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[英文字幕] [2015 SP] MIT 6-042J Mathematics for Computer Science 计算机科学领域的数学

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MIT
计算机数学
6-042J
孔乙己2049 发消息
视频选集
（33/111）
1.1.1 Welcome to 6.042
02:15
1.1.2 Intro to Proofs Part 1
09:30
1.1.3 Intro to Proofs Part 2
07:08
1.2.1 Proof By Contradiction
07:56
1.2.3 Proof By Cases
06:54
1.3.1 Well Ordering Principle 1
05:38
1.3.2 Well Ordering Principle 2
05:24
1.3.5 Well Ordering Principle 3
06:03
1.4.1 Propositional Operators
09:21
1.4.3 Digital Logic
10:03
1.4.4 Truth Tables
12:57
1.5.1 Predicate Logic 1
12:36
1.5.2 Predicate Logic 2
12:00
1.5.4 Predicate Logic 3
08:30
1.6.1 Sets Definitions
12:01
1.6.2 Sets Operations
09:15
1.7.1 Relations
25:13
1.7.3 Relational Mappings
08:53
1.7.5 Finite Cardinality
10:58
1.8.1 Induction
21:42
1.8.2 Bogus Induction
05:03
1.8.4 Strong Induction
10:03
1.8.6 WOP vs Induction [optional]
07:53
1.9.1 State Machines Invariants
26:00
1.9.3 Derived Variables
06:24
1.10.1 Recursive Data
12:43
1.10.4 Structural Induction
06:16
1.10.7 Recursive Functions
14:04
1.11.1 Cardinality
12:56
1.11.3 Countable Sets
09:46
1.11.4 Cantor's Theorem
20:23
1.11.07 The Halting Problem [Optional]
16:02
1.11.09 Russell's Paradox
13:25
1.11.11 Set Theory Axioms [Optional]
09:20
2.1.1 GCDs & Linear Combinations
09:42
2.1.2 Euclidean Algorithm
09:30
2.1.4 Pulverizer
11:49
2.1.6 Revisiting Die Hard
05:17
2.1.7 Prime Factorization
07:48
2.2.1 Congruence mod n
13:12
2.2.3 Inverses mod n
04:17
2.3.1 Modular Exponentiation Euler's Function
06:13
2.3.3 The Ring Z
16:51
2.4.1 RSA Public Key Encryption
21:45
2.4.3 Reducing Factoring To SAT
07:10
2.5.1 Digraphs Walks & Paths
03:45
2.5.3 Digraphs_ Connected Vertices
06:55
2.6.1 DAGs
11:22
2.6.3 Scheduling
13:17
2.6.5 Time versus Processors
09:45
2.7.1 Partial Orders
10:33
2.7.3 Representing Partial Orders As Subset Relations
06:58
2.7.4 Equivalence Relations
07:12
2.8.1 Degree
11:18
2.8.3 Isomorphism
11:04
2.9.1 Coloring
16:21
2.9.3 Connectivity
03:09
2.9.4 k-Connectivity
08:14
2.10.1 Trees
08:07
2.10.3 Tree Coloring
02:04
2.10.5 Spanning Trees
10:39
2.11.1 Stable Matching
11:20
2.11.2 Matching Ritual
09:18
2.11.5 Optimal Stable Matching
09:06
2.11.7 Bipartite Matching
04:02
2.11.9 Hall's Theorem
15:31
3.1.1 Arithmetic Sums
03:59
3.1.3 Geometric Sums
10:36
3.1.5 Book Stacking
07:41
3.1.7 Integral Method
09:35
3.1.9 Stirling's Formula
05:51
3.2.1 Asymptotic Notation
07:43
3.2.3 Asymptotic Properties
10:12
3.2.6 Asymptotic Blunders
04:33
3.3.1 Sum And Product Rules
07:28
3.3.3 Counting with Bijections
11:43
3.4.1 Generalized Counting Rules
10:06
3.4.3 Two Pair Poker Hands
07:46
3.4.4 Binomial Theorem
05:42
3.4.5 Multinomial Theorem
07:51
3.5.1 The Pigeonhole Principle
04:14
3.5.3 Inclusion-Exclusion Example
13:10
3.5.4 Inclusion-Exclusion 2 Sets
07:10
4.1.1 Tree Model
25:24
4.1.3 Simplified Monty Hall Tree
07:41
4.1.5 Sample Spaces
09:46
4.2.1 Conditional Probability Definitions
12:19
4.2.3 Law of Total Probability
03:33
4.2.5 Bayes' Theorem
11:39
4.2.7 Monty Hall Problem
08:42
4.3.1 Independence
03:36
4.3.3 Mutual Independence
08:19
4.4.1 Bigger Number Game
12:19
4.4.2 Random Variables_ Independence
15:31
4.4.4 Random Variables_ Uniform
11:33
4.5.1 Expectation
18:54
4.5.3 Expected Number Of Heads
04:40
4.5.5 Total Expectation
04:18
4.5.7 Mean Time to Failure
11:25
4.5.9 Linearity of Expectation
18:30
4.6.1 Deviation From The Mean
07:47
4.6.3 Markov Bounds
08:48
4.6.5 Chebyshev Bounds
10:22
4.6.7 Variance
14:35
4.7.1 Law Of Large Numbers
13:49
4.7.3 Independent Sampling Theorem
06:52
4.7.5 Birthday Matching
12:19
4.7.7 Sampling
12:57
4.8.1 Random Walks
10:35
4.8.2 Stationary Distributions
16:01
4.8.3 Page Rank
10:59

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