Lovely Professional University, Punjab

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1 Lovely Professional University, Punjab Course Code Course Title Course Planner Lectures Tutorials Practicals Credits MTH401 DISCRETE MATHEMATICS 16050::Deepak Sharma Course Weightage ATT: 5 CA: 20 MTT: 25 ETT: 50 Exam Category: 13: Mid Term Exam: All MCQ End Term Exam: MCQ + Subjective Course Orientation COMPETITIVE EXAMINATION (Higher Education), COMPETITIVE EXAMINATION(Civil Services), KNOWLEDGE ENHANCEMENT TextBooks ( T ) Sr No Title Author Publisher Name DISCRETE MATHEMATICS AND ITS APPLICATIONS(SIE) Reference Books ( R ) KENNETH H ROSEN MCGRAW HILL EDUCATION Sr No Title Author Publisher Name R-1 SCHAUM'S OUTLINE OF CALCULUS OF FINITE DIFFERENCES AND DIFFERENCE EQUATIONS DISCRETE MATHEMATICS (SCHAUM'S OUTLINES) (SIE) Other Reading ( OR ) MURRAY SPIEGEL SEYMOUR LIPSCHUTZ, MARC LIPSON, VARSHA H. PATIL MCGRAW HILL EDUCATION MCGRAW HILL EDUCATION Sr No Journals articles as Compulsary reading (specific articles, complete reference) Graph Theory with Applications to Engineering Computer Science, Relevant Websites ( RW ) Sr No (Web address) (only if relevant to the course) Salient Features RW-1 Explain directed graphs RW-2 Explain difference RW-3 Application of directed graph RW-4 Explain the Dijkstra's algorithm RW-5 Explain Equivalence relation RW-6 Explain the concept rooted tree RW-7 Explain permutation combinations

2 Audio Visual Aids ( AV ) Sr No (AV aids) (only if relevant to the course) Salient Features AV-1 Explain difference equation its solution AV-2 Explain the concept of number theory LTP week distribution: (LTP Weeks) Weeks before MTE 7 Weeks After MTE 7 Spill Over (Lecture) 7 Detailed Plan For Lectures Week Number Lecture Number Broad Topic(Sub Topic) Week 1 Lecture 1 Difference with (Difference equation) Lecture 2 Difference with (Difference equation) Chapters/Sections of Text/reference books Other Readings, Relevant Websites, Audio Visual Aids, software Virtual Labs Lecture Description R-1 AV-1 Lecture 1 should be used for zero Lecture lecture 2: Difference its applications. R-1 AV-1 Lecture 1 should be used for zero Lecture lecture 2: Difference its applications. Learning Outcomes Pedagogical Tool Demonstration/ Case Study / Images / animation / ppt etc. Planned It provides the basic idea about the course they are going to study about its purpose to study. It provides the basic idea about the course they are going to study about its purpose to study. Discussion Discussion Live Examples Google uses sophisticated mathematical statistical algorithms based on difference equation to search for the information we need. Google uses sophisticated mathematical statistical algorithms based on difference equation to search for the information we need.

3 Week 1 Lecture 3 Difference with (Solution of a difference equation) Week 2 Lecture 4 Difference with (Homogeneous linear difference with ) Lecture 5 Lecture 6 Difference with (Linearly independent solutions) Difference with (Homogeneous linear difference with ) Difference with (Linearly independent solutions) Difference with variable coefficients (Methods of finding particular solutions) Week 3 Lecture 7 Difference with variable coefficients (Methods of finding particular solutions) R-1 Introduction of Difference operator, shift operator Linear difference equation solution of a difference equation R-1 AV-1 Lecture4:Linear difference equation, Lecture5:Homogeneous with constant coefficients concept of linearly independent solutions. R-1 Linear difference equation, Homogeneous with constant coefficients concept of linearly independent solutions. R-1 AV-1 Lecture4:Linear difference equation, Lecture5:Homogeneous with constant coefficients concept of linearly independent solutions. R-1 Linear difference equation, Homogeneous with constant coefficients concept of linearly independent solutions. R-1 AV-1 Lecture6:Method of Undetermined Coefficients, lecture7:special Operator Methods R-1 AV-1 Lecture6:Method of Undetermined Coefficients, lecture7:special Operator Methods Lecture 8 Test 1 It will provide the knowledge of solutions of difference learn to solve linear difference with constant coefficients learn to solve linear difference with constant coefficients learn to solve linear difference with constant coefficients learn to solve linear difference with constant coefficients To find solution of non homogeneous difference To find solution of non homogeneous difference Lecture Delivery In medicine for modelling cancer growth or the spread of disease. In engineering for describing the movement of electricity In engineering for describing the movement of electricity In engineering for describing the movement of electricity In engineering for describing the movement of electricity In engineering for describing the movement of electricity In engineering for describing the movement of electricity

