形式逻辑导论
1387
0
2025-04-17 08:05:00
未经作者授权，禁止转载
正在缓冲...
63
24
249
10
本课程向观众介绍形式符号逻辑的入门知识。我们将涵盖论证、范畴逻辑、命题逻辑、命题证明（自然演绎）和谓词逻辑的基础知识。
哲学家约翰·洛克曾写道：“逻辑是思想的解剖学。”本课程遵循这一思路，将教授学生使用现代符号逻辑的形式技巧来分析和评估论证。
在我们的日常生活中，我们面临着大量的挑战，这些挑战需要敏锐的能力来快速解释、评估和综合信息和论证。
无论是看电视、阅读当地报纸的政治评论、倾听家人的善意想法，还是被教授提出的一系列激进观点——每个人都在争夺你的意见和同意，他们通过论证来实现这一点。
我们在生活中遇到的一些论证很强，另一些则很弱，还有许多是完全错误的。本视频旨在为学生提供必要的工具集，用于诊断合理思想领域中什么是值得信赖的，什么不是。
就像一位接受过人体解剖学训练的医生一样，逻辑学家拥有信心和能力来分解论证，并透过修辞手段的幌子来寻找真理。
本视频让学生走上了一条磨练精细的批判性技能之路，这对于现代生活至关重要。
P01 1.1 基本概念 - 论证、前提与结论
P02 1.2 识别论证
P03 1.3 演绎与归纳
P04 1.4 有效性、真、可靠性、强度、说服力
P05 1.5 论证形式 - 证明无效性
P06 2.1 意义的种类
P07 2.2 术语的内涵与外延
P08 3A 一般谬误、相关性谬误与弱归纳谬误
P09 3B 预设谬误、歧义谬误与转移谬误
P10 4.1 直言命题的组成部分
P11 4.2 数量、性质与周延性
P12 4.3 维恩图与现代对立关系方阵
P13 4.4 换位、质变与逆转
P14 4.5 传统对立关系方阵
P15 4.6 维恩图与传统观点
P16 5.1 标准形式、格与式
P17 5.2 维恩图
P18 5.3 规则与谬误
P19 5.6 简略推理
P20 5.7 连锁推理
P21 6.1 符号与翻译
P22 6.2 真值函数
P23 6.3 命题的真值表
P24 6.4 论证的真值表
P25 6.5 间接真值表
P26 7.1 蕴涵规则 I
P27 7.2 蕴涵规则 II
P28 7.3 替换规则 I
P29 7.4 替换规则 II
P30 7.5 条件证明
P31 7.6 间接证明
P32 8.1 谓词逻辑 - 符号与翻译
P33 8.2 谓词逻辑 - 推理规则的应用
P34 8.3 量词转换规则
P35 8.4 谓词逻辑 - 条件证明与间接证明
P36 8.5 谓词逻辑 - 有限论域法
P37 附录 1. 哲学逻辑
P38 附录 2 - 论证图解
P39 巴拿赫-塔斯基悖论
P40 1. 弗雷格 - 思想、意义与指称
Here is all you need | wx: mindofuture
关注 4.4万
弹幕列表
数学/优化/逻辑（更新中）
（11/35）
自动连播
6.4万播放
简介
订阅合集
【麻省理工 • 中英】线性代数 MIT 18.06SC（Linear Algebra，Fall 2011）
P01 An Interview with Gilbert Strang on Teaching Linear Algebra
07:34
P02 Course Introduction - MIT 18.06SC Linear Algebra
07:13
P03 1. The Geometry of Linear Equations
39:49
P04 Geometry of Linear Algebra
16:36
P05 Rec 1 - MIT 18.085 Computational Science and Engineering I, Fall 2008
49:32
P06 An Overview of Key Ideas
07:44
P07 2. Elimination with Matrices.
47:42
P08 Elimination with Matrices
10:18
P09 3. Multiplication and Inverse Matrices
46:49
P10 Inverse Matrices
08:25
P11 4. Factorization into A = LU
48:05
P12 LU Decomposition
09:35
P13 5. Transposes, Permutations, Spaces R^n
47:42
P14 Subspaces of Three Dimensional Space
14:45
P15 6. Column Space and Nullspace
46:01
P16 Vector Subspaces
08:46
P17 7. Solving Ax = 0 - Pivot Variables, Special Solutions
43:20
P18 Solving Ax=0
10:04
P19 8. Solving Ax = b - Row Reduced Form R
47:20
P20 Solving Ax=b
09:04
P21 9. Independence, Basis, and Dimension
50:14
P22 Basis and Dimension
08:10
P23 10. The Four Fundamental Subspaces
49:20
P24 Computing the Four Fundamental Subspaces
10:45
P25 11. Matrix Spaces Rank 1 Small World Graphs
45:56
P26 Matrix Spaces
08:56
P27 12. Graphs, Networks, Incidence Matrices
47:57
P28 Graphs and Networks
12:31
P29 13. Quiz 1 Review
47:40
P30 Exam #1 Problem Solving
14:53
P31 14. Orthogonal Vectors and Subspaces
49:48
P32 Orthogonal Vectors and Subspaces
10:20
P33 15. Projections onto Subspaces
48:51
P34 Projection into Subspaces
09:51
P35 16. Projection Matrices and Least Squares
48:05
P36 Least Squares Approximation
08:04
P37 17. Orthogonal Matrices and Gram-Schmidt
49:10
P38 Gram-Schmidt Orthogonalization
10:00
P39 18. Properties of Determinants
49:13
P40 Properties of Determinants
09:56
P41 19. Determinant Formulas and Cofactors
53:18
P42 Determinants
12:49
P43 20. Cramers Rule, Inverse Matrix, and Volume
51:01
P44 Determinants and Volume
13:50
P45 21. Eigenvalues and Eigenvectors
51:23
P46 Eigenvalues and Eigenvectors
09:23
P47 22. Diagonalization and Powers of A
51:51
P48 Powers of a Matrix
09:07
P49 23. Differential Equations and exp(At)
51:03
P50 Differential Equations and exp (At)
18:41
P51 24. Markov Matrices Fourier Series
51:12
P52 Markov Matrices
11:49
P53 24b. Quiz 2 Review
48:20
P54 Exam #2 Problem Solving
17:52
P55 25. Symmetric Matrices and Positive Definiteness
43:52
P56 Symmetric Matrices and Positive Definiteness
12:40
P57 26. Complex Matrices Fast Fourier Transform
47:52
P58 Complex Matrices
13:02
P59 27. Positive Definite Matrices and Minima
50:40
P60 Positive Definite Matrices and Minima
12:51
P61 28. Similar Matrices and Jordan Form
45:56
P62 Similar Matrices
08:13
P63 29. Singular Value Decomposition
40:29
P64 Computing the Singular Value Decomposition
11:36
P65 30. Linear Transformations and Their Matrices
49:27
P66 Linear Transformations
10:47
P67 31. Change of Basis Image Compression
50:14
P68 Change of Basis
12:26
P69 33. Left and Right Inverses Pseudoinverse
41:53
P70 Pseudoinverses
14:40
P71 32. Quiz 3 Review
