Mathematics for Computer Science (2015)

Mathematics for Computer Science (2015)

111 episodes

This course covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

Podcasts

1.2.1 Proof by Contradiction

Published: Sept. 7, 2016, 8:32 p.m.
Duration: 7 minutes 56 seconds

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1.1.3 Intro to Proofs: Part 2

Published: Sept. 7, 2016, 8:28 p.m.
Duration: 7 minutes 7 seconds

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1.1.1 Welcome to 6.042

Published: Sept. 7, 2016, 8:28 p.m.
Duration: 2 minutes 14 seconds

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1.1.2 Intro to Proofs: Part 1

Published: Sept. 7, 2016, 8:28 p.m.
Duration: 9 minutes 31 seconds

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3.2.6 Asymptotic Blunders

Published: Aug. 30, 2016, 4:16 p.m.
Duration: 4 minutes 33 seconds

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1.9.1 State Machines Invariants: Video

Published: Aug. 10, 2016, 7:14 p.m.
Duration: 26 minutes

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2.4.1 RSA Public Key Encryption: Video

Published: Aug. 10, 2016, 7:14 p.m.
Duration: 21 minutes 45 seconds

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2.10.3 Tree Coloring: Video

Published: Aug. 10, 2016, 7:14 p.m.
Duration: 2 minutes 3 seconds

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4.1.1 Tree Model: Video

Published: Aug. 10, 2016, 7:13 p.m.
Duration: 25 minutes 24 seconds

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1.8.1 Induction: Video

Published: Aug. 10, 2016, 7:13 p.m.
Duration: 21 minutes 41 seconds

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1.8.6 WOP vs Induction: Video [optional]

Published: Jan. 22, 2016, 4:35 p.m.
Duration: 7 minutes 52 seconds

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2.1.7 Prime Factorization: Video

Published: Jan. 22, 2016, 4:35 p.m.
Duration: 7 minutes 48 seconds

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2.3.3 The Ring Z: Video

Published: Jan. 22, 2016, 4:35 p.m.
Duration: 16 minutes 50 seconds

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2.10.1 Trees: Video

Published: Jan. 22, 2016, 4:35 p.m.
Duration: 8 minutes 7 seconds

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1.3.5 Well Ordering Principle 3: Video

Published: Jan. 22, 2016, 4:34 p.m.
Duration: 6 minutes 3 seconds

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1.4.4 Truth Tables: Video

Published: Jan. 22, 2016, 4:34 p.m.
Duration: 12 minutes 57 seconds

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1.11.11 Set Theory Axioms: Video [Optional]

Published: Jan. 22, 2016, 4:34 p.m.
Duration: 9 minutes 19 seconds

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1.3.1 Well Ordering Principle 1: Video

Published: Jan. 22, 2016, 4:33 p.m.
Duration: 5 minutes 38 seconds

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1.3.3 Well Ordering Principle 2: Video

Published: Jan. 22, 2016, 4:33 p.m.
Duration: 5 minutes 24 seconds

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1.6.1 Sets Definitions: Video

Published: Jan. 22, 2016, 4:31 p.m.
Duration: 12 minutes

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2.8.3 Isomorphism: Video

Published: Jan. 22, 2016, 4:31 p.m.
Duration: 11 minutes 3 seconds

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1.8.4 Strong Induction: Video

Published: Jan. 22, 2016, 4:30 p.m.
Duration: 10 minutes 3 seconds

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2.11.5 Optimal Stable Matching: Video

Published: Jan. 22, 2016, 4:30 p.m.
Duration: 9 minutes 6 seconds

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4.1.3 Simplified Monty Hall Tree: Video

Published: Jan. 22, 2016, 4:29 p.m.
Duration: 7 minutes 40 seconds

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4.8.2 Stationary Distributions: Video

Published: Jan. 22, 2016, 4:29 p.m.
Duration: 16 minutes 1 second

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1.10.4 Structural Induction: Video

Published: Jan. 22, 2016, 4:29 p.m.
Duration: 6 minutes 15 seconds

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2.11.1 Stable Matching: Video

Published: Jan. 22, 2016, 4:29 p.m.
Duration: 11 minutes 19 seconds

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2.11.2 Mating Ritual: Video

Published: Jan. 22, 2016, 4:29 p.m.
Duration: 9 minutes 18 seconds

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3.1.9 Stirling's Formula: Video

