Modules / Lectures
Module NameDownload


Sl.No Chapter Name MP4 Download
1Motivation for CountingDownload
2Paper Folding ExampleDownload
3Rubik's Cube ExampleDownload
4Factorial ExampleDownload
5Counting in Computer ScienceDownload
6Motivation for Catalan numbersDownload
7Rule of Sum and Rule of ProductDownload
8Problems on Rule of Sum and Rule of ProductDownload
9Factorial ExplainedDownload
10Proof of n! - Part 1Download
11Proof of n! - Part 2Download
12Astronomical NumbersDownload
13Permutations - Part 1Download
14Permutations - Part 2Download
15Permutations - Part 3Download
16Permutations - Part 4Download
17Problems on PermutationsDownload
18Combinations - Part 1Download
19Combinations - Part 2Download
20Combinations - Part 3Download
21Combinations - Part 4Download
22Problems on CombinationsDownload
23Difference between Permuations and CombinationsDownload
24Combination with Repetition - Part 1Download
25Combination with Repetition - Part 2Download
26Combination with Repetition - ProblemsDownload
27Binomial theoremDownload
28Applications of Binomial theoremDownload
29Properties of Binomial theoremDownload
30Multinomial theoremDownload
31Problems on Binomial theoremDownload
32Pascal's TriangleDownload
33Fun facts on Pascal's TriangleDownload
34Catalan Numbers - Part 1Download
35Catalan Numbers - Part 2Download
36Catalan Numbers - Part 3Download
37Catalan Numbers - Part 4Download
38Examples of Catalan numbersDownload
39Chapter SummaryDownload
40Introduction to Set TheoryDownload
41Example, definiton and notationDownload
42Sets - Problems Part 1Download
43Subsets - Part 1Download
44Subsets - Part 2Download
45Subsets - Part 3Download
46Union and intersections of setsDownload
47Union and intersections of sets - Part 1Download
48Union and intersections of sets - Part 2Download
49Union and intersections of sets - Part 3Download
50Cardinality of Union of two sets - Part 1Download
51Cardinality of Union of sets - Part 2Download
52Cardinality of Union of three setsDownload
53Power Set - Part 1Download
54Power set - Part 2Download
55Power set - Part 3Download
56Connection betwenn Binomial Theorem and Power SetsDownload
57Power set - ProblemsDownload
58Complement of a setDownload
59De Morgan's Laws - Part 1Download
60De Morgan's Laws - Part 2Download
61A proof techniqueDownload
62De Morgan's Laws - Part 3Download
63De Morgan's Laws - Part 4Download
64Set difference - Part 1Download
65Set difference - Part 2Download
66Symmetric differenceDownload
67HistoryDownload
68SummaryDownload
69Motivational exampleDownload
70Introduction to StatementsDownload
71Examples and Non-examples of StatementsDownload
72Introduction to NegationDownload
73Negation - ExplanationDownload
74Negation - TruthtableDownload
75Examples for NegationDownload
76Motivation for OR operatorDownload
77Introduction to OR operatorDownload
78Truthtable for OR operatorDownload
79OR operator for 3 VariablesDownload
80Truthtable for AND operatorDownload
81 AND operator for 3 VariablesDownload
82Primitive and Compound statements - Part 1 Download
83Primitive and Compound statements - Part 2Download
84Problems involoving NOT, OR and AND operatorsDownload
85Introduction to implicationDownload
86Examples and Non-examples of Implication - Part 1Download
87Examples and Non-examples of Implication - Part 2Download
88Explanation of Implication Download
89Introduction to Double ImplicationDownload
90Explanation of Double ImplicationDownload
91Converse, Inverse and ContrapositiveDownload
92XOR operator - Part 1Download
93XOR operator - Part 2Download
94XOR operator - Part 3Download
95Problems Download
96Tautology, Contradiction - Part 1Download
97Tautology, Contradiction - Part 2Download
98Tautology, Contradiction - Part 3Download
99SAT Problem - Part 1Download
100SAT Problem - Part 2Download
101Logical Equivalence - Part 1Download
102Logical Equivalence - Part 2Download
103Logical Equivalence - Part 3Download
104Logical Equivalence - Part 4Download
105Motivation for laws of logicDownload
106Double negation - Part 1Download
107Double negation - Part 2Download
108Laws of LogicDownload
109De Morgan's Law - Part 1Download
110De Morgan's Law - Part 2Download
111Rules of Inferences - Part 1Download
112Rules of Inferences - Part 2Download
113Rules of Inferences - Part 3Download
114Rules of Inferences - Part 4Download
115Rules of Inferences - Part 5Download
116Rules of Inferences - Part 6Download
117Rules of Inferences - Part 7Download
118ConclusionDownload
119Introduction to RelationDownload
120Graphical Representation of a RelationDownload
121Various setsDownload
122Matrix Representation of a RelationDownload
123Relation - An Example Download
124Cartesian Product Download
125Set Representation of a Relation Download
126Revisiting Representations of a Relation Download
127Examples of RelationsDownload
128Number of relations - Part 1Download
129Number of relations - Part 2Download
130Reflexive relation - IntroductionDownload
131Example of a Reflexive relationDownload
132Reflexive relation - Matrix representationDownload
133Number of Reflexive relationsDownload
134Symmetric Relation - IntroductionDownload
135Symmetric Relation - Matrix representationDownload
136Symmetric Relation - Examples and non examplesDownload
137Parallel lines revisitedDownload
138Number of symmetric relations - Part 1Download
139Number of symmetric relations - Part 2Download
140Examples of Reflexive and Symmetric RelationsDownload
141PatternDownload
142Transitive relation - Examples and non examplesDownload
143Antisymmetric relationDownload
144Examples of Transitive and Antisymmetric RelationDownload
