Mathematics with Finance and Investment Banking

Finance is a field that deals with the study of investments. It includes the dynamics of assets and liabilities over time under conditions of different degrees of uncertainties and risks. Finance can also be defined as the science of money management. Market participants aim to price assets based on their risk level, fundamental value, and their expected rate of return. Finance can be broken into three sub-categories: public finance, corporate finance and personal finance.

In general, to invest is to allocate money (or sometimes another resource, such as time) in the expectation of some benefit in the future – for example, investment in durable goods, in real estate by the service industry, in factories for manufacturing, in product development, and in research and development. However, this article focuses specifically on investment in financial assets.

An investment bank is typically a private company that provides various finance-related and other services to individuals, corporations, and governments such as raising financial capital by underwriting or acting as the client's agent in the issuance of securities. An investment bank may also assist companies involved in mergers and acquisitions (M&A) and provide ancillary services such as market making, trading of derivatives and equity securities, and FICC services (fixed income instruments, currencies, and commodities).

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change. It has no generally accepted definition.