4 Week 3 Lecture 9 Difference with variable coefficients (Solution of the nonhomogeneous equation) R-1 AV-1 Lecture9:Method of Variation of Parameters, Lecture10:Method of Reduction of Order, Method of Generating Functions To find solution of non homogeneous difference marker In economics to find optimum investment strategies Week 4 Lecture 10 Difference with variable coefficients (Solution of the nonhomogeneous equation) R-1 AV-1 Lecture9:Method of Variation of Parameters, Lecture10:Method of Reduction of Order, Method of Generating Functions To find solution of non homogeneous difference marker In economics to find optimum investment strategies Lecture 11 Difference with variable coefficients(linear difference with variable coefficients) R-1 Linear difference with variable coefficients Transformations to change nonlinear difference to To solve the problems which are naturally formulated as linear In physics to describe the motion of waves, pendulums or chaotic systems. Difference with variable coefficients (Non ) R-1 RW-2 AV-1 Lecture11:Linear difference with variable coefficients Lecture12 :Transformations to change nonlinear difference to To solve the problems which are naturally formulated as linear In physics to describe the motion of waves, pendulums or chaotic systems. Lecture 12 Difference with variable coefficients(linear difference with variable coefficients) R-1 Linear difference with variable coefficients Transformations to change nonlinear difference to To solve the problems which are naturally formulated as linear In physics to describe the motion of waves, pendulums or chaotic systems. Difference with variable coefficients (Non ) R-1 RW-2 AV-1 Lecture11:Linear difference with variable coefficients Lecture12 :Transformations to change nonlinear difference to To solve the problems which are naturally formulated as linear In physics to describe the motion of waves, pendulums or chaotic systems.

5 Week 5 Lecture 13 Relations(Relations their properties) Relations(Equivalence relations) Relations(Partial ordering relations) RW-5 Relations on a set, properties of relations, Equivalence relations, Equivalence Classes, Partial ordering relations RW-5 Relations on a set, properties of relations, Equivalence relations, Equivalence Classes, Partial ordering relations RW-5 Relations on a set, properties of relations, Equivalence relations, Equivalence Classes, Partial ordering relations learn about relations their basic properties like equivalence class partial ordering learn about relations their basic properties like equivalence class partial ordering learn about relations their basic properties like equivalence class partial ordering Lecture 14 Relations(Hasse diagrams) Hasse diagrams Student will learn how to order the elements of a partial ordered sets Lecture 15 Relations(Maximal minimal elements) Maximal minimal elements, upper bounds, lower bounds,superimum infimium Week 6 Lecture 16 Test 2 Lecture 17 Relations(Lattice) Lecture 17: Lattice types of Lattice Lecture18-19:sub-lattice bounded Lattice Relations(Sublattice) Lattice types of Lattice(sub-lattice bounded Lattice) Relations(Bounded Lattice) Lattice types of Lattice(sub-lattice bounded Lattice) to find out the lowest highest value of any set by using hasse diagramme marker problems Women are good for any society can be proved with the help equivalence class Women are good for any society can be proved with the help equivalence class Women are good for any society can be proved with the help equivalence class Ordering of element or members of a set which actually not comparable Model of information flow

