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A detailed tutorial on how to use algebra tiles. Step by step tutorial including several examples of how to use algebra tiles for reference.

Algebra tiles are a visual expression of polynomials and polynomial equations. Each tile is meant to represent a different polynomial. A large square tile represents the squared variable, a smaller square tile represents a single number, with no variable, and a rectangle represents the single variable. The tiles are red and green. Green represents positive monomials, and red represents negative monomials. Tiles can be combined to create equations, or the same tiles can be combined to express the coefficient. Addition and subtraction can be performed by adding and removing tiles.

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A detailed tutorial on saddle-point approximation. Step by step tutorial including several examples of saddle-point approximation for reference.

Saddle-point approximation is also referred to as the method of steepest descent and Laplace’s method. It is a way of approximating integrals in the form . f(x) is some twice-differentiable function, M is a large number, and the integral endpoints a and b have a possibilty of being infinite.