Published: Jan. 22, 2016, 4:29 p.m.
Duration: 5 minutes 51 seconds

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2.6.3 Scheduling: Video

Published: Jan. 22, 2016, 4:28 p.m.
Duration: 13 minutes 16 seconds

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2.8.1 Degree: Video

Published: Jan. 22, 2016, 4:28 p.m.
Duration: 11 minutes 18 seconds

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2.10.5 Spanning Trees: Video

Published: Jan. 22, 2016, 4:28 p.m.
Duration: 10 minutes 38 seconds

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1.6.2 Sets Operations: Video

Published: Jan. 22, 2016, 4:27 p.m.
Duration: 9 minutes 15 seconds

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2.4.3 Reducing Factoring To SAT: Video

Published: Jan. 22, 2016, 4:27 p.m.
Duration: 7 minutes 10 seconds

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2.9.1 Coloring: Video

Published: Jan. 22, 2016, 4:27 p.m.
Duration: 16 minutes 20 seconds

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2.9.3 Connectivity: Video

Published: Jan. 22, 2016, 4:27 p.m.
Duration: 3 minutes 8 seconds

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2.9.4 k-Connectivity: Video

Published: Jan. 22, 2016, 4:27 p.m.
Duration: 8 minutes 14 seconds

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2.3.1 Modular Exponentiation Euler's Function: Video

Published: Jan. 22, 2016, 4:24 p.m.
Duration: 6 minutes 12 seconds

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2.7.1 Partial Orders: Video

Published: Jan. 22, 2016, 4:24 p.m.
Duration: 10 minutes 34 seconds

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4.4.2 Random Variables: Independence: Video

Published: Jan. 22, 2016, 4:23 p.m.
Duration: 15 minutes 31 seconds

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1.7.1 Relations: Video

Published: Jan. 22, 2016, 4:23 p.m.
Duration: 25 minutes 12 seconds

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1.10.7 Recursive Functions: Video

Published: Jan. 22, 2016, 4:23 p.m.
Duration: 14 minutes 3 seconds

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1.11.9 Russell's Paradox: Video

Published: Jan. 22, 2016, 4:23 p.m.
Duration: 13 minutes 26 seconds

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4.4.1 Bigger Number Game: Video

Published: Jan. 22, 2016, 4:22 p.m.
Duration: 12 minutes 19 seconds

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4.4.4 Random Variables: Uniform & Binomial: Video

Published: Jan. 22, 2016, 4:22 p.m.
Duration: 11 minutes 33 seconds

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4.8.1 Random Walks: Video

Published: Jan. 22, 2016, 4:22 p.m.
Duration: 10 minutes 34 seconds

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1.10.1 Recursive Data: Video

Published: Jan. 22, 2016, 4:22 p.m.
Duration: 12 minutes 42 seconds

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2.7.3 Representing Partial Orders As Subset Relations: Video

Published: Jan. 22, 2016, 4:22 p.m.
Duration: 6 minutes 58 seconds

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3.3.1 Sum And Product Rules: Video

Published: Jan. 22, 2016, 4:22 p.m.
Duration: 7 minutes 27 seconds

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1.4.1 Propositional Operators: Video

Published: Jan. 22, 2016, 4:21 p.m.
Duration: 9 minutes 21 seconds

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3.5.1 The Pigeonhole Principle: Video

Published: Jan. 22, 2016, 4:20 p.m.
Duration: 4 minutes 13 seconds

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4.1.5 Sample Spaces: Video

Published: Jan. 22, 2016, 4:20 p.m.
Duration: 9 minutes 47 seconds

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4.2.3 Law of Total Probability: Video

Published: Jan. 22, 2016, 4:20 p.m.
Duration: 3 minutes 32 seconds

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2.1.4 Pulverizer: Video

Published: Jan. 22, 2016, 4:20 p.m.
Duration: 11 minutes 49 seconds

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4.3.3 Mutual Independence: Video

Published: Jan. 22, 2016, 4:19 p.m.
Duration: 8 minutes 19 seconds

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4.2.1 Conditional Probability Definitions: Video