47:06
P72 Exam #3 Problem Solving
12:50
P73 34. Final Course Review
43:26
P74 Final Exam Problem Solving
12:18
【加州大学伯克利分校 • 中英】数理逻辑导论 UCB 125A（Mathematical Logic，2020）
P01 Introduction to Mathematical Logic
13:29
P02 Strings
03:16
P03 The Language Of Sentential Logic
09:58
P04 Truth Assignments
16:52
P05 Tautological Implication
17:07
P06 The completeness of the language for sentential logic
21:41
P07 Generating sets out of functions
24:15
P08 Structural induction and Recursion
16:09
P09 The Language of First Order Logic
20:57
P10 Structures
11:00
P11 Free Variables
14:44
P12 Interpretation of Terms
10:41
P13 Interpretation of Formulas
12:12
P14 Elementary Classes
22:59
P15 Elementary Equivalence
11:34
P16 Logical Implication
09:42
P17 Definable Sets
12:04
P18 Homomorphisms
15:15
P19 Preservation results
22:20
P20 Non-definability results using automorphisms
13:33
P21 Substructures
11:57
P22 Compactness
13:28
P23 An application of compactness
20:42
P24 Proving non-definability via compactness
08:30
P25 Compactness via implication
10:38
P26 Compactness in Sentential Logic
16:20
P27 An application of Compactness for Sentential Logic
20:12
P28 Topological Compactness of [0,1]
13:26
P29 Compactness - from Cantor Set to Sentential Logic
20:52
P30 Application of compactness to graph coloring
29:14
P31 Proving Königs lemma from compactness
23:50
P32 An application to Compactness to Equivalence Relations
16:09
P33 Application of Compactness - fields of characteristic 0 not strongly element
12:28
P34 Syntactical Implication
10:10
P35 Logical Axioms
18:24
P36 Tautologies in First Order Logic
12:10
P37 The Generalization Metatheorem
16:48
P38 More Metatheorems
18:33
P39 Generalization of Constants, change of variables, equality
24:17
P40 The Soundness theorem
09:24
P41 Maximal Consistent sets of sentences
13:33
P42 Gödels Completeness theorem
07:13
P43 The Set Of Closed Terms
30:09
P44 The Term Model
11:39
P45 Term Models for maximal consistent sets of formulas
11:41
P46 Theories that contain term witnesses
15:19
P47 Finishing the proof of completeness
15:25
P48 Summing up
07:22
中英 • 拓扑学与几何学｜Tadashi Tokieda
P01 LECTURE 01 Part 01 02
27:57
P02 LECTURE 01 Part 02 02
20:13
P03 LECTURE 02 Part 01 03
32:34
P04 LECTURE 02 Part 02 03
20:32
P05 LECTURE 02 Part 03 03
20:16
P06 LECTURE 03 Part 01 03
31:52
P07 LECTURE 03 Part 02 03
28:27
P08 LECTURE 03 Part 03 03
14:51
P09 LECTURE 04 Part 01 02
30:57
P10 LECTURE 04 Part 02 02
32:20
P11 LECTURE 05 Part 01 02
36:10
P12 LECTURE 05 Part 02 02
34:27
P13 LECTURE 06 Part 01 02
25:25
P14 LECTURE 06 Part 02 02
41:32
P15 LECTURE 07 Part 01 02
29:50
P16 LECTURE 07 Part 02 02
40:34
P17 LECTURE 08 Part 01 02
32:05
P18 LECTURE 08 Part 02 02
47:35
P19 LECTURE 09 Part 01 03
25:43
P20 LECTURE 09 Part 02 03
21:23
P21 LECTURE 09 Part 03 03
24:50
P22 LECTURE 10 Part 01 02
30:32
P23 LECTURE 10 Part 02 02
32:27
P24 LECTURE 11 Part 01 03
29:30
P25 LECTURE 11 Part 02 03
36:02
P26 LECTURE 11 Part 03 03
35:52
P27 LECTURE 12 Part 01 02
37:42
P28 LECTURE 12 Part 02 02
31:05
P29 LECTURE 13 Part 01 02
34:32
P30 LECTURE 13 Part 02 02
35:51
P31 LECTURE 14 Part 01 02
36:18
P32 LECTURE 14 Part 02 02
25:39
P33 LECTURE 15 Part 01 03
14:00
P34 LECTURE 15 Part 02 03
29:58
P35 LECTURE 15 Part 03 03
08:27
代数拓扑中的微分形式 • 中英｜NCTS｜TMS 2024 Spring｜Loring Tu 杜武亮 (Tufts University)
P01 20240220_1. De Rham Complex on R^n
01:17:02
P02 20240222_2. Compact Supports, Manifolds
01:16:30
P03 20240227_3. Diffeomorphism Invariance, Exact Sequences
01:14:06
P04 20230229_4. Zig-Zag Lemma, Mayer—Vietoris Sequence
01:10:55
P05 20240305_5. Homotopy lnvariance
01:14:20
P06 20240307_6. Proof of Homotopy Axiom
01:19:20
P07 20240312_7. Cohomology with Compact Support of R^n
01:12:23
P08 20230314_8. Mayer—Vietoris with Compact Support v4
01:22:37
P09 20240319_9. Möbius Strip, Finite Dimensionality, Pairings
01:13:05
P10 20240321_10. Poincaré Duality
01:12:16
P11 20240326_11. Künneth Formula, Leray—Hirsch Theorem
01:12:44
P12 20240328_12. Cohomology with Compact Vertical Support
01:17:51
P13 20240402_13. The Thom Isomorphism
01:22:00
P14 20240409_14. The Generalized Mayer—Vietoris Sequence
01:35:14
P14 20240418_17. (TBA)
01:15:29
P15 20240411_15. The Cech—de Rham Isomorphism
01:13:57
P16 20240416_16. Product Structures, Presheaves