145Antisymmetric - Graphical representation Download
146Antisymmetric - Matrix representation Download
147Number of Antisymmetric relationsDownload
148Condition for relation to be reflexiveDownload
149Few notationsDownload
150Condition for relation to be reflexive.Download
151Condition for relation to be reflexive..Download
152Condition for relation to be symmetricDownload
153Condition for relation to be symmetric.Download
154Condition for relation to be antisymmetricDownload
155Equivalence relationDownload
156Equivalence relation - Example 4Download
157Partition - Part 1Download
158Partition - Part 2Download
159Partition - Part 3Download
160Partition - Part 4Download
161Partition - Part 5Download
162Partition - Part 5.Download
163Motivational Example - 1Download
164Motivational Example - 2Download
165Commonality in examplesDownload
166Motivational Example - 3Download
167Example - 4 ExplanationDownload
168Introduction to functions Download
169Defintion of a function - Part 1Download
170Defintion of a function - Part 2Download
171Defintion of a function - Part 3Download
172Relations vs Functions - Part 1Download
173Relations vs Functions - Part 2Download
174Introduction to One-One FunctionDownload
175One-One Function - Example 1Download
176One-One Function - Example 2Download
177One-One Function - Example 3Download
178Proving a Function is One-OneDownload
179Examples and Non- examples of One-One functionDownload
180Cardinality condition in One-One function - Part 1Download
181Cardinality condition in One-One function - Part 2Download
182Introduction to Onto Function - Part 1Download
183Introduction to Onto Function - Part 2Download
184Definition of Onto FunctionDownload
185Examples of Onto FunctionDownload
186Cardinality condition in Onto function - Part 1Download
187Cardinality condition in Onto function - Part 2Download
188Introduction to BijectionDownload
189Examples of BijectionDownload
190Cardinality condition in Bijection - Part 1Download
191Cardinality condition in Bijection - Part 2Download
192Counting number of functionsDownload
193Number of functionsDownload
194Number of One-One functions - Part 1Download
195Number of One-One functions - Part 2Download
196Number of One-One functions - Part 3Download
197Number of Onto functionsDownload
198Number of BijectionsDownload
199Counting number of functions.Download
200Motivation for Composition of functions - Part 1Download
201Motivation for Composition of functions - Part 2Download
202Definition of Composition of functionsDownload
203Why study Composition of functionsDownload
204Example of Composition of functions - Part 1Download
205Example of Composition of functions - Part 2Download
206Motivation for Inverse functionsDownload
207Inverse functions Download
208Examples of Inverse functionsDownload
209Application of inverse functions - Part 1Download
210Three storiesDownload
211Three stories - Connecting the dotsDownload
212Mathematical induction - An illustrationDownload
213Mathematical Induction - Its essenceDownload
214Mathematical Induction - The formal wayDownload
215MI - Sum of odd numbersDownload
216MI - Sum of powers of 2Download
217MI - Inequality 1Download
218MI - Inequality 1 (solution)Download
219MI - To prove divisibilityDownload
220MI - To prove divisibility (solution)Download
221MI - Problem on satisfying inequalitiesDownload
222MI - Problem on satisfying inequalities (solutions)Download
223MI - Inequality 2Download
224MI - Inequality 2 solutionDownload
225Mathematical Induction - Example 9Download
226Mathematical Induction - Example 10 solutionDownload
227Binomial Coeffecients - Proof by inductionDownload
228Checker board and Triomioes - A puzzleDownload
229Checker board and triominoes - SolutionDownload
230Mathematical induction - An important noteDownload
231Mathematical Induction - A false proofDownload
232A false proof - SolutionDownload
233Motivation for Pegionhole PrincipleDownload
234Group of n peopleDownload
235Set of n integgersDownload
23610 points on an equilateral triangleDownload
237Pegionhole Principle - A resultDownload
238Consecutive integersDownload
239Consecutive integers solutionDownload
240Matching initialsDownload
241Matching initials - SolutionDownload
242Numbers adding to 9Download
243Numbers adding to 9 - SolutionDownload
244Deck of cardsDownload
245Deck of cards - SolutionDownload
246Number of errorsDownload
247Number of errors - SolutionDownload
248Puzzle - Challenge for youDownload
249Friendship - an interesting propertyDownload
250Connectedness through Connecting peopleDownload
251Traversing the bridgesDownload
252Three utilities problemDownload
253Coloring the India mapDownload
254Defintion of a GraphDownload
255Degree and degree sequenceDownload
256Relation between number of edges and degreesDownload
257Relation between number of edges and degrees - ProofDownload
258Hand shaking lemma - CorollaryDownload
259Problems based on Hand shaking lemmaDownload
260Havel Hakimi theorem - Part 1Download
261Havel Hakimi theorem - Part 2Download
262Havel Hakimi theorem - Part 3Download
263Havel Hakimi theorem - Part 4Download
264Havel Hakimi theorem - Part 5Download
265Regular graph and irregular graphDownload
266WalkDownload
267TrailDownload
268Path and closed pathDownload
269Definitions revisitedDownload
270Examples of walk, trail and pathDownload
271Cycle and circuitDownload
272Example of cycle and circuitDownload
273Relation between walk and pathDownload
274Relation between walk and path - An induction proofDownload
275SubgraphDownload
276Spanning and induced subgraphDownload
277Spanning and induced subgraph - A resultDownload
278Introduction to TreeDownload
