A career in mathematics for a physicist would obviously be in applied mathematics, not pure mathematics. A job in applied mathematics might mean working in statistics, operations research, or computer science. A physicist interested in a career in operations research might be aiming for a successful business career as an executive. This type of job uses methods such as mathematical modeling and algorithms to help management to optimize profits, assembly line performance, crop yield, bandwidth, and transaction costs. A technology firm might offer jobs to math, physics, engineering, and computer science students to conceive new trading ideas and devise the simulations needed to test them. A job in statistics might involve describing, predicting, and collecting data. In would not involve mathematical statistics, which is concerned with the theoretical basis of the subject.
A huge number of mathematics jobs are in computer science, which is the study of information and computation on a theoretical and practical level. There are careers to be made in computer graphics, computational complexity theory, creating new programs, programming language theory, and human-computer interactions. Jobs in computer programming apply specific programming languages to solve specific computational problems.
Anyone pursuing a career in the applied science of engineering might be considered a mathematician. Jobs in biomedical instrumentation, the behavior and control of fluids on a microscale, multiphase systems, photonics, quantum optical processes in semiconductors, and robotics can all require skill and knowledge in mathematics. The semiconductor industry continuously giving jobs to physicists who can help reduce the size of integrated circuits.
Another source of jobs for a mathematically minded physicist is in high-end optical imaging instruments, like ground-based telescopes, long-range surveillance cameras and free-space optical communication systems. The resolution of images is limited by optical aberrations induced by atmospheric turbulence, misalignment, vibrations, and heat generation. There are many career opportunities in adaptive optics, which is a technology used to improve the performance of optical systems by reducing the effects of rapidly changing optical distortion. Jobs in adaptive optics requires measuring the distortions in a wavefront and compensating for them with a spatial phase modulator such as a deformable mirror or liquid crystal array. This is not the same as active optics, which works on a longer timescale to correct the primary mirror geometry itself and is also a source of jobs.
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