Math IP

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Lovely Professional University,Punjab

Course No Cours Title Course Planner Lectures Tutorial Practical Credits

MTH202 GRAPH THEORY AND PROBABILITY 14287 :: Avadhesh Kumar 3 2 0 4

Sr. No. (Web adress) (only if relevant to the courses) Salient Features

6 http://www.personal.kent.edu/~rmuhamma

/GraphTheory/graphTheory.htm

Detailed description on graph theory and its applications

7 http://users.senet.com.au/~dwsmith/boolean.htm Boolean algebra

8 http://walrandpc.eecs.berkeley.edu/126notes.pdf Euler circuits ,Hamiltonian circuits

9http://www.dgp.toronto.edu/people/JamesStewart/270/9798s/Laffra/DijkstraApplet.html

Construct graph

10 http://www.personal.kent.edu/~rmuhamma/GraphTheory/MyGraphTheory/connectivity.htm

Connectivity of Graphs

Sr No Jouranls atricles as compulsary readings (specific articles, Complete reference)

5 Yongtaek LIM, Hyunmyung KIM, A SHORTEST PATH ALGORITHM FOR REAL ROAD NETWORK BASED ON PATH OVERLAP, Journal of the Eastern AsiaSociety for Transportation Studies, Vol. 6, pp. 1426 - 1438, 2005

Lipchutz S and Lipson M, Discrete Mathematics, Tata Mcgraw-Hill publishing House, New Delhi, 20061Text Book:

Other Specific Book:Rosen Kenneth H., Discrete Mathematics and its Applications, Mcgraw-Hill, International Editions, Singapore, 20002

RK Jain & SRK Iyengar, Advanced Engineering Mathematics, Narosa Publications3

Grewal B. S., Higher Engineering Mathematics4

Relevant Websites

Other Reading

Format For Instruction Plan [for Courses with Lectures and Tutorials

1 Approved for Spring Session 2010-11

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11 http://mathform.org/ issac/problems/bridges/.html Seven Bridges of Konnigsberg

12 http://www.math.washington.edu/~ejpecp Journal of Probability

13 http://www.google.co.in/images?hl=en&biw=1003&bih=385&q=isomorphic+graphs&um=1&ie=UTF-8&source=univ&ei=HWXiTJ3HAYeEvAPF-s3dDg&sa=X&oi=image_result_group&ct=title&resnum=2&ved=0CC8QsAQwAQ

Images of isomorphic graphs

Detailed Plan For Lectures

Week Number Lecture Number Lecture Topic Chapters/Sections ofTextbook/otherreference

Homework to be Assignedto students

Pedagogical toolDemonstration/casestudy/images/anmation ctc. planned

Part 1Week 1 Lecture 1 Introduction of Graph and related terms ->Reference :1,8.2

Lecture 2 Multigraphs, Subgraphs ->Reference :1,8.2 8.3

Lecture 3 Isomorphic, homomorphism graphs ->Reference :1,8.3->Reference :13,

Week 2 Lecture 4 Path, Connectivity ->Reference :1,8.4 HomeWork 1 Allocation Lecture with animatedimages

Lecture 5 The bridges of Konigsberg, Traversable multigraphs ->Reference :1,8.5

Lecture 6 Labeled and weighted graphs ->Reference :1,8.6

Week 3 Lecture 7 Complete, Regular and Bipartite Graphs ->Reference :1,8.7 Term Paper 1 Allocation

Lecture 8 Tree Graphs ->Reference :1,8.8 Lecture with animatedimages

Lecture 9 Planar Graphs ->Reference :1,8.9 HomeWork 1 Submission Lecture with animated

imagesWeek 4 Lecture 10 Graph Colorings and Chromatic Number ->Reference :1,8.10

Part 2Week 4 Lecture 11 Directed Graphs, ->Reference :1,9.2 9.3 HomeWork 2 Allocation

