LAZARUS Research Areas
Machine Learning is a subfield of Artificial Intelligence which makes use of advanced mathematical and statistical results to construct algorithms that are capable of extracting meaningful information from data. In simpler terms, Machine Learning is an alternate approach to solving computational problems, where instead of providing the instructions on how to complete a task, we provide instructions on how to learn to complete a task.
This leads to an incredibly broad and diverse range of algorithms which fall into the category of Machine Learning. At LAZARUS we are attempting to increase the mathematical understanding of these algorithms by using traditional mathematical tools in addition to running our algorithms on the Schoenberg Cluster.
Numerical Analysis is the mathematical analysis of numerical algorithms. In more simple terms, it could be described as the intersection of mathematics and computer science. In fact, Numerical Analysts may find themselves placed either in a mathematics department or computer science department depending on the university!
There are many subfields to Numerical Analysis: Numerical Linear Algebra, Approximation Theory, Optimization Theory, and many more. It is not uncommon to find work which includes more than one of these subfields. As LAZARUS is a mathematical computing lab, it should come as no surprise that the majority of the participants specialize in Numerical Analysis. Students interested in doing research as part of the LAZARUS should strongly consider studying the subject.
Quantum Computing is the name given to a new approach to computation based upon quantum mechanics. By exploiting properties of quantum mechanics we could, in theory, achieve computations that would take longer than the lifetime of the universe to compute.
Research into quantum computing falls under two broad categories, Quantum Computers and Quantum Algorithms. The former focuses on how to physically build a computer capable of quantum computation. The later is focused on how to make use of these computers once they are built. LAZARUS is primarily concerned with research into Quantum Algorithms. We are able to obtain more concrete examples of our work by using the Schoenberg Cluster and packages such as Google's Cirq or IBM's Qiskit.
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