How can I use the mathematical symbols like alpha, beta, implies and many more symbols in the tex file?
LaTeX needs to know beforehand that the subsequent text does indeed contain mathematical elements. This is because LaTeX typesets maths notation differently from normal text. Therefore, special environments have been declared for this purpose.
Greek letters are commonly used in mathematics, and they are very easy to type in math mode. You just have to type the name of the letter after a backslash: if the first letter is lowercase, you will get a lowercase Greek letter, if the first letter is uppercase (and only the first letter), then you will get an uppercase letter. Note that some uppercase Greek letters look like Latin ones, so they are not provided by LaTeX (e.g. uppercase Alpha and Beta are just "A" and "B" respectively). Lowercase epsilon, theta, kappa, phi, pi, rho, and sigma are provided in two different versions. The alternate, or variant, version is created by adding "var" before the name of the letter:
See more in: http://en.wikibooks.org/wiki/LaTeX/Mathematics