MIT 6.042J Mathematics for Computer Science, Spring 2015
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23 learners
What you'll learn
This course includes
- 18.5 hours of video
- Certificate of completion
- Access on mobile and TV
Course content
1 modules • 111 lessons • 18.5 hours of video
MIT 6.042J Mathematics for Computer Science, Spring 2015
111 lessons
• 18.5 hours
MIT 6.042J Mathematics for Computer Science, Spring 2015
111 lessons
• 18.5 hours
- 1.1.1 Welcome to 6.04202:15
- 1.1.2 Intro to Proofs: Part 109:30
- 1.1.3 Intro to Proofs: Part 207:08
- 1.2.1 Proof by Contradiction07:55
- 1.2.3 Proof by Cases06:54
- 1.3.1 Well Ordering Principle 1: Video05:38
- 1.3.3 Well Ordering Principle 2: Video05:24
- 1.3.5 Well Ordering Principle 3: Video06:03
- 1.4.1 Propositional Operators: Video09:21
- 1.4.3 Digital Logic: Video10:03
- 1.4.4 Truth Tables: Video12:57
- 1.5.1 Predicate Logic 1: Video12:35
- 1.5.2 Predicate Logic 2: Video12:00
- 1.5.4 Predicate Logic 3: Video08:30
- 1.6.1 Sets Definitions: Video12:00
- 1.6.2 Sets Operations: Video09:15
- 1.7.1 Relations: Video25:13
- 1.7.3 Relational Mappings: Video08:53
- 1.7.5 Finite Cardinality: Video10:58
- 1.8.1 Induction: Video21:42
- 1.8.2 Bogus Induction: Video05:03
- 1.8.4 Strong Induction: Video10:03
- 1.8.6 WOP vs Induction: Video [optional]07:53
- 1.9.1 State Machines Invariants: Video26:00
- 1.9.3 Derived Variables: Video06:24
- 1.10.1 Recursive Data: Video12:42
- 1.10.4 Structural Induction: Video06:16
- 1.10.7 Recursive Functions: Video14:04
- 1.11.1 Cardinality: Video12:56
- 1.11.3 Countable Sets: Video09:46
- 1.11.4 Cantor's Theorem: Video20:23
- 1.11.7 The Halting Problem: Video [Optional]16:02
- 1.11.9 Russell's Paradox: Video13:25
- 1.11.11 Set Theory Axioms: Video [Optional]09:20
- 2.1.1 GCDs & Linear Combinations: Video09:42
- 2.1.2 Euclidean Algorithm: Video09:30
- 2.1.4 Pulverizer: Video11:49
- 2.1.6 Revisiting Die Hard: Video05:17
- 2.1.7 Prime Factorization: Video07:48
- 2.2.1 Congruence mod n: Video13:12
- 2.2.3 Inverses mod n: Video04:17
- 2.3.1 Modular Exponentiation Euler's Function: Video06:13
- 2.3.3 The Ring Z: Video16:51
- 2.4.1 RSA Public Key Encryption: Video21:45
- 2.4.3 Reducing Factoring To SAT: Video07:10
- 2.5.1 Digraphs: Walks & Paths: Video03:45
- 2.5.3 Digraphs: Connected Vertices: Video06:55
- 2.6.1 DAGs: Video11:22
- 2.6.3 Scheduling: Video13:17
- 2.6.5 Time versus Processors: Video09:45
- 2.7.1 Partial Orders: Video10:33
- 2.7.3 Representing Partial Orders As Subset Relations: Video06:58
- 2.7.4 Equivalence Relations: Video07:12
- 2.8.1 Degree: Video11:18
- 2.8.3 Isomorphism: Video11:04
- 2.9.1 Coloring: Video16:21
- 2.9.3 Connectivity: Video03:09
- 2.9.4 k-Connectivity: Video08:14
- 2.10.1 Trees: Video08:07
- 2.10.3 Tree Coloring: Video02:04
- 2.10.5 Spanning Trees: Video10:39
- 2.11.1 Stable Matching: Video11:20
- 2.11.2 Matching Ritual: Video09:18
- 2.11.5 Optimal Stable Matching: Video09:06
- 2.11.7 Bipartite Matching04:02
- 2.11.9 Hall's Theorem15:31
- 3.1.1 Arithmetic Sums: Video03:59
- 3.1.3 Geometric Sums: Video10:36
- 3.1.5 Book Stacking: Video07:41
- 3.1.7 Integral Method: Video09:35
- 3.1.9 Stirling's Formula: Video05:51
- 3.2.1 Asymptotic Notation: Video07:43
- 3.2.3 Asymptotic Properties: Video10:12
- 3.2.6 Asymptotic Blunders04:33
- 3.3.1 Sum And Product Rules: Video07:27
- 3.3.3 Counting with Bijections: Video11:43
- 3.4.1 Generalized Counting Rules: Video10:06
- 3.4.3 Two Pair Poker Hands: Video07:46
- 3.4.4 Binomial Theorem: Video05:42
- 3.4.5 Multinomial Theorem: Video07:51
- 3.5.1 The Pigeonhole Principle: Video04:14
- 3.5.3 Inclusion-Exclusion Example: Video13:10
- 3.5.4 Inclusion-Exclusion 2 Sets: Video07:10
- 4.1.1 Tree Model: Video25:24
- 4.1.3 Simplified Monty Hall Tree: Video07:41
- 4.1.5 Sample Spaces: Video09:46
- 4.2.1 Conditional Probability Definitions: Video12:19
- 4.2.3 Law of Total Probability: Video03:33
- 4.2.5 Bayes' Theorem: Video11:39
- 4.2.7 Monty Hall Problem: Video08:42
- 4.3.1 Independence: Video03:36
- 4.3.3 Mutual Independence: Video08:19
- 4.4.1 Bigger Number Game: Video12:19
- 4.4.2 Random Variables: Independence: Video15:31
- 4.4.4 Random Variables: Uniform & Binomial: Video11:33
- 4.5.1 Expectation: Video18:53
- 4.5.3 Expected Number Of Heads: Video04:39
- 4.5.5 Total Expectation: Video04:18
- 4.5.7 Mean Time to Failure: Video11:25
- 4.5.9 Linearity of Expectation: Video18:30
- 4.6.1 Deviation From The Mean: Video07:47
- 4.6.3 Markov Bounds: Video08:48
- 4.6.5 Chebyshev Bounds: Video10:22
- 4.6.7 Variance: Video14:35
- 4.7.1 Law Of Large Numbers: Video13:49
- 4.7.3 Independent Sampling Theorem: Video06:52
- 4.7.5 Birthday Matching: Video12:19
- 4.7.7 Sampling & Confidence: Video12:57
- 4.8.1 Random Walks: Video10:34
- 4.8.2 Stationary Distributions: Video16:01
- 4.8.3 Page Rank: Video10:58