6 Week 6 Lecture 18 Relations(Lattice) Lecture 17: Lattice types of Lattice Lecture18-19:sub-lattice bounded Lattice Relations(Sublattice) Lattice types of Lattice(sub-lattice bounded Lattice) Relations(Bounded Lattice) Lattice types of Lattice(sub-lattice bounded Lattice) Week 7 Lecture 19 Relations(Lattice) Lecture 17: Lattice types of Lattice Lecture18-19:sub-lattice bounded Lattice Relations(Sublattice) Lattice types of Lattice(sub-lattice bounded Lattice) Relations(Bounded Lattice) Lattice types of Lattice(sub-lattice bounded Lattice) SPILL OVER Week 7 Lecture 20 Spill Over Lecture 21 Week 8 Lecture 22 Graphs(Graph terminology special types of graphs) Graphs(Paths, cycles connectivity) RW-1 RW-1 RW-3 Spill Over MID-TERM Introduction of graphs special types of graphs Paths, cycles connectivity Introduction of graphs special types of graphs Paths, cycles connectivity To develop a basic understing of graphs To develop a basic understing of graphs Discussion with Discussion with Graph models are used to road maps the assignment jobs to employees of an organisation.

7 Week 8 Lecture 23 Graphs(Graph isomorphism) Isomorphism of Graphs learn how to prove two graph are equal with different shapes Lecture 24 Graphs(Euler Hamilton paths) Graphs(Shortest path problems) RW-4 Euler paths circuits, Hamilton paths circuits, Shortest path problem, Dijkstras algorithm Euler paths circuits, Hamilton paths circuits, Shortest path problem, Dijkstras algorithm Week 9 Lecture 25 Graphs(Planner graphs) Planner graphs, Eulers formula, graph coloring The four color Lecture 26 Graphs(Graph coloring) Planner graphs, Eulers formula, graph coloring The four color Graphs(Kuratowski's ) Graphs(Crossing number thickness) Kuratowski Theorem, Crossing Number thickness, Chromatic Number Kuratowski Theorem, Crossing Number thickness, Chromatic Number To learn about Euler Hamilton paths. how to calculate the shortest path To learn about Euler Hamilton paths. how to calculate the shortest path To underst the relation among vertices, regions edges of graph To underst the relation among vertices, regions edges of graph It will make to use Kuratowski in graph theory, It makes to Know about Crossing number Thickness, Chromatic number of graphs It will make to use Kuratowski in graph theory, It makes to Know about Crossing number Thickness, Chromatic number of graphs problems Lecture Delivery Lecture Delivery Helpful to choose most convenient representation in working with a graph.

8 Week 9 Lecture 26 Graphs(Chromatic number) Kuratowski Theorem, Crossing Number thickness, Chromatic Number Lecture 27 Trees(Tree graphs) Lecture27: Introduction to trees their properties Full m-ary tree, Lecture28:Binary Search tree Trees(Rooted trees) Introduction to trees their properties Full m-ary tree, Binary Search tree Trees(Binary search trees) Introduction to trees their properties Full m-ary tree, Binary Search tree Week 10 Lecture 28 Trees(Tree graphs) Lecture27: Introduction to trees their properties Full m-ary tree, Lecture28:Binary Search tree Lecture 29 Trees(Rooted trees) Introduction to trees their properties Full m-ary tree, Binary Search tree Trees(Binary search trees) Introduction to trees Trees(Spanning trees cut sets) RW-6 their properties Full m-ary tree, Binary Search tree Spanning trees cut sets It will make to use Kuratowski in graph theory, It makes to Know about Crossing number Thickness, Chromatic number of graphs to underst the basic knowledge of tree graphs to underst the basic knowledge of tree graphs to underst the basic knowledge of tree graphs to underst the basic knowledge of tree graphs to underst the basic knowledge of tree graphs to underst the basic knowledge of tree graphs To develop a basic understing of the ideas of spaning trees Communication networks using minimum cost

