Introduction to Discrete Mathematics and Fourier Analysis. A Practical Guide for third Year Undergraduate Students.

Abstract

This book covers a quick introduction to high school mathematics, arithmetic and geometric series, infinite geometric series, mathematical induction, binomial theorem, factorials, permutations and combinations, determinants, systems of linear equations, boolean algebra, orthogonal functions, Legendre, Hermite, and Laguerre polynomials and orthogonal properties. For example, mathematical induction is a proof based on logical assumptions of equations that involve integers of one number that shows the proof for the next number. It is based on the base step and the inductive step. The base step is to prove the integers based on a formula. The inductive step involves statement of one integer number that shows the proof of the statement for the next integer. The determinant is a scalar and it is found by multiplying the two elements of the principal diagonal and subtracting them from the multiplication of the elements of the other diagonal.