Assuming that I remember only basic arithmetic, what (if any) mathematics must I learn before tackling Boas' Mathematical Methods in the Physical Sciences?
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You would need to work your way through high school algebra (typically, 2 years of coverage, such as the two Mary P. Dolciani texts Algebra, Book 1 and Algebra, Book 2) and precalculus (another year of coverage, such as Mary P. Dolciani's Modern Introductory Analysis), then a standard 3-semester calculus text (diff. calculus, integral calculus, multivariable calculus -- such as Thomas/Finney's Calculus and Analytic Geometry). That might be minimally enough, but better would be to also cover a one-semester course in ordinary differential equations (such as Abell/Braselton's Introductory Differential Equations) and a one-semester course in elementary linear algebra (such as Howard Anton's Elementary Linear Algebra).