279Connected and Disconnected graphsDownload
280Property of a cycleDownload
281Edge condition for connectivityDownload
282Connecting connectedness and pathDownload
283Connecting connectedness and path - An illustrationDownload
284Cut vertexDownload
285Cut edgeDownload
286Illustration of cut vertices and cut edgesDownload
287NetworkX - Need of the hourDownload
288Introduction to Python - InstallationDownload
289Introduction to Python - BasicsDownload
290Introduction to NetworkXDownload
291Story so far - Using NetworkXDownload
292Directed, weighted and multi graphsDownload
293Illustration of Directed, weighted and multi graphsDownload
294Graph representations - IntroductionDownload
295Adjacency matrix representationDownload
296Incidence matrix representationDownload
297Isomorphism - IntroductionDownload
298Isomorphic graphs - An illustrationDownload
299Isomorphic graphs - A challengeDownload
300Non - isomorphic graphsDownload
301Isomorphism - A questionDownload
302Complement of a Graph - IntroductionDownload
303Complement of a Graph - IlliustrationDownload
304Self complementDownload
305Complement of a disconnected graph is connectedDownload
306Complement of a disconnected graph is connected - SolutionDownload
307Which is more? Connected graphs or disconnected graphs?Download
308Bipartite graphsDownload
309Bipartite graphs - A puzzleDownload
310Bipartite graphs - Converse part of the puzzleDownload
311Definition of Eulerian GraphDownload
312Illustration of eulerian graphDownload
313Non- example of Eulerian graphDownload
314Litmus test for an Eulerian graphDownload
315Why even degree?Download
316Proof for even degree implies graph is eulerianDownload
317A condition for Eulerian trailDownload
318Why the name EulerianDownload
319Can you traverse all location?Download
320Defintion of Hamiltonian graphsDownload
321Examples of Hamiltonian graphsDownload
322Hamiltonian graph - A resultDownload
323A result on connectednessDownload
324A result on PathDownload
325Dirac's TheoremDownload
326Dirac's theorem - A noteDownload
327Ore's TheoremDownload
328Dirac's Theorem v/s Ore's TheoremDownload
329Eulerian and Hamiltonian Are they relatedDownload
330Importance of Hamiltonian graphs in Computer scienceDownload
331Constructing non intersecting roadsDownload
332Definition of a Planar graphDownload
333Examples of Planar graphsDownload
334V - E + R = 2Download
335Illustration of V - E + R =2Download
336V - E + R = 2; Use inductionDownload
337Proof of V - E + R = 2 Download
338Famous non-planar graphsDownload
339Litmus test for planarityDownload
340Planar graphs - Inequality 1Download
3413 Utilities problem - RevisitedDownload
342Complete graph on 5 vertices is non-planar - ProofDownload
343Prisoners and cellsDownload
344Prisoners example and Proper coloringDownload
345Chromatic number of a graphDownload
346Examples on Proper coloringDownload
347Recalling the India map problemDownload
348Recalling the India map problem - SolutionDownload
349NetworkX - DigraphsDownload
350NetworkX - Adjacency matrixDownload
351NetworkX- Random graphsDownload
352NetworkX - SubgarphDownload
353NetworkX - Isomorphic graphs Part 1Download
354NetworkX - Isomorphic graphs Part 2Download
355NetworkX - Isomorphic graphs: A game to playDownload
356NetworkX - Graph complementDownload
357NetworkX - Eulerian graphsDownload
358NetworkX - Bipaprtite graphsDownload
359NetworkX - ColoringDownload
360Counting in a creative wayDownload
361Example 1 - Fun with wordsDownload
362Words and the polynomialDownload
363Words and the polynomial - ExplainedDownload
364Example 2 - Picking five ballsDownload
365Picking five balls - SolutionDownload
366Picking five balls - Another versionDownload
367Defintion of Generating functionDownload
368Generating function examples - Part 1Download
369Generating function examples - Part 2Download
370Generating function examples - Part 3Download
371Binomial expansion - A generating functionDownload
372Binomial expansion - ExplainedDownload
373Picking 7 balls - The naive wayDownload
374Picking 7 balls - The creative wayDownload
375Generating functions - Problem 1Download
376Generating functions - Problem 2Download
377Generating functions - Problem 3Download
378Why Generating function?Download
379Introduction to Advanced CountingDownload
380Example 1 : Dogs and CatsDownload
381Inclusion-Exclusion FormulaDownload
382Proof of Inclusion - Exlusion formulaDownload
383Example 2 : Integer solutions of an equationDownload
384Example 3 : Words not containing some stringsDownload
385Example 4 : Arranging 3 x's, 3 y's and 3 z'sDownload
386Example 5 : Non-multiples of 2 or 3Download
387Example 6 : Integers not divisible by 5, 7 or 11Download
388A tip in solving problemsDownload
389Example 7 : A dog nor a catDownload
390Example 8 : Brownies, Muffins and CookiesDownload
391Example 10 : Integer solutions of an equationDownload
392Example 11 : Seating Arrangement - Part 1Download
393Example 11 : Seating Arrangement - Part 2Download
394Example 12 : Integer solutions of an equationDownload
395Number of Onto Functions.Download
396Formula for Number of Onto FunctionsDownload
397Example 13 : Onto FunctionsDownload
398Example 14 : No one in their own houseDownload
399DerangementsDownload
400Derangements of 4 numbersDownload
401Example 15 : Bottles and capsDownload
402Example 16 : Self gradingDownload
403Example 17 : Even integers and their placesDownload
404Example 18 : Finding total number of itemsDownload
405Example 19 : Devising a secret codeDownload
406Placing rooks on the chessboardDownload
407Rook PolynomialDownload
408Rook Polynomial.Download
409Motivation for recurrence relationDownload
