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From Wikipedia: In American mathematics education, precalculus (or Algebra 3 in some areas), an advanced form of secondary school algebra, is a foundational mathematical discipline. It is also called Introduction to Analysis. In many schools, precalculus is actually two separate courses: Algebra and Trigonometry. Precalculus prepares students for calculus the same way as pre-algebra prepares students for Algebra I. While pre-algebra teaches students many different fundamental algebra topics, precalculus does not involve calculus, but explores topics that will be applied in calculus. Some precalculus courses might differ with others in terms of content. For example, an honors level course might spend more time on topics such as conic sections, vectors, and other topics needed for calculus. A lower level class might focus on topics used in a wider selection of higher mathematical areas, such as matrices, which are used in business. ~~~ Algebra (from Arabic al-jebr meaning reunion of broken parts ) is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. ~~~ Elementary algebra, often part of the curriculum in secondary education, introduces the concept of variables representing numbers. Statements based on these variables are manipulated using the rules of operations that apply to numbers, such as addition. This can be done for a variety of reasons, including equation solving. Algebra is much broader than elementary algebra and studies what happens when different rules of operations are used and when operations are devised for things other than numbers. Addition and multiplication can be generalized and their precise definitions lead to structures such as groups, rings and fields...