01:19:43
P18 20240423_18. Cech Cohomology of a Topological Space
01:15:41
P19 20240425_19. Cohomology of a Double Complex
01:20:37
P20 20240430_20. Thom Isomorphism Revisited
01:20:00
P21 20240502_21. Spectral Sequence of a Filtered Complex
01:14:36
P22 20240507_22. Filtrations of Finite Length
01:09:01
P23 20240509_23. Filtrations of Infinite Length, Double Complexes
01:17:42
P24 20240514_24. Spectral Sequence of a Double Complex
01:11:42
P25 20240516_25. Applications of Spectral Sequences
01:02:17
P26 20240521_26. The Leray Spectral Sequence of a Map
01:18:50
P27 20240523_27. U(2), Lerays Method
01:15:20
P28 20240528_28. Monodromy
01:20:30
P29 20240530_29. TMS - Differential Forms in Algebraic Topology
02:06:12
【麻省理工 • 中英】实分析 MIT 18.100A（Real Analysis，Fall 2020 | Undergraduate, Graduate）
P01 Sets, Set Operations and Mathematical Induction
01:14:22
P02 Cantors Theory of Cardinality (Size)
01:25:07
P03 Cantors Remarkable Theorem and the Rationals Lack of the Least Upper Bound P
01:18:40
P04 The Characterization of the Real Numbers
01:22:04
P05 The Archimedian Property, Density of the Rationals, and Absolute Value
01:18:13
P06 The Uncountabality of the Real Numbers
01:21:41
P07 Convergent Sequences of Real Numbers
01:00:39
P08 The Squeeze Theorem and Operations Involving Convergent Sequences
01:14:53
P09 Limsup, Liminf, and the Bolzano-Weierstrass Theorem
01:13:43
P10 The Completeness of the Real Numbers and Basic Properties of Infinite Series
01:15:37
P11 Absolute Convergence and the Comparison Test for Series
01:00:03
P12 The Ratio, Root, and Alternating Series Tests
01:00:21
P13 Limits of Functions
01:12:54
P14 Limits of Functions in Terms of Sequences and Continuity
01:01:14
P15 The Continuity of Sine and Cosine and the Many Discontinuities of Dirichlets
01:01:59
P16 The Min Max Theorem and Bolzanos Intermediate Value Theorem
01:08:25
P17 Uniform Continuity and the Definition of the Derivative
01:12:55
P18 Weierstrasss Example of a Continuous and Nowhere Differentiable Function
01:15:36
P19 Differentiation Rules, Rolles Theorem, and the Mean Value Theorem
01:14:27
P20 Taylors Theorem and the Definition of Riemann Sums
52:33
P21 The Riemann Integral of a Continuous Function
01:06:35
P22 Fundamental Theorem of Calculus, Integration by Parts, and Change of Variabl
01:12:13
P23 Pointwise and Uniform Convergence of Sequences of Functions
01:09:17
P24 Uniform Convergence, the Weierstrass M-Test, and Interchanging Limits
01:15:10
P25 Power Series and the Weierstrass Approximation Theorem
01:16:07
【麻省理工 • 中英】数据分析、信号处理和机器学习中的矩阵方法 MIT 18.065 | Spring 2018
P01 Course Introduction of 18.065 by Professor Strang
07:04
P02 An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis
08:07
P03 Lecture 1 - The Column Space of A Contains All Vectors Ax
52:15
P04 Lecture 2 - Multiplying and Factoring Matrices
48:26
P05 3. Orthonormal Columns in Q Give QQ = I
49:24
P06 4. Eigenvalues and Eigenvectors
48:56
P07 5. Positive Definite and Semidefinite Matrices
45:28
P08 6. Singular Value Decomposition (SVD)
53:34
P09 7. Eckart-Young - The Closest Rank k Matrix to A
47:16
P10 Lecture 8 - Norms of Vectors and Matrices
49:21
P11 9. Four Ways to Solve Least Squares Problems
49:51
P12 Lecture 10 - Survey of Difficulties with Ax = b
49:36
P13 Lecture 11 - Minimizing ‖x‖ Subject to Ax = b
50:22
P14 12. Computing Eigenvalues and Singular Values
49:28
P15 Lecture 13 - Randomized Matrix Multiplication
52:24
P16 14. Low Rank Changes in A and Its Inverse
50:34
P17 15. Matrices A(t) Depending on t, Derivative = dA dt
50:52
P18 16. Derivatives of Inverse and Singular Values
43:08
P19 Lecture 17 - Rapidly Decreasing Singular Values
50:34
P20 Lecture 18 - Counting Parameters in SVD, LU, QR, Saddle Points
49:00
P21 19. Saddle Points Continued, Maxmin Principle
52:13
P22 20. Definitions and Inequalities
55:01
P23 Lecture 21 - Minimizing a Function Step by Step
53:45
P24 22. Gradient Descent - Downhill to a Minimum
52:44
P25 23. Accelerating Gradient Descent (Use Momentum)
49:02
P26 24. Linear Programming and Two-Person Games
53:34
P27 25. Stochastic Gradient Descent
53:03
P28 26. Structure of Neural Nets for Deep Learning
53:17
P29 27. Backpropagation - Find Partial Derivatives
52:38
P30 Lecture 30 - Completing a Rank-One Matrix, Circulants!
