Master Thesis Viva in the College of Education for Pure Science entitled ” Hybrid conjugated gradient algorithms in unconstrained optimization”The College of Education for Pure Science, University of Mosul, has done the Master Thesis Viva entitled ” Hybrid conjugated gradient algorithms in unconstrained optimization”,On Thursday, July 7, 2022, the College staff including the respected Dean of the College, Assistant Professor Dr. Qais Ismail Ibrahim, the Honorable Scientific Associate and Administrative Associate, the Honorable Head of the Department of Mathematics, and a number of the college’s teachers were attended the viva.This study, presented by the Master student Basma Tariq Fathy in the Department of Mathematics, This thesis suggest three new hybrids conjugate gradient algorithms. The suggested Algorithms depend on combining those three algorithms; BA1, BA2, and BA3 with FR algorithm, by using convex combinations under strong Wolfe line search conditions (SWC), we studied the new suggested algorithms theoretically and practically, then we compared the new algorithms with the original classical algorithms from which they are developed. Using assumption, we have shown that the proposed algorithms achieve sufficient gradient and global convergence. The numerical results showed that the proposed algorithms were effective in solving a set of nonlinear function in an unconstrained optimization problem.The Viva committee was chaired by Prof. Dr. Abbas Younis Albayati, University of Telafer, College of Basic Education and the membership of Asst. Prof. Dr. Zeyad Mohammed Abdullah, Tikrit University, College of Computer Science and Mathematics, Lecturer. Dr. Azzam S.Y.Aladool, University of Mosul, College of Education for Pure Science and under the supervision and membership of Asst. Prof. Dr. Maha S. Younis, University of Mosul, College of Education for Pure Science.