Lecture 12 Rooted Tree, Binary tree ->Reference :1,9.4->Reference :1,10.2


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Week 5 Lecture 13 Minimal Spanning tree, Prim's Algorithm

Lecture 14 Shortest path, Di jkstra's Algorithm

Lecture 15 Propositions and compound propositions ->Reference :1,15.215.3->Reference :2,Ch 1section 1.1

Week 6 Lecture 16 Basic Logical Operations ->Reference :1,15.4->Reference :2,Ch 1section 1.2

HomeWork 2 Submission

Lecture 17 Truth Tables ->Reference :1,15.11->Reference :2,CH 1section 1.2

Lecture 18 Tautologies and Contradictions ->Reference :2,CH 1section 1.2

Week 7 Lecture 19 Logical Equivalence ->Reference :2,Ch 1section 1.2

Lecture 20 Algebra of Propositions ->Reference :1,4.7

Lecture 21 Conditional and Biconditional statements ->Reference :1,4.8

MID-TERM

Part 3Week 8 Lecture 22 Partially Ordered Set ->Reference :1,14.2

Lecture 23 Hasse Diagrams of POSET ->Reference :1,14.3

Lecture 24 Consistent Enumeration ->Reference :1,14.4

Week 9 Lecture 25 Supremum and Infimum ->Reference :1,14.5 HomeWork 3 Allocation

Lecture 26 Isomorphic Order Sets ->Reference :1,14.6

Lecture 27 Lattices, Bounded Lattices ->Reference :1,14.814.9

Week 10 Lecture 28 Sample Space and Events ->Reference :1,7.2

Lecture 29 Finite Probability Spaces ->Reference :1,7.3

Part 4Week 10 Lecture 30 Conditional Probability, Independent Events ->Reference :1,7.4 7.5 HomeWork 3 Submission

Week 11 Lecture 31 Independent Repeated Trials ->Reference :1,7.6

Lecture 32 Random Variables ->Reference :1,7.7 HomeWork 4 Allocation


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Week 11 Lecture 33 Baye's Theorem ->Reference :4,18.5->Reference :3,19.6

Week 12 Lecture 34 Random Variables, Probabi li ty Mass Functions ->Reference :4,18.7->Reference :3,19.7

Term Paper 1 Submission

Lecture 35 Binomial Distribution ->Reference :4,18.8->Reference :3,19.8

Lecture 36 Poisson Distribution ->Reference :4,18.8->Reference :3,19.8.2

HomeWork 4 Submission

Week 13 Lecture 37 Geometric Distribution ->Reference :4,18.8

Lecture 38 Expectation, Variance of Random Variable ->Reference :4,18.718.8->Reference :3,19.8

Lecture 39 Expectation, Variance of Random Variable ->Reference :4,18.6->Reference :3,19.8

Spill OverWeek 14 Lecture 40 Hamiltonian circuits, Eulerian graphs ->Reference :2,8.7

Lecture 41 Lattices as boolean algebra ->Reference :2,10.3

Lecture 42 Discrete and continuous Random Variables ->Reference :3,19.7

Week 15 Lecture 43 Mean and Standard Deviation ->Reference :3,19.719.8

Details of homework and case studies

Homework No. Topic of the Homework Nature of homework(group/individuals/field work

Homework 1 Introduction of Graph and related terms of graph , Multi graphs, subgraph, Isomorphic, homomorphismgraphs, Paths, Connectivity.The Bridges of Konigsberg, Transversal Multigraphs, Labeled and Weightedgraphs

Individual

Homework 2 Complete, regular and bipartite graphs, planar graphs, Graph colourings, Chromatic number. Directedgraphs, Tree graphs, rooted treeBinary trees, minimal spanning tree, Prims algorithm, shortest path, Dijkstras Algorithm

Individual

Homework 3 Partially ordered set, Hasse diagrams of POSET. Consistent Enumeration. Supremum and Infimum,Isomorphic Order Sets. Lattices, Bounded Lattices.

