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课程主页: https://www.udemy.com/course/discrete-mathematics-ugc-net/
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**课程名称：** UGC NET 计算机科学离散数学：第一部分 **课程概述：** 本课程是UGC NET及相关计算机科学考试中离散数学的基础性部分。离散数学是计算机科学的重要基石，它研究不连续的数据，是理解计算机信息处理方式的关键。本课程深入探讨了离散数学的各个核心概念，并结合了UGC NET、SLET及其他竞争性考试中常见的问题类型。 **课程内容涵盖：** * **命题逻辑与谓词逻辑：** 命题等价、范式、谓词与量词、嵌套量词、推理规则。 * **集合论：** 集合运算、关系表示与性质、等价关系、偏序。 * **计数基础：** 鸽巢原理、排列与组合、容斥原理、数学归纳法。 * **概率论：** 概率、贝叶斯定理。 * **代数结构：** 群、子群、半群、代数结构的积与商、同构、同态、自同构。 * **环与域：** 环、整环、域、群论的应用。 * **图论基础：** 简单图、多重图、加权图、路径与回路、加权图最短路径、欧拉路径与回路、哈密顿路径与回路、平面图、图的着色、二分图。 * **树结构：** 树与有根树、前缀码、树的遍历、生成树与割集。 * **布尔代数：** 布尔函数及其表示、布尔函数的化简。 * **线性规划：** 图解法、单纯形法、对偶单纯形法、敏感性分析、整数规划。 * **项目管理：** PERT-CPM图、关键路径计算、资源平滑。 **课程价值：** 本课程全面覆盖了离散数学的主要概念，旨在帮助学习者自信地应对UGC NET、SLET及其他竞争性考试中关于离散数学的考题。通过系统学习，学员将能扎实掌握离散数学的核心知识。
Discrete mathematics refers to a branch of mathematics that deals with non-continuous (i.e., discontinuous or discrete) data. Discrete mathematics is a fundamental course in computer science as it is extremely vital for understanding how computers process information. Discrete mathematics has many applications in computer science and engineering. In fact, it is the foundation for much of the technology we use every day.This course offers you an in-depth introduction to discrete mathematics covering various concepts and kinds of questions asked in discrete mathematics topics in UGC NET, SLET and other competitive examinations. More specifically, this course will cover the following topics:Proposition Logic and Predicate LogicProposiotion EquivalenceNormal FormPredicates and QuantifiersNested QuantifiersRules of InferenceSet OperationsRepresentation and properties of RelationsEquivalennce RelationsPartially orderingBasics of CountingPigeonhole PrinciplePermutation and CombinationsInclusion-Exclusion PrincipleMathematical InductionProbabilityBayes' TheoremGroupsSubgroupsSemi GroupsProduct and Quotients of Algebraic StructuresIsomorphismHomomorphismAutomorphismRingsIntegral DomainsFieldsApplications of Group TheorySimple GraphMultigraphWeighted GraphPaths and circuitsShortest Path in Weighted GraphEulerian Paths and CircuitsHamiltonian Paths and CircuitsPlanner GraphsGraph ColoringBipartite GraphsTree and Rooted TreePrefix CodesTree TraversalSpanning Tree and Cut-setsBoolean Function and its RepresentsSimplifications of Boolean FunctionsLinear ProgrammingGraphical solutionSimplex and Dual Simplex MethodSensitive AnalysisInteger ProgrammingTransportation and Assignment ModelPERT-CPM - Diagram RepresentationCritical Path CalculationsResource LevellingWe have built this course to help you sail through all major concepts of discrete mathematics. Comprehensive coverage offered in this course would be of immense value for you in approaching the topic of Discrete Mathematics for your UGC NET, SLET, and other competitive exams with confidence.So, Click on the Sign Up button and start learning Discrete Mathematics today.