49:53
P31 31. Eigenvectors of Circulant Matrices - Fourier Matrix
52:37
P32 Lecture 32 - ImageNet is a Convolutional Neural Network (CNN), The Convoluti
47:19
P33 33. Neural Nets and the Learning Function
56:07
P34 34. Distance Matrices, Procrustes Problem
29:17
P35 35. Finding Clusters in Graphs
34:49
P36 Lecture 36 - Alan Edelman and Julia Language
38:11
【麻省理工 • 中英】泛函分析导论 MIT 18.102（Introduction to Functional Analysis, Spring 2021）
P01 Basic Banach Space Theory
01:15:19
P02 Bounded Linear Operators
01:24:11
P03 Quotient Spaces, the Baire Category Theorem and the Uniform Boundedness Theo
01:04:03
P04 The Open Mapping Theorem and the Closed Graph Theorem
01:14:58
P05 Zorn’s Lemma and the Hahn-Banach Theorem
01:10:24
P06 The Double Dual and the Outer Measure of a Subset of Real Numbers
01:20:58
P07 Sigma Algebras
01:20:24
P08 Lebesgue Measurable Subsets and Measure
01:14:02
P09 Lebesgue Measurable Functions
01:24:57
P10 Simple Functions
01:22:55
P11 The Lebesgue Integral of a Nonnegative Function and Convergence Theorems
01:21:39
P12 Lebesgue Integrable Functions, the Lebesgue Integral and the Dominated Conve
01:24:57
P13 Lp Space Theory
01:23:59
P14 Basic Hilbert Space Theory
01:23:24
P15 Orthonormal Bases and Fourier Series
01:16:02
P16 Fejer’s Theorem and Convergence of Fourier Series
01:21:23
P17 Minimizers, Orthogonal Complements and the Riesz Representation Theorem
01:16:04
P18 The Adjoint of a Bounded Linear Operator on a Hilbert Space
01:12:18
P19 Compact Subsets of a Hilbert Space and Finite-Rank Operators
01:23:23
P20 Compact Operators and the Spectrum of a Bounded Linear Operator on a Hilbert
01:22:25
P21 The Spectrum of Self-Adjoint Operators and the Eigenspaces of Compact Self-A
01:10:51
P22 The Spectral Theorem for a Compact Self-Adjoint Operator
01:24:07
P23 The Dirichlet Problem on an Interval
01:23:54
【斯坦福】EE364A 凸优化（ Convex Optimization，2023）
P01 Lecture 1
01:18:27
P02 Lecture 2
01:20:23
P03 Lecture 3
01:20:28
P04 Lecture 4
01:20:14
P05 Lecture 5
01:20:24
P06 Lecture 6
01:17:50
P07 Lecture 7
01:20:39
P08 Lecture 8
01:20:46
P09 Lecture 9
01:20:05
P10 Lecture 10
01:20:04
P11 Lecture 11
01:19:35
P12 Lecture 12
01:18:56
P13 Lecture 13
01:18:20
P14 Lecture 14
01:17:50
P15 Lecture 15
01:17:08
P16 Lecture 16
01:21:58
P17 Lecture 17
01:17:05
P18 Lecture 18
01:13:44
【麻省理工】MIT18.226组合数学中的概率方法
Large Bipartite Subgraph
06:44
Lower Bounds to Ramsey Numbers
43:08
Extremal Set Theory: Sperner's Theorem
12:49
Extremal Set Theory: Intersecting Families
17:20
Linearity of Expectations
12:55
Independent Sets and Turán's Theorem
14:52
Crossing Number Inequality
18:26
Markov, Chebyshev, and Chernoff
16:30
Bounded Differences Inequality (aka Azuma-Hoeffding Inequality)
19:47
Threshold for a Random Graph to Contain a Triangle
28:52
Existence of Graphs with High Girth and High Chromatic Number
25:19
【伯克利 • 中英】数论导论 Berkeley 115（Introduction to number theory）
P01 lecture 1.
44:04
P02 lecture 2 - Survey.
32:03
P03 lecture 3 - Divisibility and Euclids algorithms.
42:32
P04 lecture 4. More on Euclids algorithm
28:57
P05 lecture 5. Primes.
44:51
P06 lecture 6. Multiplicative functions.
32:17
P07 lecture 7. Binomial coefficients.
41:00
P08 lecture 8. Applications of binomial coefficients
43:26
P09 lecture 9 - Congruences
40:57
P10 lecture 10. Fermats theorem
28:11
P11 lecture 11. Eulers theorem
35:20
P12 lecture 12 Wilsons theorem
29:55
P13 lecture 13. The Chinese remainder theorem.
34:47
P14 lecture 14. Eulers totient function
48:51
P15 lecture 15. Numerical calculation
40:25
P16 lecture 16. More numerical calculation
25:37
P17 lecture 17. Factorization.
22:37
P18 lecture 18. Cryptography
37:21
P19 lecture 19. Hensel and Newtons method
31:29
P20 lecture 20. p-adic numbers.
28:10
P21 lecture 21. Congruences modulo a prime.
38:18
P22 lecture 22. Chevalley-Warning theorem
16:02
P23 lecture 23. Primitive roots.
35:01
P24 lecture 24. Primitive roots for prime powers
20:19
P25 lecture 25. Quadratic equations mod p.
21:41
P26 lecture 26. Roots of polynomials modulo a prime.
17:00
P27 lecture 27. Groups and number theory
29:34
P28 lecture 28. Products of groups
23:23
P29 lecture 29. Rings in number theory
38:15
P30 lecture 30. Fields in number theory
24:50
P31 lecture 31. Quadratic residues.
32:26
P32 lecture 32. Calculation of the Legendre symbol
28:02
P33 lecture 33. Quadratic reciprocity
32:47
P34 lecture 34. Gauss sums
17:48
P35 lecture 35 Jacobi symbol
38:05
P36 lecture 36 Kronecker symbol
21:02
P37 lecture 37 Continued fractions
26:22
P38 lecture 38. Binary quadratic forms
23:42
P39 lecture 39 - Equivalence of binary quadratic forms
22:54
P40 lecture 40. Examples of positive definite forms
28:08
P41 lecture 41 - More examples of binary quadratic forms
29:57
P42 lecture 42. Examples of indefinite binary quadratic forms.
22:29
P43 lecture 43 Gaussian integers
35:59
P44 lecture 44 Pythagorean triangles
23:08
P45 lecture 45 Dirichlet series
31:04
P46 lecture 46. Products of Dirichlet series
17:45
P47 lecture 47. The prime number theorem
27:16
P48 lecture 48 Proof of the prime number theorem
17:40
P49 lecture 49. Dirichlets theorem
35:45
P50 lecture 50. Dirichlet characters
20:50
P51 lecture 51. Proof of Dirichlets theorem
24:31
P52 lecture 52. Nonvanishing of L series at s=1.