410Getting started with recurrence relationsDownload
411What is a recurrence relation?Download
412Compound Interest as a recurrence relationDownload
413Examples of recurrence relationsDownload
414Example - Number of ways of climbing stepsDownload
415Number of ways of climbing steps: Recurrence relationDownload
416Example - Rabbits on an islandDownload
417Example - n-bit stringDownload
418Example - n-bit string without consecutive zeroDownload
419Solving Linear Recurrence Relations - A theoremDownload
420A note on the proofDownload
421Soving recurrence relation - Example 1Download
422Soving recurrence relation - Example 2Download
423Fibonacci SequenceDownload
424Introduction to Fibonacci sequenceDownload
425Solution of Fibbonacci sequenceDownload
426A basic introduction to 'complexity'Download
427Intuition for 'complexity'Download
428Visualizing complexity order as a graphDownload
429Tower of HanoiDownload
430Reccurence relation of Tower of HanoiDownload
431Solution for the recurrence relation of Tower of HanoiDownload
432A searching techniqueDownload
433Recurrence relation for Binary searchDownload
434Solution for the recurrence relation of Binary searchDownload
435Example: Door knocks exampleDownload
436Example: Door knocks example solutionDownload
437Door knock example and Merge sortDownload
438Introduction to Merge sort - 1Download
439Recurrence relation for Merge sortDownload
440Intoduction to advanced topicsDownload
441Introduction to Chromatic polynomialDownload
442Chromatic polynomial of complete graphsDownload
443Chromatic polynomial of cycle on 4 vertices - Part 1Download
444Chromatic polynomial of cycle on 4 vertices - Part 2Download
445Correspondence between partition and generating functionsDownload
446Correspondence between partition and generating functions: In generalDownload
447Distinct partitions and odd partitionsDownload
448Distinct partitions and generating functionsDownload
449Odd partitions and generating functionsDownload
450Distinct partitions equals odd partitions: ObservationDownload
451Distinct partitions equals odd partitions: ProofDownload
452Why 'partitions' to 'polynomial'?Download
453Example: Picking 4 letters from the word 'INDIAN'Download
454Motivation for exponential generating functionDownload
455Recurrrence relation: The theorem and its proofDownload
456Introduction to Group TheoryDownload
457Uniqueness of the identity elementDownload
458Formal definition of a GroupDownload
459Groups: Examples and non-examplesDownload
460Groups: Special Examples Part 1Download
461Groups: Special Examples Part 2Download
462Subgroup: Defintion and examplesDownload
463Lagrange's theoremDownload
464Summary.Download
465Conclusion.Download

Sl.No Chapter Name English
1Motivation for CountingDownload
Verified
2Paper Folding ExampleDownload
Verified
3Rubik's Cube ExampleDownload
Verified
4Factorial ExampleDownload
Verified
5Counting in Computer ScienceDownload
Verified
6Motivation for Catalan numbersDownload
Verified
7Rule of Sum and Rule of ProductDownload
Verified
8Problems on Rule of Sum and Rule of ProductDownload
Verified
9Factorial ExplainedDownload
Verified
10Proof of n! - Part 1Download
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11Proof of n! - Part 2Download
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12Astronomical NumbersDownload
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13Permutations - Part 1Download
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14Permutations - Part 2Download
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15Permutations - Part 3Download
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16Permutations - Part 4Download
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17Problems on PermutationsDownload
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18Combinations - Part 1Download
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19Combinations - Part 2Download
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20Combinations - Part 3Download
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21Combinations - Part 4Download
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22Problems on CombinationsDownload
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23Difference between Permuations and CombinationsDownload
Verified
24Combination with Repetition - Part 1Download
Verified
25Combination with Repetition - Part 2Download
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26Combination with Repetition - ProblemsDownload
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27Binomial theoremDownload
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28Applications of Binomial theoremDownload
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29Properties of Binomial theoremDownload
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30Multinomial theoremDownload
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31Problems on Binomial theoremDownload
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32Pascal's TriangleDownload
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33Fun facts on Pascal's TriangleDownload
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34Catalan Numbers - Part 1Download
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35Catalan Numbers - Part 2Download
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36Catalan Numbers - Part 3Download
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37Catalan Numbers - Part 4Download
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38Examples of Catalan numbersDownload
