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Sets, relations, and integers, introduction to groups, permutation groups, subgroups and normal subgroups, homomorphisms and isomorphisms of groups, direct product of groups, introduction to rings. It is designed both for engineering and science majors, but has enough abstraction to be useful for potential math majors. Free college algebra textbook available for download openstax. Peanos axioms, rational numbers, nonrigorous proof of the fundamental theorem of algebra, polynomial equations, matrix theory, groups, rings, and fields, vector spaces, linear maps and the dual space, wedge products and some differential geometry, polarization of a polynomial, philosophy of the lefschetz theorem, hodge star.

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