## Discrete Mathematics Research ProgressDiscrete mathematics, also called finite mathematics or Decision Maths, is the study of mathematical structures that are fundamentally discrete, in the sense of not supporting or requiring the notion of continuity. Most, if not all, of the objects studied in finite mathematics are countable sets, such as integers, finite graphs, and formal languages. Discrete mathematics has become popular in recent decades because of its applications to computer science. Concepts and notations from discrete mathematics are useful to study or describe objects or problems in computer algorithms and programming languages. In some mathematics curricula, finite mathematics courses cover discrete mathematical concepts for business, while discrete mathematics courses emphasise concepts for computer science majors. |

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### Contents

Selfconcept and Selfefficacy in Mathematics Relation with Mathematics Motivation and Achievement | 1 |

Some Topics in Galois Geometry Symplectic Spreads Containing a Regulus | 25 |

Algebraic Topics on Discrete Mathematics | 41 |

Optimal Processes in Irreversible Microeconomics | 91 |

Hamiltonicity of 3 Connected L1 Graphs | 115 |

algorithms for computing the myerson Value by Dividends | 125 |

### Common terms and phrases

3-connected claw-free graph academic achievement algorithm cl(G claw closest closure combinatorial component computing Conjecture contained contradiction shows convex geometry cycle in G defined denote Discrete Math Discrete Mathematics dividends edge elements eulerian subgraph Example feasible coalitions finite finite field following result function G E(G G is hamiltonian geometry goal orientation grades graph G graph is hamiltonian graph of order Graph Theory hamiltonian connected Hamiltonian cycles hamiltonian path hamiltonicity Hence induced subgraph intermediary isomorphic Latin squares Lemma Let G line graph lines of W(q locally connected longest cycle Marsh Myerson value neighbor NP-complete obtain optimal orbit orthogonal pair pancyclic path permutation Petersen graph points polynomial problem projective plane proof of Theorem Proposition proved the following PTS\o quadric quotient set regulus relation ring Riordan array Ryjacek self-concept self-concept and self-efficacy self-efficacy self-esteem self-perception Skaalvik subgraph of G subsequent achievement subsystem vertexes colored zero divisor