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39Chapter SummaryDownload
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40Introduction to Set TheoryDownload
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41Example, definiton and notationDownload
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42Sets - Problems Part 1Download
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43Subsets - Part 1Download
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44Subsets - Part 2Download
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45Subsets - Part 3Download
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46Union and intersections of setsDownload
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47Union and intersections of sets - Part 1Download
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48Union and intersections of sets - Part 2Download
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49Union and intersections of sets - Part 3Download
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50Cardinality of Union of two sets - Part 1Download
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51Cardinality of Union of sets - Part 2Download
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52Cardinality of Union of three setsDownload
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53Power Set - Part 1Download
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54Power set - Part 2Download
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55Power set - Part 3Download
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56Connection betwenn Binomial Theorem and Power SetsDownload
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57Power set - ProblemsDownload
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58Complement of a setDownload
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59De Morgan's Laws - Part 1Download
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60De Morgan's Laws - Part 2Download
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61A proof techniqueDownload
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62De Morgan's Laws - Part 3Download
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63De Morgan's Laws - Part 4Download
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64Set difference - Part 1Download
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65Set difference - Part 2Download
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66Symmetric differenceDownload
Verified
67HistoryDownload
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68SummaryDownload
Verified
69Motivational examplePDF unavailable
70Introduction to StatementsPDF unavailable
71Examples and Non-examples of StatementsPDF unavailable
72Introduction to NegationPDF unavailable
73Negation - ExplanationPDF unavailable
74Negation - TruthtablePDF unavailable
75Examples for NegationPDF unavailable
76Motivation for OR operatorPDF unavailable
77Introduction to OR operatorPDF unavailable
78Truthtable for OR operatorPDF unavailable
79OR operator for 3 VariablesPDF unavailable
80Truthtable for AND operatorPDF unavailable
81 AND operator for 3 VariablesPDF unavailable
82Primitive and Compound statements - Part 1 PDF unavailable
83Primitive and Compound statements - Part 2PDF unavailable
84Problems involoving NOT, OR and AND operatorsPDF unavailable
85Introduction to implicationPDF unavailable
86Examples and Non-examples of Implication - Part 1PDF unavailable
87Examples and Non-examples of Implication - Part 2PDF unavailable
88Explanation of Implication PDF unavailable
89Introduction to Double ImplicationPDF unavailable
90Explanation of Double ImplicationPDF unavailable
91Converse, Inverse and ContrapositivePDF unavailable
92XOR operator - Part 1PDF unavailable
93XOR operator - Part 2PDF unavailable
94XOR operator - Part 3PDF unavailable
95Problems PDF unavailable
96Tautology, Contradiction - Part 1PDF unavailable
97Tautology, Contradiction - Part 2PDF unavailable
98Tautology, Contradiction - Part 3PDF unavailable
99SAT Problem - Part 1PDF unavailable
100SAT Problem - Part 2PDF unavailable
101Logical Equivalence - Part 1PDF unavailable
102Logical Equivalence - Part 2PDF unavailable
103Logical Equivalence - Part 3PDF unavailable
104Logical Equivalence - Part 4PDF unavailable
105Motivation for laws of logicPDF unavailable
106Double negation - Part 1PDF unavailable
107Double negation - Part 2PDF unavailable
108Laws of LogicPDF unavailable
109De Morgan's Law - Part 1PDF unavailable
110De Morgan's Law - Part 2PDF unavailable
111Rules of Inferences - Part 1PDF unavailable
112Rules of Inferences - Part 2PDF unavailable
113Rules of Inferences - Part 3PDF unavailable
114Rules of Inferences - Part 4PDF unavailable
115Rules of Inferences - Part 5PDF unavailable
116Rules of Inferences - Part 6PDF unavailable
117Rules of Inferences - Part 7PDF unavailable
118ConclusionPDF unavailable
119Introduction to RelationPDF unavailable
120Graphical Representation of a RelationPDF unavailable
121Various setsPDF unavailable
122Matrix Representation of a RelationPDF unavailable
123Relation - An Example PDF unavailable
124Cartesian Product PDF unavailable
125Set Representation of a Relation PDF unavailable
126Revisiting Representations of a Relation PDF unavailable
127Examples of RelationsPDF unavailable
128Number of relations - Part 1PDF unavailable
129Number of relations - Part 2PDF unavailable
130Reflexive relation - IntroductionPDF unavailable
131Example of a Reflexive relationPDF unavailable
132Reflexive relation - Matrix representationPDF unavailable
133Number of Reflexive relationsPDF unavailable