24:14
P53 lecture 53. Three calculators for number theorists
12:34
形式逻辑导论
P01 1.1 Basic Concepts - Arguments, Premises, & Conclusions
35:33
P02 1.2 Recognizing Arguments
26:03
P03 1.3 Deduction & Induction
36:08
P04 1.4 Validity, Truth, Soundness, Strength, Cogency
34:27
P05 1.5 Argument Forms - Proving Invalidity
26:45
P06 2.1 Varieties of Meaning
25:13
P07 2.2 The Intension and Extension of Terms
31:36
P08 3A Fallacies in General, Revelavnce, & Weak Induction
51:20
P09 3B Fallacies of Presumptionm, Ambiguity, and Transference
46:45
P10 4.1 The Components of Categorical Propositions
20:00
P11 4.2 Quantity, Quality, & Distribution
20:11
P12 4.3 Venn Diagrams & The Modern Square of Opposition
40:20
P13 4.4 Conversion, Obversion, and Contraposition
29:57
P14 4.5 The Traditional Square of Opposition
28:53
P15 4.6 Venn Diagrams and the Traditional Standpoint
22:16
P16 5.1 Standard Form, Mood, and Figure
29:45
P17 5.2 Venn Diagrams
48:08
P18 5.3 Rules and Fallacies
30:06
P19 5.6 Enthymemes
17:57
P20 5.7 Sorites
32:22
P21 6.1 Symbols & Translation
49:04
P22 6.2 Truth Functions
57:50
P23 6.3 Truth Tables for Propositions
51:45
P24 6.4 Truth Tables for Arguments
39:26
P25 6.5 Indirect Truth Tables
34:10
P26 7.1 Rules of Implication I
53:05
P27 7.2 Rules of Implication II
43:07
P28 7.3 Rules of Replacement I
52:50
P29 7.4 Rules of Replacement II
32:06
P30 7.5 Conditional Proof
25:00
P31 7.6 Indirect Proof
24:05
P32 8.1 Predicate Logic - Symbols & Translation
57:48
P33 8.2 Predicate Logic - Using the Rules of Inference
50:51
P34 8.3 Change of Quantifier Rule
33:01
P35 8.4 Predicate Logic - Condition & Indirect Proof
42:33
P36 8.5 Predciate Logic - Finite Universe Method
01:08:53
P37 Appendix 1. Philosophical Logic
01:17:05
P38 Appendix 2 - Diagramming Arguments
20:54
P39 The Banach–Tarski Paradox
24:14
P40 1. Frege - Thought, Sense, & Reference
01:22:46
【麻省理工】离散随机过程 MIT 6.262（Discrete Stochastic Processes，2011）
P01 1. Introduction and Probability Review
01:16:27
P02 2. More Review The Bernoulli Process
01:08:20
P03 3. Law of Large Numbers, Convergence
01:21:28
P04 4. Poisson (the Perfect Arrival Process)
01:17:14
P05 5. Poisson Combining and Splitting
01:24:32
P06 6. From Poisson to Markov
01:19:17
P07 7. Finite-state Markov Chains The Matrix Approach
55:34
P08 8. Markov Eigenvalues and Eigenvectors
01:23:38
P09 9. Markov Rewards and Dynamic Programming
01:23:36
P10 10. Renewals and the Strong Law of Large Numbers
01:21:53
P11 11. Renewals - Strong Law and Rewards
01:18:17
P12 12. Renewal Rewards, Stopping Trials, and Walds Inequality
01:26:22
P13 13. Little, M G 1, Ensemble Averages
01:14:53
P14 14. Review
01:19:19
P15 15. The Last Renewal
01:15:44
P16 16. Renewals and Countable-state Markov
01:19:40
P17 17. Countable-state Markov Chains
01:23:46
P18 18. Countable-state Markov Chains and Processes
01:16:29
P19 19. Countable-state Markov Processes
01:22:14
P20 20. Markov Processes and Random Walks
01:23:09
P21 21. Hypothesis Testing and Random Walks
01:25:23
P22 22. Random Walks and Thresholds
01:21:17
P23 23. Martingales (Plain, Sub, and Super)
01:22:40
P24 24. Martingales - Stopping and Converging
01:20:44
P25 25. Putting It All Together
01:21:27
【斯坦福】 应用线性代数导论 ENGR108（Introduction to Applied Linear Algebra，2020）
P01 Lecture 1 - Introduction
10:26
P02 Lecture 2 - vector notation
20:00
P03 Lecture 3 - vector examples
18:24
P04 Lecture 4-addition & scalar mult.
27:52
P05 Lecture 5 - VMLS inner product
14:05
P06 Lecture 6 - VMLS complexity
06:16
P07 Lecture 7 - VMLS linear functions
13:59
P08 Lecture 8-VMLS taylor approx & reg
20:49
P09 Lecture 9 - VMLS norm
15:05
P10 Lecture 10 - VMLS distance
14:15
P11 Lecture 11-VMLS std. deviation
16:15
P12 Lecture 12 - VMLS angle
23:39
P13 Lecture 13 - VMLS k means
31:38
P14 Lecture 14-VMLS k means app.
19:10
P15 Lecture 15-VMLS linear ind.
25:09
P16 Lecture 16-VMLS Gram Schmidt algo.
15:24
P17 Lecture 17 - VMLS matrix notation
42:25
P18 Lecture 18-VMLS matrix vector mult
08:10
P19 Lecture 19-VMLS matrix vector ex.
28:10
P20 Lecture 20-VMLS selector matrices
06:04
P21 Lecture 21 - VMLS incidence matrix
15:42
P22 Lecture 22 - VMLS convolution
16:10
P23 Lecture 23-VMLS vector linear func
15:59
P24 Lecture 24-VMLS linear func models
17:26
P25 Lecture 25 - VMLS linear equations
22:43
P26 Lecture 26-VMLS linear dynamic sys
39:25
P27 Lecture 27-VMLS matrix mult
25:25
P28 Lecture 28-VMLS matrix mult ex
08:18
P29 Lecture 29-VMLS mtrx pwrs & QR fac
16:01
P30 Lecture 30-VMLS left & right inv.
35:22
P31 Lecture 31-VMLS solving linear eqs
20:02
P32 Lecture 32 - VMLS pseudo inverse
14:26
P33 Lecture 33 - VMLS least squares
28:07
P34 Lecture 34-VMLS least squares ex.
