There has never been a more exciting time to study Mathematics and Physics. Our 4th Industry Revolution is bringing incredibly exciting innovations. Traditionally Mathematics supported design of roads, aeroplanes, pharmaceuticals, renewables, meteorology, banking, statistics, and more. Combined with Physics you can innovate in signal processing (IOT), medical devices, instrumentation, software, quantum technologies, autonomous vehicles, quantum computing, artificial intelligence and more.Mathematics is the language of physics and the two are very closely connected. It is the means by which theories of Physics are described and how the complex mathematical relations between force fields, matter and light are expressed. Advanced Mathematics looks at Calculus, Algebra, Probability, Analysis, Theories, and Modelling to give you a solid grounding in advanced applications of Mathematics. These are directly applicable to a lot of new Industry 4.0 applications and traditional areas of business which are now evolving and requiring new applications of Mathematics and Physics.For Physicists working at the frontiers of modern physics, there is a great need to be able to understand advanced mathematical techniques to apply to the latest industry needs in high growth application areas. The subject is so diverse it can apply to the theoretical and the physical such as Quantum Mechanical Engineering, Optics, Electricity and Magnetism and Signal Processing, to advanced Computing. Industry 4.0 has pushed traditional computing needs into 'Big Data' and an interplay between signalling circuits, engineering and IOT behind much of our modern advances in sensor technology, smart devices and their application.