Individual

Homework 4 Sample space, events, Finite probability Spaces, Conditional probability, independent events,independent repeated trials. Random variables, Baye's theorem

Individual


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Scheme for CA:out of 100*

Component Frequency Out Of Each Marks Total Marks

Homework 3 4 25 75

Term Paper 1 25 25

Total :- 50 100

* In ENG courses wherever the total exceeds 100, consider x best out of y components of CA, as explained in teacher's guide available on theUMS

List of suggested topics for term paper[at least 15] (Student to spend about 15 hrs on any one specified term paper)

Sr. No. Topic

1 Applications of graph colouring.

2 Disuss the various distributions of continuous random variable.

3 Explain graph coloring and various methods to find out chromatic number of a graph and uses of graph coloring in daily routine.

4 Discuss Chinese postman problem and explain how to solve the problem

5 Explain the various algorithms to find out shortest path in a graph.

6 What are the constraints in proving 4-coloring theorm analytically

7 Explain the problem of Bridges of Konigsberg and method adopted by Euler to solve it

8 Explain various algorithms to find out minimum spanning tree.

9 Explain how graph colouring can be used in a variety of different models.

10 Discuss various discrete random variables and distributions.

11 Explain Baye's theorem and its applications.

12 Discuss binomial distribution and poisson ditribution. Compare and differentiate.

13 Explain Random variables and probability mass function.

14 Explain theorem of Total Probability and its applications in everyday life.

15 Show that if n people attend a party and some shake hands with others (but not with themselves),then at the end, there are at least two people who have shaken hands with the samenumber of people.

16 Explain Eulerian and Hamiltonian circuts with examples .Discuss their applications.


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17 Discuss all kinds of graphs with examples .What are the uses of graphs in daily life.

Plan for Tutorial: (Please do not use these time slots for syllabus coverage)

Tutorial No. Lecture Topic Type of pedagogical tool(s) planned(case analysis,problem solving test,role play,business game etc)

utorial 1 Introduction of Graph and related terms, Multigraphs Problem solving

utorial 2 Subgraphs, Isomorphic, homomorphism graphs Problem solving

utorial 3 Path, Connectivity, The bridges of Konigsberg Problem solving

utorial 4 Traversable Mult igraphs, Labeled and weighted graphs Problem solving

utorial 5 Complete, Regular and Bipartite Graphs Problem solving

utorial 6 Planar Graphs, Tree graphs Problem solving

utorial 7 Graph Colorings and Chromatic Number Problem solving,Test

utorial 8 Directed Graphs, Rooted Tree, Binary tree Problem solving

utorial 9 Minimal Spanning tree, Prim's Algorithm, Shortest path Problem solving

utorial 10 Dijkstra's Algorithm, Propositions and compoundpropositions

Problem solving

utorial 11 Basic Logical Operations, Truth Tables Problem solving,Test

utorial 12 Tautologies and Contradictions Problem solving

utorial 13 Logical equivalence, Algebra of Propositions Problem solving

utorial 14 Conditional and Biconditional statements Problem solving

After Mid-Termutorial 15 Partially ordered set, Hasse Diagrams of POSET Problem solving

utorial 16 Consistent Enumeration Problem solving

utorial 17 Supremum and Infimum, Isomorphic Order Sets Problem solving

utorial 18 Lattices, Bounded Lattices Problem solving

utorial 19 Sample space and events, Finite Probability Spaces Problem solving

utorial 20 Conditional Probability, Independent Events Problem solving

utorial 21 Independent Repeated Trials Problem solving,Test

utorial 22 Random Variables, Baye's Theorem Problem solving


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utorial 23 Random Variables, Probability Mass Functions Problem solving

utorial 24 Binomial Distribution, Poisson Distribution Problem solving,Test

utorial 25 Geometric Distribution Problem solving

utorial 26 Expectation, Variance of Random Variable Problem solving


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Math IP