Published: Jan. 22, 2016, 4:18 p.m.
Duration: 12 minutes 18 seconds

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4.2.7 Monty Hall Problem: Video

Published: Jan. 22, 2016, 4:18 p.m.
Duration: 8 minutes 41 seconds

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1.5.1 Predicate Logic 1: Video

Published: Jan. 22, 2016, 4:18 p.m.
Duration: 12 minutes 35 seconds

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4.2.5 Bayes' Theorem: Video

Published: Jan. 22, 2016, 4:17 p.m.
Duration: 11 minutes 39 seconds

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4.3.1 Independence: Video

Published: Jan. 22, 2016, 4:17 p.m.
Duration: 3 minutes 36 seconds

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1.5.2 Predicate Logic 2: Video

Published: Jan. 22, 2016, 4:17 p.m.
Duration: 12 minutes

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4.7.3 Independent Sampling Theorem: Video

Published: Jan. 22, 2016, 4:16 p.m.
Duration: 6 minutes 52 seconds

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4.8.3 Page Rank: Video

Published: Jan. 22, 2016, 4:16 p.m.
Duration: 10 minutes 58 seconds

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1.5.4 Predicate Logic 3: Video

Published: Jan. 22, 2016, 4:16 p.m.
Duration: 8 minutes 30 seconds

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2.6.5 Time versus Processors: Video

Published: Jan. 22, 2016, 4:16 p.m.
Duration: 9 minutes 45 seconds

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3.5.3 Inclusion-Exclusion Example: Video

Published: Jan. 22, 2016, 4:09 p.m.
Duration: 13 minutes 10 seconds

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4.7.1 Law Of Large Numbers: Video

Published: Jan. 22, 2016, 4:08 p.m.
Duration: 13 minutes 49 seconds

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1.7.3 Relational Mappings: Video

Published: Jan. 22, 2016, 4:08 p.m.
Duration: 8 minutes 53 seconds

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2.2.3 Inverses mod n: Video

Published: Jan. 22, 2016, 4:08 p.m.
Duration: 4 minutes 16 seconds

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3.1.7 Integral Method: Video

Published: Jan. 22, 2016, 4:08 p.m.
Duration: 9 minutes 35 seconds

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3.5.4 Inclusion-Exclusion 2 Sets: Video

Published: Jan. 22, 2016, 4:07 p.m.
Duration: 7 minutes 9 seconds

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2.11.8 The Halting Problem: Video [Optional]

Published: Jan. 22, 2016, 4:07 p.m.
Duration: 16 minutes 2 seconds

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2.11.9 Hall's Theorem: Video

Published: Jan. 22, 2016, 4:07 p.m.
Duration: 15 minutes 31 seconds

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3.4.1 Generalized Counting Rules: Video

Published: Jan. 22, 2016, 3:53 p.m.
Duration: 10 minutes 5 seconds

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2.1.1 GCDs & Linear Combinations: Video

Published: Jan. 22, 2016, 3:53 p.m.
Duration: 9 minutes 41 seconds

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2.1.2 Euclidean Algorithm: Video

Published: Jan. 22, 2016, 3:53 p.m.
Duration: 9 minutes 30 seconds

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3.1.3 Geometric Sums: Video

Published: Jan. 22, 2016, 3:53 p.m.
Duration: 10 minutes 35 seconds

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4.5.5 Total Expectation: Video

Published: Jan. 22, 2016, 3:52 p.m.
Duration: 4 minutes 18 seconds

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4.5.9 Linearity of Expectation: Video

Published: Jan. 22, 2016, 3:52 p.m.
Duration: 18 minutes 29 seconds

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1.7.5 Finite Cardinality: Video

Published: Jan. 22, 2016, 3:52 p.m.
Duration: 10 minutes 57 seconds

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2.7.4 Equivalence Relations: Video

Published: Jan. 22, 2016, 3:52 p.m.
Duration: 7 minutes 12 seconds

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4.5.3 Expected Number Of Heads: Video

Published: Jan. 22, 2016, 3:51 p.m.
Duration: 4 minutes 39 seconds

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4.5.7 Mean Time to Failure: Video