134Symmetric Relation - IntroductionPDF unavailable
135Symmetric Relation - Matrix representationPDF unavailable
136Symmetric Relation - Examples and non examplesPDF unavailable
137Parallel lines revisitedPDF unavailable
138Number of symmetric relations - Part 1PDF unavailable
139Number of symmetric relations - Part 2PDF unavailable
140Examples of Reflexive and Symmetric RelationsPDF unavailable
141PatternPDF unavailable
142Transitive relation - Examples and non examplesPDF unavailable
143Antisymmetric relationPDF unavailable
144Examples of Transitive and Antisymmetric RelationPDF unavailable
145Antisymmetric - Graphical representation PDF unavailable
146Antisymmetric - Matrix representation PDF unavailable
147Number of Antisymmetric relationsPDF unavailable
148Condition for relation to be reflexivePDF unavailable
149Few notationsPDF unavailable
150Condition for relation to be reflexive.PDF unavailable
151Condition for relation to be reflexive..PDF unavailable
152Condition for relation to be symmetricPDF unavailable
153Condition for relation to be symmetric.PDF unavailable
154Condition for relation to be antisymmetricPDF unavailable
155Equivalence relationPDF unavailable
156Equivalence relation - Example 4PDF unavailable
157Partition - Part 1PDF unavailable
158Partition - Part 2PDF unavailable
159Partition - Part 3PDF unavailable
160Partition - Part 4PDF unavailable
161Partition - Part 5PDF unavailable
162Partition - Part 5.PDF unavailable
163Motivational Example - 1PDF unavailable
164Motivational Example - 2PDF unavailable
165Commonality in examplesPDF unavailable
166Motivational Example - 3PDF unavailable
167Example - 4 ExplanationPDF unavailable
168Introduction to functions PDF unavailable
169Defintion of a function - Part 1PDF unavailable
170Defintion of a function - Part 2PDF unavailable
171Defintion of a function - Part 3PDF unavailable
172Relations vs Functions - Part 1PDF unavailable
173Relations vs Functions - Part 2PDF unavailable
174Introduction to One-One FunctionPDF unavailable
175One-One Function - Example 1PDF unavailable
176One-One Function - Example 2PDF unavailable
177One-One Function - Example 3PDF unavailable
178Proving a Function is One-OnePDF unavailable
179Examples and Non- examples of One-One functionPDF unavailable
180Cardinality condition in One-One function - Part 1PDF unavailable
181Cardinality condition in One-One function - Part 2PDF unavailable
182Introduction to Onto Function - Part 1PDF unavailable
183Introduction to Onto Function - Part 2PDF unavailable
184Definition of Onto FunctionPDF unavailable
185Examples of Onto FunctionPDF unavailable
186Cardinality condition in Onto function - Part 1PDF unavailable
187Cardinality condition in Onto function - Part 2PDF unavailable
188Introduction to BijectionPDF unavailable
189Examples of BijectionPDF unavailable
190Cardinality condition in Bijection - Part 1PDF unavailable
191Cardinality condition in Bijection - Part 2PDF unavailable
192Counting number of functionsPDF unavailable
193Number of functionsPDF unavailable
194Number of One-One functions - Part 1PDF unavailable
195Number of One-One functions - Part 2PDF unavailable
196Number of One-One functions - Part 3PDF unavailable
197Number of Onto functionsPDF unavailable
198Number of BijectionsPDF unavailable
199Counting number of functions.PDF unavailable
200Motivation for Composition of functions - Part 1PDF unavailable
201Motivation for Composition of functions - Part 2PDF unavailable
202Definition of Composition of functionsPDF unavailable
203Why study Composition of functionsPDF unavailable
204Example of Composition of functions - Part 1PDF unavailable
205Example of Composition of functions - Part 2PDF unavailable
206Motivation for Inverse functionsPDF unavailable
207Inverse functions PDF unavailable
208Examples of Inverse functionsPDF unavailable
209Application of inverse functions - Part 1PDF unavailable
210Three storiesPDF unavailable
211Three stories - Connecting the dotsPDF unavailable
212Mathematical induction - An illustrationPDF unavailable
213Mathematical Induction - Its essencePDF unavailable
214Mathematical Induction - The formal wayPDF unavailable
215MI - Sum of odd numbersPDF unavailable
216MI - Sum of powers of 2PDF unavailable
217MI - Inequality 1PDF unavailable
218MI - Inequality 1 (solution)PDF unavailable
219MI - To prove divisibilityPDF unavailable
220MI - To prove divisibility (solution)PDF unavailable
221MI - Problem on satisfying inequalitiesPDF unavailable
222MI - Problem on satisfying inequalities (solutions)PDF unavailable
223MI - Inequality 2PDF unavailable
224MI - Inequality 2 solutionPDF unavailable
225Mathematical Induction - Example 9PDF unavailable
226Mathematical Induction - Example 10 solutionPDF unavailable
227Binomial Coeffecients - Proof by inductionPDF unavailable
228Checker board and Triomioes - A puzzlePDF unavailable
229Checker board and triominoes - SolutionPDF unavailable
230Mathematical induction - An important notePDF unavailable
231Mathematical Induction - A false proofPDF unavailable
232A false proof - SolutionPDF unavailable
233Motivation for Pegionhole PrinciplePDF unavailable
234Group of n peoplePDF unavailable
235Set of n integgersPDF unavailable
23610 points on an equilateral trianglePDF unavailable
237Pegionhole Principle - A resultPDF unavailable
238Consecutive integersPDF unavailable
239Consecutive integers solutionPDF unavailable
240Matching initialsPDF unavailable
241Matching initials - SolutionPDF unavailable
242Numbers adding to 9PDF unavailable
243Numbers adding to 9 - SolutionPDF unavailable
244Deck of cardsPDF unavailable
245Deck of cards - SolutionPDF unavailable
