The Furious M Guide to Higher Mathematics

Don't be intimidated by the impenetrably dense and abstract material of higher mathematics. Once you wade through the extraneous material and cut to the heart of the coursework it is actually quite simple. So without further ado here is a "cheat sheet" I compiled to help anybody fake their way through a degree in mathematics, much as I am doing right now. This is the sort of resource I wish I would have had before taking these classes.

Linear Algebra: All you actually need to learn is how to row reduce a matrix, then on any homework problem or test question row reduce the matrix given in the problem. You are assured at minimum a B even if this is all you do.
Probability Theory: Sort of like Calc 3 (the multivariable calculus class) except easier. Let me explain--most probability theory is multivariate calculus except function values are always positive and everything integrates to one. Hence, it is a simplified version of multivariate calculus. If you even remotely understood Calc 3 then you're golden here.
Real Analysis: Keep quoting the Bolzano-Weierstrass Theorem until you fool everyone into thinking you know what you're talking about.
Complex Analysis: The integral will always equal 2*Pi*i. This will help you achieve massive style points as you can consider any complicated looking integral in the complex plane and make people think you're a genius by correctly predicting the solution without any calculations.
Numerical Analysis: Write the Taylor Expansion and start rearranging terms in a clever way.
Partial Differential Equations: This one is more difficult because I couldn't find any shortcuts in the coursework. Try to recognize that in heat transfer problems the temperature distribution will usually end up being either constant or linear, and if that fails then write an infinite series of sines and cosines with liberal use of the number Pi. If you're still having trouble then send me an email and I'll provide you with the infamous Logsdon Polynomials that I had to invent when the Legendre Polynomials weren't pulling their weight.