"Advances in Mathematics Research" presents original studies on the leading edge of mathematics. Each article has been carefully selected in an attempt to present substantial research results across a broad spectrum. Topics discussed include the complexities of math skills development; construction of an NP problem with an exponential lower bound; misconceptions and misunderstandings (M&M) of exploratory factor analysis; exploratory structural equation modeling; quantum information measures and molecular phase equilibria; a mathematical model and optimisation of rectangular mufflers hybridised with one-channel splitters by SA method; worst-case analysis versus average-case analysis for combinatorial optimisation problems; mathematical and statistical applied methods; and quantum cryptography within several sequential attacks in BB84 protocol.