The study of Algebra was first mentioned in the curriculum at Harvard University in 1786. However, it is believed that Algebra was actually studied at Harvard as early as 1726.
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Linear algebra is usually taught in the last year of high school or the first year of college. Most schools will have calculus prerequisites for those who are seeking a degree in engineering.
Pre-algebra is essentially the basics of algebra. Algebra can be tough for many, so as a way to break the ice, you (ussually) take a pre-algebra course before algebra itself. Algebra is a very large subject, spanning multiple years of courses in most (if not all) schools. After pre-algebra, you have to work with many algebraic equations in the later courses, which cannot be understood without learning the basics that are taught in pre-algebra.
Math is taught like this: Pre-Algebra, Algebra I, Geometry, Algebra 2, Pre-Calculus, Calculus, Trigonometry. Algebra I is similar to Algebra 2, but Algebra 2 has more difficult concepts, such as imaginary numbers. Added: I would have put statistics and trig in between Algebra 2 and Pre-calculus. You review trig in precalculus and statistics is the first transferable math course in college.
Basic Algebra which is one of the main topics or branches of mathematics is taught in 7th grade, 9th grade and in secondary school. It however may also be taught as early as 4th grade.
Well, honey, there's no official "Algebra 3" course recognized by most education systems. Typically, after Algebra 2, students move on to more advanced math courses like pre-calculus or calculus. But hey, if you want to create your own Algebra 3 course and teach the world your math wizardry, go for it!