9 Week 10 Lecture 30 Trees(Minimum spanning trees) Minimum spanning trees, Algorithms for minimum spanning trees learn how to calculate minimum spanning tree Communication networks using minimum cost Week 11 Lecture 31 Trees(Types of Enumeration) Lecture31:Enumeration of Graphs, Lecture32:Labeled unlabeled trees, Lecture33:Polya's Theorem Trees(Counting labeled unlabeled trees) Enumeration of Graphs, Labeled unlabeled trees, Polya's Theorem Trees(Polya's ) Enumeration of Graphs, Labeled unlabeled trees, Polya's Theorem Lecture 32 Trees(Types of Enumeration) Lecture31:Enumeration of Graphs, Lecture32:Labeled unlabeled trees, Lecture33:Polya's Theorem Trees(Counting labeled unlabeled trees) Enumeration of Graphs, Labeled unlabeled trees, Polya's Theorem Trees(Polya's ) Enumeration of Graphs, Labeled unlabeled trees, Polya's Theorem Lecture 33 Trees(Types of Enumeration) Lecture31:Enumeration of Graphs, Lecture32:Labeled unlabeled trees, Lecture33:Polya's Theorem

10 Week 11 Lecture 33 Trees(Counting labeled unlabeled trees) Trees(Polya's ) Week 12 Lecture 34 Test 3 Lecture 35 Lecture 36 Number theory cryptography(divisibility) Number theory cryptography(greatest common divisor) Week 13 Lecture 37 Number theory cryptography(congruences) Lecture 38 Lecture 39 Number theory cryptography(congruences) Number theory cryptography(cryptography) Enumeration of Graphs, Labeled unlabeled trees, Polya's Theorem Enumeration of Graphs, Labeled unlabeled trees, Polya's Theorem AV-2 Divisibility definition,properties,the division algorithm, Modular arithmetic Primes, Greatest common divisor, Euclidean algorithm Lecture37:Solving linear congruences, properties of congruences, Lecture38:The Chinese remainder. Lecture37:Solving linear congruences, properties of congruences, Lecture38:The Chinese remainder. AV-2 Cryptography (encrypt decrypt) learn the use of modular arithmetic Explores distribution of primes many famous open questions concerning primes learn how to solve linear congruences as well as systems of linear congruences learn how to solve linear congruences as well as systems of linear congruences To develop a basic understing of the ideas of cryptography Discussion Discussion To generate pseudo rom numbers which has become an essential tool in providing computer Internet security

11 Week 14 Lecture 40 Number theory cryptography(cryptography) AV-2 Cryptography (encrypt decrypt) To develop a basic understing of the ideas of cryptography SPILL OVER Week 14 Lecture 41 Spill Over Lecture 42 Spill Over Week 15 Lecture 43 Spill Over Lecture 44 Spill Over Lecture 45 Spill Over which has become an essential tool in providing computer Internet security Scheme for CA: CA Category of this Course Code is:a0203 (2 best out of 3) Component Weightage Test 50 Test 50 Test 50 Details of Academic Task(s) Academic Task Objective Detail of Academic Task Nature of Academic Task (group/individuals) Test 1 To test the understing of difference among Difference equation, General particular solution of a difference equation, Linear difference equation, Homogeneous with, Linearly independence of solutions Academic Task Mode Marks Allottment / submission Week Individual Offline 30 2 / 3

12 Test 2 Test 3 To test the Solution of the non homogeneous understing of equation, Methods of finding particular solutions, Linear in nonhomogeneous difference, relations its types difference with variable coefficients, Nonlinear difference alongwith basics of relations. TO check the understing of concepts of graph theory graph representation. ntroduction of graphs special types of graphs, Isomorphism of Graphs, Paths, cycles connectivity, Euler paths circuits, Hamilton paths circuits, Shortest path problem, Dijkstras algorithm, planar graph,euler's formula, Graph coloring, The four color, Kuratowski's, Crossing number thickness. Individual Offline 30 5 / 6 Individual Offline / 11