
MDU Mathematical Foundation of Computer Science  Sem I Unit 1 : Relation(Relations, Properties of Binary relation, Matrix representation of relations, Closures of relations, Equivalence relations, Partial order relation Function Types, Composition of function,Recursively defined function) 


1. Types of Relations and Representing Relations Using Matrices and Digraphs(Mathematics) 
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This section deals with the study of concept of binary relation and give you several geometric, computer and algebraic method of representations. Relationship between number, people, sets and any other entities can be formulated in the idea of the binary relation. In this section you will also learn the different properties that a binary relation can posess.
Title: Math 1.4 Discrete Mathematics




2. Relations(Discrete Mathematics) 
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Introduction, Binary relations, Displaying Relations, Some Definitions and Terminology, Arrow Diagram of a Relation, The Inverse of a Relation, nAry Relations, Domain and Range of a Relation, Composition of Relations, Properties of Relations, Representing Relations, Partition, Partial Ordered Relations, Digraphs of Posets, Hasse Diagram, Some Definitions, Lattice, Digraph and Emergence of Structu
......
Title: Mathematical Foundations for Computer Science Engineers




3. Matrices of Relation, Transitive Closure and Warshall's Algorithm(Mathematics) 
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Through this unit we discuss about matrix digraphs relation along with transitive closure. Also of interest in how the relation matrix is used in the study of Graph theory.
Title: Math 1.4 Discrete Mathematics




4. Set Theory(Applied Mathematics) 
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One of the most important tools in mathematics is the theory of sets. The notation, terminology and concepts of set theory are helpful in studying any branch of mathematics. Every branch of mathematics can be considered as a study of sets of objects of one kind or another. Further, sets and mathematical logic are now basic to the design of computers and electrical circuits.
Title: Discrete Structures and Graph Theory




5. Relations  II(Discrete Mathematical Structures
) 
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In this chapter we will study the properties of relations, their representation as a matrix or a directed graph. Further we will also discuss about a special kind of relation called partial order.
Title: Discrete Mathematical Structures




6. Graph Matrices and Applications(Software Testing
) 
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Graph Matrices and Applications, Objectives, Overview, Path Tracing Issues in Graphs and Matrix Representation, Graph and The Matrix of a Graph, Terminology: The Matrix of a Graph, Examples on Matrix Representations, Cyclomatic Complexity, Graph, Relations and Properties of Relations, Transitive Property, Reflexive Property, Symmetric Property, Equivalence Relation, Antisymmetric Relation, Partial
......
Title: Software Testing Techniques & Applications




7. Partial Ordering and Totally Ordered Set(Mathematics) 
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We shall emphasize the study of a relation on a set A. various properties of relations are developed along with ways to represent finite relation.
Title: Math 1.4 Discrete Mathematics




8. Equivalence Relation(Computer Science) 
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Naturally we can now ask: Are there relations that simultaneously manifest all three properties? The answer is yes; For instance the relation is logically equivalent to on the set of propositions has all these properties. Such as a relation is an equivalence relation. For example in some programming languages .the names of variables can contain an unlimited
number of characters that are checked w
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Title: MSCS501 Discrete Mathematics




9. Groups, subgroups and Lagrange's theorem(Mathematics) 
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Among several algebraic structures that appear in mathematics, groups are the simplest one. Originally groups consisted of only transformation groups and later in 19th century groups appeared in the context of theory of algebraic equations. Later, to be exact in 1882, these were generalized to abstract groups defined by a set of axioms.
Title: Math 1.1 Algebra




10. Relations II(Discrete Mathematical Structures
) 
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This chapter is a continuation of Chapter 5. In this chapter, the topic of relations is discussed further. Special types of relations called equivalence relations and partial orders are dealthwith in some detail. The matrix representation of relations and the pictorial representation of relations (known as digraphs) are used to illustrate the concepts and results.
Title: Discrete Mathematical Structures




11. Additional TopicsA Bird's Eye View(Formal Languages & Automata Theory) 
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Equivalence between Turing Machines and Type0 languages: For every TM M, we can construct an equivalent grammar G and viceversa. Equivalence between Context Sensitive Languages and Linear Bounded Automata: Linear Bounded Automata is a nondeterministic TM which does not use any tape space beyond input limits. For every CSG G, there is an equivalent LBAM and viceversa. A brief outline of space co
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Title: Formal Languages & Automata Theory




