figure - brendan tierney' depiction of data science as true multi-disciplinary field if you observe his depiction closelyyou will see lot of the domains mentioned here are what we just talked about in the previous sections and matches substantial part of figure - you can clearly see data science being the center of attention and drawing parts from all the other fields and machine learning as sub-field mathematics the field of mathematics deals with numberslogicand formal systems the best definition of mathematics was coined by aristotle as "the science of quantitythe scope of mathematics as scientific field is huge spanning across areas including algebratrigonometrycalculusgeometryand number theory just to name few major fields linear algebra and probability are two major sub-fields under mathematics that are used extensively in machine learning and we will be covering few important concepts from them in this section our major focus will always be on practical machine learningand applied mathematics is an important aspect for the same linear algebra deals with mathematical objects and structures like vectorsmatriceslinesplaneshyperplanesand vector spaces the theory of probability is mathematical field and framework used for studying and quantifying events of chance and uncertainty and deriving theorems and axioms from the same these laws and axioms help us in reasoningunderstandingand quantifying uncertainty and its effects in any real-world system or scenariowhich helps us in building our machine learning models by leveraging this framework