22:25
P35 Lecture 35-VMLS LS data fitting
15:11
P36 Lecture 36-VMLS fit univariate fnc
38:02
P37 Lecture 37 - VMLS validation
30:38
P38 Lecture 38 - VMLS classification
19:01
P39 Lecture 39-VMLS LS classification
16:46
P40 Lecture 40-VMLS multiclass classif
19:41
P41 Lecture 41-VMLS multi objective LS
21:25
P42 Lecture 42-ctrl via multi obj LS
12:05
P43 Lecture 43-MLS est & inversion
23:51
P44 Lecture 44-VMLS reg data fitting
14:15
P45 Lecture 45-VMLS constrained LS
22:03
P46 Lecture 46-VMLS solve cstr LS prob
16:44
P47 Lecture 47-VMLS portfolio optim
49:48
P48 Lecture 48-VMLS linear quadrt ctrl
23:55
P49 Lecture 49-VMLS lin quadrt st est
15:45
P50 Lecture 50-VMLS nonlinear eq. & LS
20:01
P51 Lecture 51-VMLS Leven. Marq. algo
20:02
P52 Lecture 52-VMLS nonlin mdl fitting
15:57
P53 Lecture 53-VMLS cstrd nonlinear LS
17:13
P54 Lecture 54-VMLS aug Lagragian mthd
21:43
代数几何（伯克利数学 256A 2020年秋季）| Richard E Borcherds
P01 Algebraic geometry 1 Introduction
20:58
P02 Algebraic geometry 2 Two cubic curves.
21:58
P03 algebraic geometry 3 Bezout, Pappus, Pascal
21:03
P04 algebraic geometry 4 Kakeya sets
18:02
P05 algebraic geometry 5 Affine space and the Zariski topology
23:45
P06 algebraic geometry 6 Noetherian spaces
22:20
P07 algebraic geometry 7 weak nullstellensatz
19:37
P08 algebraic geometry 8 strong nullstellensatz
23:16
P09 algebraic geometry 9 The Lasker Noether theorem
13:52
P10 algebraic geometry 10 Proof of the Lasker Noether theorem
11:29
P11 algebraic geometry 11 Quotients of varieties by groups
15:26
P12 algebraic geometry 12 Hilberts finiteness theorem
23:55
P13 algebraic geometry 13 Three examples of quotients
20:27
P14 algebraic geometry 14 Dimension
23:51
P15 algebraic geometry 15 Projective space
20:11
P16 algebraic geometry 16 Desarguess theorem
14:11
P17 algebraic geometry 17 Affine and projective varieties
31:35
P18 algebraic geometry 18 Products of varieties
18:36
P19 algebraic geometry 19 The Veronese surface and the variety of lines in space
24:36
P20 algebraic geometry 20 Grassmannians
23:50
P21 algebraic geometry 21 Projective space bundles
21:02
P22 algebraic geometry 22 Toric varieties
24:37
P23 algebraic geometry 23 Categories
15:13
P24 algebraic geometry 24 Regular functions
24:13
P25 algebraic geometry 25 Morphisms of varieties
18:33
P26 algebraic geometry 26 Affine algebraic sets and commutative rings
24:35
P27 algebraic geometry 27 The twisted cubic
15:31
P28 algebraic geometry 28 Products of projective varieties
11:54
P29 algebraic geometry 29 Automorphisms of space
17:07
P30 algebraic geometry 30 The Ax Grothendieck theorem
20:38
P31 algebraic geometry 31 Rational maps
21:38
P32 algebraic geometry 32 Elliptic functions and cubic curves
19:44
P33 algebraic geometry 33 Rationality of cubic surfaces
23:16
P34 algebraic geometry 34 Blowing up a point
23:09
P35 algebraic geometry 35 More on blow ups
22:35
P36 algebraic geometry 36 The Atiyah flop
12:07
P37 Algebraic geometry 37 - Singular points (replacement video))
20:34
P38 Algebraic geometry 38 - The Zariski tangent space (replacement)
22:25
P39 algebraic geometry 39 Du Val singularities
19:26
P40 algebraic geometry 40 Examples of resolutions
22:01
P41 Algebraic geometry 41 - Completions
19:40
P42 Algebraic geometry 42 - Resultants
14:47
P43 Algebraic geometry 43 - Proper maps
25:59
P44 Algebraic geometry 44 - Survey of curves
25:42
P45 Algebraic geometry 45 - Hurwitz curves
17:17
P46 Algebraic geometry 46 - Examples of Hurwitz curves
13:44
P47 Algebraic geometry 47 - Resolution of curve singularities
21:36
P48 Algebraic geometry 48 - Newtons rotating ruler
23:35
P49 Algebraic geometry 49 - Hilbert polynomials
15:23
P50 Algebraic geometry 50 - The degree of a projective variety
19:39
P51 Algebraic geometry 51 - Bezouts theorem
34:10
高级复分析 Math 246C | 陶哲轩 | Terry Tao
P01 246C lec 1
49:34
P02 246C lec 2
49:36
P03 246C lec 3
52:56
P04 246C lec 4
01:01:10
P05 246C lec 5
51:34
P06 246C lec 6
54:04
P07 246C lec 7
56:02
P08 246C lec 9
53:00
P09 246C lec 10
50:18
P10 246C lec 11
54:16
P11 246C lec 12
55:04
P12 246C lec 13
47:58
P13 246C lec 14
53:52
P14 246C lec 15
51:44
P15 246C lec 16
54:16
P16 246C lec 17
53:48
P17 246C lec 18
50:14
P18 246C lec 19
52:05
P19 246C lec 20
52:55
P20 246C lec 21
55:41
P21 246C lec 22
52:01
P22 246C lec 23
48:16
P23 246C lec 24
56:53
P24 246C lec 25
53:47
P25 246C lec 26
52:20
P26 246C lec 27
58:01
P27 246C lec 28
51:53
P28 246C lec 29
