Course Overview
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Course Synopsis
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The course uses the patterns found in Sets, Relations and Functions. Mathematical ideas and concepts relevant to Logic, Combinatorics and Probability will be studied in this course. Matrices will be used to solve problems. The course also include: Mathematical Induction, Algorithm and Graph theory.
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Course Learning Outcomes
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At the end of the course, you should be able to:
- Express statements with the precision of formal logic
- Analyze arguments to test their validity
- Apply the basic properties and operations related to sets
- Apply to sets the basic properties and operations related to relations and functions
- Define terms recursively
- To prove a given statement using mathematical induction
- To prove statements using direct and indirect methods
- To compute probability of simple and conditional events
- Identify and use formulae of Combinatorics in different problems
- Illustrate the basic definitions of graph theory and properties of graphs
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Course Calendar
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1
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Introduction to Discrete Math ,Statements,Negation,Conjunction and disjunction(Lecture# 1)
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2
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Truth Tables, Logical Equivalence and De Morgan`s Law(Lecture # 2)
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3
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Laws of Logic their Applications and implications(Lecture # 3)
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4
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Biconditional,Laws of Logic involving biconditional and their Application(Lecture # 4)
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5
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Valid and Invalid Argument(Lecture # 5)
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6
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Application To Digital Circuits(Lecture # 6)
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7
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Sets ,Reprsentation of Sets,Membership Table(Lecture# 7)
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8
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Union ,Intersection,And some application(Lecture# 8)
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9
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Set Identities and Their Application(Lecture# 9)
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10
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Application of Venn Diagram, Partition of a set , Power set(Lecture# 10)
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Assignment
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11
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Cartesian Product ,Relations And Their Representations(Lecture# 11)
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12
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Reflexive,Symmetric and Tranisitive and Equivalence Relations(Lecture# 12)
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13
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Irreflexive,Anti-symmetric and Partial order Relations(Lecture# 13)
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14
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Inverse ,Complementary ,Composite Relations(Lecture# 14)
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15
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Functions,Arrow Diagram,Grapgh of Functions.(Lecture# 15)
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Quiz 1
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16
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Injective,Surjective and Bijective Functions.(Lecture# 16)
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17
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Equality,Inverse and Composition of Functions(Lecture# 17)
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18
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Algebra of Functions, Image& Inverse Image Functions,Finite & Infinite sets.(Lecture#18)
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19
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Arithmetic and Geometric Sequences.(Lecture# 19)
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Quiz 2
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20
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Series, Arithmetic and Geometric Series.(Lecture# 20)
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21
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Recursion , Recursively defined Functions and Sequences.(Lecture# 21)
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22
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Recursive definition of Sets ,Union, Intersection ,Boolean Expressions etc(Lecture# 22)
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Mid Term Exam
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23
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Introduction to Mathematical Induction(Lecture# 23)
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24
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Mathematical I nduction for Divisibility and Inequalities.(Lecture# 24)
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25
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Methods of Proof, Direct Proof, Disproof by counter example.(Lecture# 25)
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26
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In direct Proof, Proof by Contradiction and Proof by Contraposition.(Lecture# 26)
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27
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Pre-& Post-conditions of an Algorithm, Loop Invariant& Theorem.(Lecture # 27)
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Quiz 3
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28
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Loop to compute a Product , Division Algorithm ,Euclidean Algorithm.(Lecture# 28)
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29
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Combinatorics (Lecture# 29)
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30
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K- Sample , K - Permutation.(Lecture# 30)
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31
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K - Combinations , K - Selections.(Lecture# 31)
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32
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Ordered and unordered Partitions,Permutations with repititons(Lecture# 32)
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Quiz 4
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33
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Tree Diagram , Inclusion - Exclusion Principle.(Lecture# 33)
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34
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Pigeonhole Principle(Lecture# 34)
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35
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Introduction to Probability.(Lecture# 35)
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36
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Addition Law of Probability.(Lecture# 36)
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37
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Conditional Probability, Independent Events.(Lecture# 37)
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38
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Random Variables.Probability Distribution,Expectation and Variance(Lecture# 38)
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39
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Introduction to Graph Theory.(Lecture# 39)
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40
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Paths and Circuits.(Lecture# 40)
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41
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Matrix Reprsentation Of Graphs.(Lecture# 41)
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42
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Isomorphisms of Graphs.(Lecture# 42)
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43
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Planar Graphs and Graph Coloring.(Lecture# 43)
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45
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Spanning Trees.(Lecture# 45)
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Final Term Exams
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