246Number of errorsPDF unavailable
247Number of errors - SolutionPDF unavailable
248Puzzle - Challenge for youPDF unavailable
249Friendship - an interesting propertyPDF unavailable
250Connectedness through Connecting peoplePDF unavailable
251Traversing the bridgesPDF unavailable
252Three utilities problemPDF unavailable
253Coloring the India mapPDF unavailable
254Defintion of a GraphPDF unavailable
255Degree and degree sequencePDF unavailable
256Relation between number of edges and degreesPDF unavailable
257Relation between number of edges and degrees - ProofPDF unavailable
258Hand shaking lemma - CorollaryPDF unavailable
259Problems based on Hand shaking lemmaPDF unavailable
260Havel Hakimi theorem - Part 1PDF unavailable
261Havel Hakimi theorem - Part 2PDF unavailable
262Havel Hakimi theorem - Part 3PDF unavailable
263Havel Hakimi theorem - Part 4PDF unavailable
264Havel Hakimi theorem - Part 5PDF unavailable
265Regular graph and irregular graphPDF unavailable
266WalkPDF unavailable
267TrailPDF unavailable
268Path and closed pathPDF unavailable
269Definitions revisitedPDF unavailable
270Examples of walk, trail and pathPDF unavailable
271Cycle and circuitPDF unavailable
272Example of cycle and circuitPDF unavailable
273Relation between walk and pathPDF unavailable
274Relation between walk and path - An induction proofPDF unavailable
275SubgraphPDF unavailable
276Spanning and induced subgraphPDF unavailable
277Spanning and induced subgraph - A resultPDF unavailable
278Introduction to TreePDF unavailable
279Connected and Disconnected graphsPDF unavailable
280Property of a cyclePDF unavailable
281Edge condition for connectivityPDF unavailable
282Connecting connectedness and pathPDF unavailable
283Connecting connectedness and path - An illustrationPDF unavailable
284Cut vertexPDF unavailable
285Cut edgePDF unavailable
286Illustration of cut vertices and cut edgesPDF unavailable
287NetworkX - Need of the hourPDF unavailable
288Introduction to Python - InstallationPDF unavailable
289Introduction to Python - BasicsPDF unavailable
290Introduction to NetworkXPDF unavailable
291Story so far - Using NetworkXPDF unavailable
292Directed, weighted and multi graphsPDF unavailable
293Illustration of Directed, weighted and multi graphsPDF unavailable
294Graph representations - IntroductionPDF unavailable
295Adjacency matrix representationPDF unavailable
296Incidence matrix representationPDF unavailable
297Isomorphism - IntroductionPDF unavailable
298Isomorphic graphs - An illustrationPDF unavailable
299Isomorphic graphs - A challengePDF unavailable
300Non - isomorphic graphsPDF unavailable
301Isomorphism - A questionPDF unavailable
302Complement of a Graph - IntroductionPDF unavailable
303Complement of a Graph - IlliustrationPDF unavailable
304Self complementPDF unavailable
305Complement of a disconnected graph is connectedPDF unavailable
306Complement of a disconnected graph is connected - SolutionPDF unavailable
307Which is more? Connected graphs or disconnected graphs?PDF unavailable
308Bipartite graphsPDF unavailable
309Bipartite graphs - A puzzlePDF unavailable
310Bipartite graphs - Converse part of the puzzlePDF unavailable
311Definition of Eulerian GraphPDF unavailable
312Illustration of eulerian graphPDF unavailable
313Non- example of Eulerian graphPDF unavailable
314Litmus test for an Eulerian graphPDF unavailable
315Why even degree?PDF unavailable
316Proof for even degree implies graph is eulerianPDF unavailable
317A condition for Eulerian trailPDF unavailable
318Why the name EulerianPDF unavailable
319Can you traverse all location?PDF unavailable
320Defintion of Hamiltonian graphsPDF unavailable
321Examples of Hamiltonian graphsPDF unavailable
322Hamiltonian graph - A resultPDF unavailable
323A result on connectednessPDF unavailable
324A result on PathPDF unavailable
325Dirac's TheoremPDF unavailable
326Dirac's theorem - A notePDF unavailable
327Ore's TheoremPDF unavailable
328Dirac's Theorem v/s Ore's TheoremPDF unavailable
329Eulerian and Hamiltonian Are they relatedPDF unavailable
330Importance of Hamiltonian graphs in Computer sciencePDF unavailable
331Constructing non intersecting roadsPDF unavailable
332Definition of a Planar graphPDF unavailable
333Examples of Planar graphsPDF unavailable
334V - E + R = 2PDF unavailable
335Illustration of V - E + R =2PDF unavailable
336V - E + R = 2; Use inductionPDF unavailable
337Proof of V - E + R = 2 PDF unavailable
338Famous non-planar graphsPDF unavailable
339Litmus test for planarityPDF unavailable
340Planar graphs - Inequality 1PDF unavailable
3413 Utilities problem - RevisitedPDF unavailable
342Complete graph on 5 vertices is non-planar - ProofPDF unavailable
343Prisoners and cellsPDF unavailable
344Prisoners example and Proper coloringPDF unavailable
345Chromatic number of a graphPDF unavailable
346Examples on Proper coloringPDF unavailable
347Recalling the India map problemPDF unavailable
348Recalling the India map problem - SolutionPDF unavailable
349NetworkX - DigraphsPDF unavailable
350NetworkX - Adjacency matrixPDF unavailable
351NetworkX- Random graphsPDF unavailable
352NetworkX - SubgarphPDF unavailable
353NetworkX - Isomorphic graphs Part 1PDF unavailable
354NetworkX - Isomorphic graphs Part 2PDF unavailable
355NetworkX - Isomorphic graphs: A game to playPDF unavailable
356NetworkX - Graph complementPDF unavailable
357NetworkX - Eulerian graphsPDF unavailable
358NetworkX - Bipaprtite graphsPDF unavailable
359NetworkX - ColoringPDF unavailable
360Counting in a creative wayPDF unavailable
361Example 1 - Fun with wordsPDF unavailable
362Words and the polynomialPDF unavailable