12. Sets, Relations, and Functions(Mathematics) 
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• Recapitulation of sets
• Cartesian product of two sets
• Relations  Types of relations
• Functions  Types of functions
• Graphs of and
Title: Mathematics I




13. Relation and its Properties(Computer Science) 
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Relationships between elements of sets occur in many contexts everyday we deal with relations such as the relations of father to son, brother to sisters etc. Relationships between elements of sets are represented using the structure called a relation, which is just a subset of the Cartesian product of the sets. Relations can be used to solve problems such as determining which pairs of cities are l
......
Title: MSCS501 Discrete Mathematics




14. Algebraic Structures(Discrete Mathematics) 
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Mathematical Structure (or Algebraic Structures), Binary Operation, Properties of Mathematical Structures, Some Important Theorems, Composition Table, Semigroups, Isomorphism, Groups, Some Special Groups, Integral Powers of an Element, Subgroups, Euler φFunction, φ(n), Quotient Group, Homomorphism of Groups
Title: Mathematical Foundations for Computer Science Engineers




15. INTRODUCTION(Computer Science) 
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An Algorithm is any welldefined computational procedure that takes some value or set of values as input and produces a set of values or some value as output. Thus algorithm is a sequence of computational steps that transforms the input into the output.
Title: DESIGN AND ANALYSIS OF ALGORITHMS
Published on: 01/10/18
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17. Difference Equations and Generating Functions(Mathematics) 
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After going through this unit we can define and construct generating functions for sequences arising in various types of combination problems. Also we use generating functions to find the number of integer solution to linear equations. We solve recurrence relation using generating functions.
Title: Math 1.4 Discrete Mathematics




18. Reccurrence Relation(Mathematics) 
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This unit mainly deals with the study of recurrence relation with examples to familiarize with the process of formulating recurrences.
Title: Math 1.4 Discrete Mathematics




19. Lattices(Mathematics) 
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In this section we learn more advanced feature on the relation like partial ordered sets and Lattices. These structures are useful in set theory, algebra, sorting and searching.
Title: Math 1.4 Discrete Mathematics




20. Representation of Forest of Trees(Computer Science) 
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In this unit we shall consider general type of tree there a node can have any number of child nodes. In its most abstract sense, a tree is simply a data structure capable of representing a hierarchical relationship between a parent node and an unlimited number of children nodes.
Title: MSCS504 Data Structure




21. Density Based and Model Based Clustering(Computer Science) 
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Modelbased methods hypothesize a model for each of the clusters and find the best fit of the data to the given model. A model based method hypothesize a model for each of the clusters and find the best fit of the data to the given model A modelbased algorithm may locate clusters
by constructing a density function that reflects the spatial distribution of the data points.
Title: MSCS516A Data Mining




22. Manipulation of Relations(Computer Science) 
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We are very familiar with the concept of relations, operations of relations, properties of relations and equivalence class of relations. In this unit, we also consider the various manipulation , such as union , intersection, compliment and inverse that can be performed on relations. Also we proved the fundamental ideas of partition' and covering.
Title: MSCS501 Discrete Mathematics




23. Introduction to Finite Element Method(Finite Element Method) 
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Introduction, General Description of the Finite Element Method, List of Steps Involved in the Finite Element Method, Engineering Applications of Finite Element Method, Advantages of the Finite Element Method.
Title: Finite Element Method




24. Fundamental of Analysis of Algorithms(Analysis and Design of Algorithms (ADA)) 
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◙ Introduction, ◙ Analyzing an Algorithm, ◙ Analysis of
Nonrecursive Algorithms, ◙ Analysis of Recursive Algorithms, ◙ Exercises, ◙ Solutions for Selected Problems.
Title: Introduction to ADA




25. Data Mining Query Language(Computer Science) 
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The feature of the data mining systems is the ability to support adhoc and interactive data mining in order to facilitate flexible and effective knowledge discovery. Data mining query languages can be designed to support such a feature. The importance of the design of a good data
mining query language can also be seen from observing the history of relational database systems. Relational database
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Title: MSCS516A Data Mining






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