EPH - International Journal of Mathematics and Statistics (ISSN: 2208-2212) https://ephjournal.org/index.php/ms <p><strong><span id="cell-5-name" class="gridCellContainer"><span class="label">EPH - International Journal of Mathematics and Statistics (ISSN: 2208-2212)&nbsp;</span></span></strong> publishes a wide range of high quality research articles in the field (but not limited to) given below: mathematics, applied mathematics, applied commutative algebra and algebraic geometry, mathematical biology, physics and engineering, theoretical bioinformatics, experimental mathematics, theoretical computer science, numerical computation etc. <br><span style="font-size: 1.5em;"><strong> <span style="text-shadow: #ff6600 0px 0px 3px;">Current Impact Factor: 2.387</span></strong></span></p> EPH Journal en-US EPH - International Journal of Mathematics and Statistics (ISSN: 2208-2212) 2208-2212 <ul> <li>All contributor(s) agree to transfer the copyright of this article to <strong>EPH Journal.</strong></li> <li><strong>EPH Journal</strong> will have all the rights to distribute, share, sell, modify this research article with proper reference of the contributors.&nbsp;</li> <li><strong>EPH Journal</strong> will have the right to edit or completely remove the published article on any misconduct happening.</li> </ul> Singular and Simplicial Homology Groups https://ephjournal.org/index.php/ms/article/view/1820 <p>&nbsp;&nbsp;&nbsp;&nbsp; This paper identified the homology groups &nbsp;of -simplex, -dimensional simplicial complex and -complex. We show that a -simplex &nbsp;is a point or a vertex, -simplex &nbsp;is a line or an edge, a -simplex &nbsp;is defined to be a triangle with its interior included and a -simplex &nbsp;is a solid tetrahedron. It is easy to continue to any -simplex . The aims of this paper are to construct and defined Singular Homology Groups and Simplicial Homology Groups in terms of -dimensional simplicial complex &nbsp;and a topological space . We followed the historical analysis mathematical method. We found that simplexes are building blocks of polyhedron, both approaches yield the same results, and the homology groups &nbsp;are quotient groups of -cycle groups &nbsp;and -boundary groups .</p> Hisham Ali Ahmed Ghanim Mohammed Ali Bashir Hussein Abdel Radi Abdel Rahman Abdel Gadir Abdel Rahman Copyright (c) 2021 EPH - International Journal of Mathematics and Statistics (ISSN: 2208-2212) http://creativecommons.org/licenses/by-nc-nd/4.0 2021-08-25 2021-08-25 7 8 01 10