57:40
【加州大学伯克利分校 - 中英】 数值分析 MATH 128A（Numerical Analysis，Fall 2020）
P01 128A_Sec1.1_Part1-Limits
11:33
P02 128A_Sec1.1_Part2-Derivatives
10:34
P03 128A_Sec1.1_Part3-Integrals
13:29
P04 128A_Sec1.1_Part4-Taylor_Polynomials
14:24
P05 128A_Sec1.2_Part1-Floating_Point_Numbers
16:31
P06 128A_Sec1.2_Part2-Binary_Numbers
07:17
P07 128A_Sec1.2_Part3-Double_Precision_1
15:30
P08 128A_Sec1.2_Part4-Double_Precision_2
11:45
P09 128A_Sec1.2_Part5-Roundoff_Errors
17:05
P10 128A_Sec1.3_Part1-Error_Growth
08:59
P11 128A_Sec1.3_Part2-Rate_of_Convergence
10:29
P12 128A_Sec2.1_Part1-Bisection_Method
09:01
P13 128A_Sec2.1_Part2-MATLAB_Demo
09:28
P14 128A_Sec2.1_Part3-Convergence
08:55
P15 128A_Sec2.2_Part1-Fixed_Points
10:43
P16 128A_Sec2.2_Part2-Existence_Uniqueness_Proof
11:07
P17 128A_Sec2.2_Part3-Fixed_Point_Iteration
10:17
P18 128A_Sec2.2_Part4-Fixed_Point_Theorem
08:50
P19 128A_Sec2.2_Part5-Examples
08:24
P20 128A_Sec2.3_Part1-Newton_Graphically
10:02
P21 128A_Sec2.3_Part2-Newton_Taylor_and_MATLAB_Demo
12:18
P22 128A_Sec2.3_Part3-Convergence_Proof
15:41
P23 128A_Sec2.3_Part4-Secant_Method
05:32
P24 128A_Sec2.4_Part1-Order_of_Convergence
09:11
P25 128A_Sec2.4_Part2-Convergence_Proofs
10:15
P26 128A_Sec2.4_Part3-Newton_as_Fixed_Point
04:30
P27 128A_Sec2.4_Part4-Modified_Newton
11:00
P28 128A_Sec2.5_Part1-Aitken_Steffensen
11:22
P29 128A_Sec2.6_Part1_Polynomials
07:53
P30 128A_Sec2.6_Part2_Horners_Method
11:51
P31 128A_Sec2.6_Part3_Deflation
08:08
P32 128A_Sec2.6_Part4_Mullers_Method
09:33
P33 128A_Sec3.1_Part1-Lagrange_Polynomials_1
13:52
P34 128A_Sec3.1_Part2-Lagrange_Polynomials_2
12:13
P35 128A_Sec3.1_Part3-Error_Bound
13:14
P36 128A_Sec3.3_Part1-Divided_Differences
11:44
P37 128A_Sec3.3_Part2-Example
09:12
P38 128A_Sec3.3_Part3-Derivatives
10:00
P39 128A_Sec3.3_Part4-Equal_Spacing
10:00
P40 128A_Sec3.3_Part5-Forward_Differences_Example
07:12
P41 128A_Sec3.4_Part1-Osculating_Polynomials
10:27
P42 128A_Sec3.4_Part2-Hermite_Polynomials
07:29
P43 128A_Sec3.4_Part3-Hermite_Proof
06:45
P44 128A_Sec3.4_Part4-Divided_Differences_Examples
12:44
P45 128A_Sec3.5_Part1-Spline_Interpolation_Motivation
14:14
P46 128A_Sec3.5_Part2-Cubic_Spline_Definition
14:34
P47 128A_Sec3.5_Part3-Spline_Example
14:55
P48 128A_Sec3.5_Part4-MATLAB_Demo
13:07
P49 128A_Sec4.1_Part1-Forward_Backward_Differences
13:11
P50 128A_Sec4.1_Part2-Three_Point_Formulas
18:58
P51 128A_Sec4.1_Part3-Second_Derivatives
08:27
P52 128A_Sec4.1_Part4-Optimal_h
06:14
P53 128A_Sec4.2_Part1-Richardsons_Extrapolation
08:04
P54 128A_Sec4.2_Part2-MATLAB_Demo
06:15
P55 128A_Sec4.3_Part1-Numerical_Integration
07:21
P56 128A_Sec4.3_Part2-Trapezoidal_Rule
09:31
P57 128A_Sec4.3_Part3-Simpsons_Rule
09:45
P58 128A_Sec4.4_Part1-Composite_Trapezoidal_Rule
12:10
P59 128A_Sec4.4_Part2-Composite_Simpsons_Rule
06:10
P60 128A_Sec4.4_Part3-Error_Term
09:42
P61 128A_Sec4.4_Part4-Numerical_Example
09:50
P62 128A_Sec4.5_Part1_Romberg_Integration
08:54
P63 128A_Sec4.5_Part2_MATLAB_Demo
09:42
P64 128A_Sec4.6_Part1-Adaptive_Quadrature
07:02
P65 128A_Sec4.6_Part2-Error_Estimation
13:12
P66 128A_Sec4.7_Part1-Gaussian_Quadrature
08:24
P67 128A_Sec4.7_Part2-Two_Point_Rule
06:02
P68 128A_Sec4.7_Part3-Legendre_Polynomials
06:31
P69 128A_Sec4.7_Part4-Proof_Gaussian_Quadrature
12:29
P70 128A_Sec4.7_Part5-Arbitrary_Intervals
13:18
P71 128A_Sec4.8_Part1-Double_Integrals
13:59
P72 128A_Sec4.8_Part2-Example
13:28
P73 128A_Sec4.8_Part3-Non_Rectangular_and_MATLAB
10:06
P74 128A_Sec4.9_Part1-Improper_Integrals
17:41
P75 128A_Sec4.9_Part2-Infinite_Limits_Example
04:40
P76 128A_Sec5.1_Part1-Initial_Value_Problems
14:34
P77 128A_Sec5.1_Part2-Lipschitz_Continuity
12:24
P78 128A_Sec5.1_Part3-Examples
14:20
P79 128A_Sec5.1_Part4-Well_Posedness
06:31
P80 128A_Sec5.2_Part1_Eulers_Method
09:27
P81 128A_Sec5.2_Part2_Error_Bound_Proof_1
08:24
P82 128A_Sec5.2_Part3_Error_Bound_Proof_2
09:15
P83 128A_Sec5.2_Part3_MATLAB_Demo
07:54
P84 128A_Sec5.3_Part1_Taylor_Methods
14:52
P85 128A_Sec5.3_Part2_MATLAB_Demo
09:24
P86 128A_Sec5.4_Part1_Midpoint_Method
12:44
P87 128A_Sec5.4_Part2_MATLAB_Demo
10:08
P88 128A_Sec5.4_Part3_Graphical_Interpretation
10:22
P89 128A_Sec5.4_Part4_Higher-Order_Runge-Kutta_Methods
09:47
P90 128A_Sec5.6_Part1_Multistep_Methods
12:03
P91 128A_Sec5.6_Part2_Adams_Bashforth
11:21
P92 128A_Sec5.6_Part3_Adams_Moulton
06:48
P93 128A_Sec5.9_Part1_Systems_of_Equations
12:49
P94 128A_Sec5.9_Part2_Higher_Order_Equations
12:00