363Words and the polynomial - ExplainedPDF unavailable
364Example 2 - Picking five ballsPDF unavailable
365Picking five balls - SolutionPDF unavailable
366Picking five balls - Another versionPDF unavailable
367Defintion of Generating functionPDF unavailable
368Generating function examples - Part 1PDF unavailable
369Generating function examples - Part 2PDF unavailable
370Generating function examples - Part 3PDF unavailable
371Binomial expansion - A generating functionPDF unavailable
372Binomial expansion - ExplainedPDF unavailable
373Picking 7 balls - The naive wayPDF unavailable
374Picking 7 balls - The creative wayPDF unavailable
375Generating functions - Problem 1PDF unavailable
376Generating functions - Problem 2PDF unavailable
377Generating functions - Problem 3PDF unavailable
378Why Generating function?PDF unavailable
379Introduction to Advanced CountingPDF unavailable
380Example 1 : Dogs and CatsPDF unavailable
381Inclusion-Exclusion FormulaPDF unavailable
382Proof of Inclusion - Exlusion formulaPDF unavailable
383Example 2 : Integer solutions of an equationPDF unavailable
384Example 3 : Words not containing some stringsPDF unavailable
385Example 4 : Arranging 3 x's, 3 y's and 3 z'sPDF unavailable
386Example 5 : Non-multiples of 2 or 3PDF unavailable
387Example 6 : Integers not divisible by 5, 7 or 11PDF unavailable
388A tip in solving problemsPDF unavailable
389Example 7 : A dog nor a catPDF unavailable
390Example 8 : Brownies, Muffins and CookiesPDF unavailable
391Example 10 : Integer solutions of an equationPDF unavailable
392Example 11 : Seating Arrangement - Part 1PDF unavailable
393Example 11 : Seating Arrangement - Part 2PDF unavailable
394Example 12 : Integer solutions of an equationPDF unavailable
395Number of Onto Functions.PDF unavailable
396Formula for Number of Onto FunctionsPDF unavailable
397Example 13 : Onto FunctionsPDF unavailable
398Example 14 : No one in their own housePDF unavailable
399DerangementsPDF unavailable
400Derangements of 4 numbersPDF unavailable
401Example 15 : Bottles and capsPDF unavailable
402Example 16 : Self gradingPDF unavailable
403Example 17 : Even integers and their placesPDF unavailable
404Example 18 : Finding total number of itemsPDF unavailable
405Example 19 : Devising a secret codePDF unavailable
406Placing rooks on the chessboardPDF unavailable
407Rook PolynomialPDF unavailable
408Rook Polynomial.PDF unavailable
409Motivation for recurrence relationPDF unavailable
410Getting started with recurrence relationsPDF unavailable
411What is a recurrence relation?PDF unavailable
412Compound Interest as a recurrence relationPDF unavailable
413Examples of recurrence relationsPDF unavailable
414Example - Number of ways of climbing stepsPDF unavailable
415Number of ways of climbing steps: Recurrence relationPDF unavailable
416Example - Rabbits on an islandPDF unavailable
417Example - n-bit stringPDF unavailable
418Example - n-bit string without consecutive zeroPDF unavailable
419Solving Linear Recurrence Relations - A theoremPDF unavailable
420A note on the proofPDF unavailable
421Soving recurrence relation - Example 1PDF unavailable
422Soving recurrence relation - Example 2PDF unavailable
423Fibonacci SequencePDF unavailable
424Introduction to Fibonacci sequencePDF unavailable
425Solution of Fibbonacci sequencePDF unavailable
426A basic introduction to 'complexity'PDF unavailable
427Intuition for 'complexity'PDF unavailable
428Visualizing complexity order as a graphPDF unavailable
429Tower of HanoiPDF unavailable
430Reccurence relation of Tower of HanoiPDF unavailable
431Solution for the recurrence relation of Tower of HanoiPDF unavailable
432A searching techniquePDF unavailable
433Recurrence relation for Binary searchPDF unavailable
434Solution for the recurrence relation of Binary searchPDF unavailable
435Example: Door knocks examplePDF unavailable
436Example: Door knocks example solutionPDF unavailable
437Door knock example and Merge sortPDF unavailable
438Introduction to Merge sort - 1PDF unavailable
439Recurrence relation for Merge sortPDF unavailable
440Intoduction to advanced topicsPDF unavailable
441Introduction to Chromatic polynomialPDF unavailable
442Chromatic polynomial of complete graphsPDF unavailable
443Chromatic polynomial of cycle on 4 vertices - Part 1PDF unavailable
444Chromatic polynomial of cycle on 4 vertices - Part 2PDF unavailable
445Correspondence between partition and generating functionsPDF unavailable
446Correspondence between partition and generating functions: In generalPDF unavailable
447Distinct partitions and odd partitionsPDF unavailable
448Distinct partitions and generating functionsPDF unavailable
449Odd partitions and generating functionsPDF unavailable
450Distinct partitions equals odd partitions: ObservationPDF unavailable
451Distinct partitions equals odd partitions: ProofPDF unavailable
452Why 'partitions' to 'polynomial'?PDF unavailable
453Example: Picking 4 letters from the word 'INDIAN'PDF unavailable
454Motivation for exponential generating functionPDF unavailable
455Recurrrence relation: The theorem and its proofPDF unavailable
456Introduction to Group TheoryPDF unavailable
457Uniqueness of the identity elementPDF unavailable
458Formal definition of a GroupPDF unavailable
459Groups: Examples and non-examplesPDF unavailable
460Groups: Special Examples Part 1PDF unavailable
461Groups: Special Examples Part 2PDF unavailable
462Subgroup: Defintion and examplesPDF unavailable
463Lagrange's theoremPDF unavailable
464Summary.PDF unavailable
465Conclusion.PDF unavailable


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