redemption and a great reminder that personal responsibility helps pave the road to success. From his early days involving drugs, prison, and obesity, to his current stage of life as a successful entrepreneur, business owner and speaker, Matt invites readers to re-examine and take stock of their own lives through his "Life Prescriptions" -- proven life lessons he has learned from his unbelievable experiences.

After hitting rock bottom, Matt had to pick up...

Matthew D. Hirschberg's extraordinary journey serves as proof that any obstacle in life can be overcome. Matt's story is one of redemption and a great reminder that personal responsibility helps pave the road to success. From his early days involving drugs, prison, and obesity, to his current stage of life as a successful entrepreneur, business owner and speaker, Matt invites readers to re-examine and take stock of their own lives through his "Life Prescriptions" -- proven life lessons he has learned from his unbelievable experiences.

After hitting rock bottom, Matt had to pick up...