Tangent and q-tangent numbers and polynomials

This thesis was formed from six sections. In first section, it has been dealt with backgrounds. In the second section, Tangent numbers and polynomials were defined and their properties were investigated. In third section, Bernstein polynomials were presented and derived relations with Tangent numbers. In fourth section, q-Tangent numbers and polynomials were studied in details. In fifth section, a generalization of Tangent polynomials was considered and symmetric, derivable and relations with zeta functions were given. In the final section, by applying fermionic p-adic integral to Bernstein polynomials, generalized Tangent numbers were obtained.