Homework is defined as out-of-class tasks assigned to students as an extension or elaboration of classroom work. There are three types of homework: practice, preparation, and extension.

Practice assignments reinforce newly acquired skills. For example, students who have just learned a new method of solving a mathematical problem should be given sample problems to complete on their own. Preparation assignments help students get ready for activities that will occur in the classroom. Students may, for example, be required to do background research on a topic to be discussed later in class. Extension assignments are frequently long-term continuing projects that parallel class work. Students must apply previous learning to complete these assignments, which include science fair projects and term papers.

Mathematics is an essential subject of academics including schooling to many professional courses. Students have to score good marks in mathematics in order to get good academic scores. Hence mathematics is needed to deeply study.

Mathematicians seek out patterns and formulate new conjectures. Mathematicians determine the truth or falsity of conjectures by mathematical proof. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. When those mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature.

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