Mathematics IB (Advanced)
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MATH133 is the next step in first year advanced mathematics, for the calculus stream it cover Sequences and Series (convergence tests, Taylor Series, Maclaurin Series), Functions of Several Variables (continuity, limits, differentiation, maxima, minima, Lagrange Multipliers) and Differential Equations (first, second order / partial). The algebra stream is much simpler it covers Vector spaces/subspaces, spans and linear combinations, basis and dimension and then vector spaces and matrices, eigenvalues and eigenvectors, orthogonality, diagonalisation, discrete dynamical systems and systems of linear differential equations. Coming from either MATH132 or MATH135, brush up on solving linear equations (row reduction, RREF), differential equations and techniques of integration. Rest is fairly straight forward. Algebra lecturer was very good. Assessments were simpler than some of the examples in lectures (or very similar). Best to use Stewart book for calculus, this covers most of the course pretty well. And for linear algebra I recommend Lay. For linear Algebra a lot will be redone in MATH235 if you are taking it. Functions of several variables will also be the crux of MATH235 calculus. If you are coming from MATH135 and worried about the application of complex numbers, don't be too worried, they do exist in the course, but not as common as you think. Maybe watch a few videos on Youtube or something, its not really touched on.