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This book is designed as an advanced guide for mathematical methods in the science. It covers many topics of practical mathematical methods applied in the science: solution of systems of equations: Gauss, Gauss-Jordan, Cramer, Inverse Matrix, Jacobi, Gauss-Seidel, Gauss-Seidel with relaxation, etc., the method of the least square method for a polynomial fit (regression analysis), etc., the covariance ellipse, the method of the least square in connection with the maximum likehood, covariance ellipse and the determination of the energy calibration-channel numbers (k energies), Moseley Law, etc. It is included the deduction of many formulas in order to clear the concepts of the mathematical methods applied in Science. It is hoped that this book fills all needs of the students to get the fundaments of the mathematical methods and to achieve the interest and motivation of the students for this topic.