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Households, corporations, governments, and financial firms, such as commercial and investment banks, insurance companies, asset management companies, and hedge funds, all participate in financial markets and employ a variety of products and increasingly sophisticated quantitative methods (see Table 1.6). The mathematics includes results and techniques from calculus, linear algebra, probability and statistics, numerical methods, optimization techniques, stochastic processes, differential equations, and machine learning techniques. In the following chapters, we will introduce these techniques as used in different markets and financial products.