Explain the principles behind 'machine learning' and how it differs from traditional programming paradigms. Provide examples of real-world applications where machine learning has demonstrated significant impact and effectiveness."

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Theoretical Computer Science

Usually, computer science seems like a practical field that involves studying, building, and working closely with computers. However, a subclass of this discipline also centers on the mathematical factors of the same. This is called theoretical computer science, and its focal point differentiates it from other branches of computer science: the rigorous mathematical approach it takes. This discipline falls under the umbrella of discrete mathematics, which is the study of countable or discontinuous mathematical structures.