MIT计算机专业数学基础@每天5分钟，全部学完。
https://www.youtube.com/watch?v=wIq4CssPoO0&list=PLUl4u3cNGP60UlabZBeeqOuoLuj_KNphQ
More courses at http://ocw.mit.edu
MIT OpenCourseWare
视频选集
（102/110）
01.1.1.1 Welcome to 6.042
02:15
02.1.1.2 Intro to Proofs- Part 1
09:30
03.1.1.3 Intro to Proofs- Part 2
07:08
04.1.2.1 Proof by Contradiction
07:55
05.1.2.3 Proof by Cases
06:54
09.1.4.1 Propositional Operators- Video
09:21
10.1.4.3 Digital Logic- Video
10:03
11.1.4.4 Truth Tables- Video
12:57
12.1.5.1 Predicate Logic 1- Video
12:35
13.1.5.2 Predicate Logic 2- Video
12:00
14.1.5.4 Predicate Logic 3- Video
08:30
15.1.6.1 Sets Definitions- Video
12:01
16.1.6.2 Sets Operations- Video
09:15
17.1.7.1 Relations- Video
25:13
18.1.7.3 Relational Mappings- Video
08:53
19.1.7.5 Finite Cardinality- Video
10:58
20.1.8.1 Induction- Video
21:42
21.1.8.2 Bogus Induction- Video
05:03
22.1.8.4 Strong Induction- Video
10:03
23.1.8.6 WOP vs Induction- Video [optional]
07:53
24.1.9.3 Derived Variables- Video
06:24
25.1.10.1 Recursive Data- Video
12:43
26.1.10.4 Structural Induction- Video
06:16
27.1.10.7 Recursive Functions- Video
14:04
28.1.11.1 Cardinality- Video
12:56
29.1.11.3 Countable Sets- Video
09:46
30.1.11.4 Cantor
20:23
31.1.11.7 The Halting Problem- Video [Optional]
16:02
32.1.11.9 Russell
13:25
33.1.11.11 Set Theory Axioms- Video [Optional]
09:20
34.2.1.1 GCDs & Linear Combinations- Video
09:42
35.2.1.2 Euclidean Algorithm- Video
09:30
36.2.1.4 Pulverizer- Video
11:49
37.2.1.6 Revisiting Die Hard- Video
05:17
38.2.1.7 Prime Factorization- Video
07:48
39.2.2.1 Congruence mod n- Video
13:12
40.2.2.3 Inverses mod n- Video
04:17
41.2.3.1 Modular Exponentiation Euler
06:13
42.2.3.3 The Ring Z- Video
16:51
43.2.4.1 RSA Public Key Encryption- Video
21:45
44.2.4.3 Reducing Factoring To SAT- Video
07:10
46.2.5.3 Digraphs- Connected Vertices- Video
06:55
47.2.6.1 DAGs- Video
11:22
48.2.6.3 Scheduling- Video
13:17
49.2.6.5 Time versus Processors- Video
09:45
50.2.7.1 Partial Orders- Video
10:33
51.2.7.3 Representing Partial Orders As Subset Relations- Video
06:58
52.2.7.4 Equivalence Relations- Video
07:12
53.2.8.1 Degree- Video
11:18
54.2.8.3 Isomorphism- Video
11:04
55.2.9.1 Coloring- Video
16:21
56.2.9.3 Connectivity- Video
03:09
57.2.9.4 k-Connectivity- Video
08:14
58.2.10.1 Trees- Video
08:07
59.2.10.3 Tree Coloring- Video
02:04
60.2.10.5 Spanning Trees- Video
10:39
61.2.11.1 Stable Matching- Video
11:20
62.2.11.2 Matching Ritual- Video
09:18
63.2.11.5 Optimal Stable Matching- Video
09:06
64.2.11.7 Bipartite Matching
04:02
65.2.11.9 Hall
15:31
66.3.1.1 Arithmetic Sums- Video
03:59
67.3.1.3 Geometric Sums- Video
10:36
68.3.1.5 Book Stacking- Video
07:41
69.3.1.7 Integral Method- Video
09:35
70.3.1.9 Stirling
05:51
71.3.2.1 Asymptotic Notation- Video
07:43
72.3.2.3 Asymptotic Properties- Video
10:12
73.3.2.6 Asymptotic Blunders
04:33
74.3.3.1 Sum And Product Rules- Video
07:28
75.3.3.3 Counting with Bijections- Video
11:43
76.3.4.1 Generalized Counting Rules- Video
10:06
77.3.4.3 Two Pair Poker Hands- Video
07:46
78.3.4.4 Binomial Theorem- Video
05:42
79.3.4.5 Multinomial Theorem- Video
07:51
80.3.5.1 The Pigeonhole Principle- Video
04:14
81.3.5.3 Inclusion-Exclusion Example- Video
13:10
82.3.5.4 Inclusion-Exclusion 2 Sets- Video
07:10
83.4.1.1 Tree Model- Video
25:24
84.4.1.3 Simplified Monty Hall Tree- Video
07:41
85.4.1.5 Sample Spaces- Video
09:46
86.4.2.1 Conditional Probability Definitions- Video
12:19
87.4.2.3 Law of Total Probability- Video
03:33
88.4.2.5 Bayes
11:39
89.4.2.7 Monty Hall Problem- Video
08:42
90.4.3.1 Independence- Video
03:36
91.4.3.3 Mutual Independence- Video
08:19
92.4.4.1 Bigger Number Game- Video
12:19
93.4.4.2 Random Variables- Independence- Video
15:31
94.4.4.4 Random Variables- Uniform & Binomial- Video
11:33
95.4.5.1 Expectation- Video
18:53
96.4.5.3 Expected Number Of Heads- Video
04:40
97.4.5.5 Total Expectation- Video
04:18
98.4.5.7 Mean Time to Failure- Video
11:25
99.4.5.9 Linearity of Expectation- Video
18:30
100.4.6.1 Deviation From The Mean- Video
07:47
101.4.6.3 Markov Bounds- Video
08:48
102.4.6.5 Chebyshev Bounds- Video
10:22
103.4.6.7 Variance- Video
14:35
104.4.7.1 Law Of Large Numbers- Video
13:49
105.4.7.3 Independent Sampling Theorem- Video
06:52
106.4.7.5 Birthday Matching- Video
12:19
107.4.7.7 Sampling & Confidence- Video
12:57
108.4.8.1 Random Walks- Video
10:34
109.4.8.2 Stationary Distributions- Video
16:01
110.4.8.3 Page Rank- Video
10:59
Directed Graphs
03:45
The well ordering principle I
05:38
The well ordering principle II
05:24
The well ordering principle III
06:03
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