Published: Jan. 22, 2016, 3:51 p.m.
Duration: 11 minutes 25 seconds

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4.5.1 Expectation: Video

Published: Jan. 22, 2016, 3:50 p.m.
Duration: 18 minutes 53 seconds

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4.6.3 Markov Bounds: Video

Published: Jan. 22, 2016, 3:49 p.m.
Duration: 8 minutes 47 seconds

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1.4.3 Digital Logic: Video

Published: Jan. 22, 2016, 3:49 p.m.
Duration: 10 minutes 3 seconds

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2.5.1 Digraphs: Walks & Paths: Video

Published: Jan. 22, 2016, 3:49 p.m.
Duration: 3 minutes 44 seconds

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4.6.5 Chebyshev Bounds: Video

Published: Jan. 22, 2016, 3:48 p.m.
Duration: 10 minutes 22 seconds

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4.6.7 Variance: Video

Published: Jan. 22, 2016, 3:48 p.m.
Duration: 14 minutes 35 seconds

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1.9.3 Derived Variables: Video

Published: Jan. 22, 2016, 3:48 p.m.
Duration: 6 minutes 23 seconds

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2.1.6 Revisiting Die Hard: Video

Published: Jan. 22, 2016, 3:48 p.m.
Duration: 5 minutes 17 seconds

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2.6.1 DAGs: Video

Published: Jan. 22, 2016, 3:48 p.m.
Duration: 11 minutes 23 seconds

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4.6.1 Deviation From The Mean: Video

Published: Jan. 22, 2016, 3:47 p.m.
Duration: 7 minutes 46 seconds

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1.2.3 Proof by Cases

Published: Jan. 22, 2016, 3:44 p.m.
Duration: 6 minutes 53 seconds

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1.11.1 Cardinality: Video

Published: Jan. 22, 2016, 3:44 p.m.
Duration: 12 minutes 55 seconds

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3.4.3 Two Pair Poker Hands: Video

Published: Jan. 22, 2016, 3:43 p.m.
Duration: 7 minutes 45 seconds

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1.11.3 Countable Sets: Video

Published: Jan. 22, 2016, 3:43 p.m.
Duration: 9 minutes 46 seconds

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2.5.3 Digraphs: Connected Vertices: Video

Published: Jan. 22, 2016, 3:43 p.m.
Duration: 6 minutes 54 seconds

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3.2.3 Asymptotic Properties: Video

Published: Jan. 22, 2016, 3:43 p.m.
Duration: 10 minutes 11 seconds

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3.4.5 Multinomial Theorem: Video

Published: Jan. 22, 2016, 3:42 p.m.
Duration: 7 minutes 51 seconds

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4.7.7 Sampling & Confidence: Video

Published: Jan. 22, 2016, 3:42 p.m.
Duration: 12 minutes 56 seconds

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1.11.4 Cantor's Theorem: Video

Published: Jan. 22, 2016, 3:42 p.m.
Duration: 20 minutes 23 seconds

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2.2.1 Congruence mod n: Video

Published: Jan. 22, 2016, 3:42 p.m.
Duration: 13 minutes 12 seconds

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3.1.5 Book Stacking: Video

Published: Jan. 22, 2016, 3:42 p.m.
Duration: 7 minutes 40 seconds

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3.3.3 Counting with Bijections: Video

Published: Jan. 22, 2016, 3:41 p.m.
Duration: 11 minutes 42 seconds

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3.4.4 Binomial Theorem: Video

Published: Jan. 22, 2016, 3:41 p.m.
Duration: 5 minutes 42 seconds

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4.7.5 Birthday Matching: Video

Published: Jan. 22, 2016, 3:41 p.m.
Duration: 12 minutes 19 seconds

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1.8.2 Bogus Induction: Video

Published: Jan. 22, 2016, 3:41 p.m.
Duration: 5 minutes 3 seconds

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2.11.7 Bipartite Matching: Video

Published: Jan. 22, 2016, 3:41 p.m.
Duration: 4 minutes 2 seconds

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3.1.1 Arithmetic Sums: Video

Published: Jan. 22, 2016, 3:40 p.m.
Duration: 3 minutes 58 seconds

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3.2.1 Asymptotic Notation: Video

Published: Jan. 22, 2016, 3:40 p.m.
Duration: 7 minutes 42 seconds

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