P95 128A_Sec5.10_Part1_One_Step_Method_Convergence
14:30
P96 128A_Sec5.10_Part2_Unstable_Multistep_Method
11:59
P97 128A_Sec5.10_Part3_Root_Condition
07:37
P98 128A_Sec5.11_Part1_Stiff_Differential_Equations
09:21
P99 128A_Sec5.11_Part2_Stability_Regions
10:46
P100 128A_Sec6.1_Part1_Gaussian_Elimination
10:54
【卡耐基梅隆 - 中英】凸优化 CMU 10-725（2018年秋季）
P01 Lecture 01 Optimization in Machine Learning and Statistics
01:16:57
P02 Lecture 02 Convexity I - Sets and Functions
01:16:35
P03 Lecture 03 Convexity II - Optimization Basics
01:20:28
P04 Lecture 04 Canonical problem forms
01:10:25
P05 Lecture 05 Gradient descent
01:20:54
P06 Lecture 06 Subgradients
01:13:55
P07 Lecture 07 Subgradient method
01:15:10
P08 Lecture 08 Proximal gradient descent
01:16:32
P09 Lecture 09 Stochastic gradient descent
01:22:42
P10 Lecture 10 Duality in linear programs
01:14:01
P11 Lecture 11 Duality in general programs
01:15:00
P12 Lecture 12 KKT conditions
01:19:07
P13 Lecture 13 Duality uses and correspondences
01:17:33
P14 Lecture 14 Newtons method
01:18:38
P15 Lecture 15 Barrier method
01:09:33
P16 Lecture 16 Primal-dual interior-point methods
01:15:55
P17 Lecture 17 Quasi-Newton methods
01:20:05
P18 Lecture 18 Proximal Newton method
01:14:57
P19 Lecture 19 Numerical linear algebra
01:17:51
P20 Lecture 20 Coordinate descent
01:15:16
P21 Lecture 21 Dual ascent
01:14:51
P22 Lecture 22 Alternating direction method of multipliers
01:13:29
P23 Lecture 23 Frank-Wolfe method
01:17:15
P24 Lecture 24 Modern stochastic methods
01:16:45
P25 Lecture 25 Mirror descent
01:14:13
P26 Lecture 26 Semester Review
01:14:53
【麻省理工 - 中英】 形状分析 MIT 6.838 (Shape Analysis, Spring 2021)
P01 (Lecture 1) - Introduction
01:01:40
P02 (Lecture 2) - Linear and variational problems
01:27:50
P03 (Lecture 2, extra content) - Gentler variational (Gateaux) derivatives, cubi
45:16
P04 (Lecture 3) - Differential geometry of smooth curves
01:26:08
P05 (Lecture 3, extra content) - First variation of arc length in R^n
18:17
P06 (Lecture 4) - Discrete differential geometry of polyline curves
54:45
P07 (Lecture 5) - Defining surfaces and (sub)manifolds mesh data structures
01:35:07
P08 (Lecture 6) - Second fundamental form and surface curvature
01:11:15
P09 (Lecture 6, extra content) - First variation of surface area, mean curvature
46:33
P10 (Lecture 7) - Approximating Gaussian mean principal curvatures on triangle m
01:31:42
P11 (Lecture 8) - Geodesic distances
01:16:12
P12 (Lecture 9) - Geodesic distance algorithms, fast marching
01:25:47
P13 (Lecture 10) - Metric spaces and embeddings
43:30
P14 (Lecture 10, part 2) - Algorithms for embedding into Euclidean space
01:18:31
P15 (Lecture 11) - Structure-preserving embedding (ISOMAP, LLE) manifold learnin
01:20:08
P16 (Lectures 12-13) - The Laplacian operator on intervals, regions, graphs, and
02:29:36
P17 (Lectures 13, extra content) - Divergence of tangent vector fields
45:54
P18 (Lectures 14) - Laplacian operators via first-order Galerkin finite elements
01:15:03
P19 (Lectures 14, extra content) - A simple Laplacian on point clouds
23:20
P20 (Lecture 15) - Applications of the Laplacian in graphics, vision, and learni
01:25:56
P21 (Lecture 16) - Vector fields, Lie covariant derivatives, frame fields
01:36:17
P22 (Lectures 16, extra content) - Frame (octahedral odeco) fields in volumes
16:30
P23 (Lecture 17) - Vector fields on triangle meshes
54:46
P24 (Lectures 17, extra content) - Continuous normalizing flows
45:18
P25 (Lecture 18) - Optimization on manifolds retractions
01:25:49
P26 (Lectures 18, extra content) - Manifold optimization for PCA problems
30:18
P27 (Lecture 19) - Optimal transport
01:24:41
P28 (Lecture 20) - Segmentation and clustering (k-means, Frechet means, normaliz
01:30:28
P29 (Lecture 21) - Surface correspondence algorithms
01:44:15
P30 (Lectures 21, extra content) - Reversible harmonic maps between discrete sur
30:53
P31 (Lecture 22) - Consistent correspondence and cycle consistency
01:56:57
P32 (Lectures 22, extra content) - Angular synchronization w eigenvectors SDP,
58:58
【佩珀代因大学 - 中英】离散结构 Discrete Structures
P01 Math 221 Lecture 1
40:50
P02 Math 221 Lecture 2
43:31
P03 Math 221 Lecture 3
50:01
P04 Math 221 Lecture 4
49:52
P05 Math 221 Lecture 5
46:42
P06 Math 221 Lecture 6
51:17
P07 Math 221 Lecture 7
47:24
P08 Math 221 Lecture 8
49:25
P09 Math 221 Lecture 9
40:50
P10 Math 221 Lecture 10
51:37
P11 Math 221 Lecture 11
42:33
P12 Math 221 Lecture 12
42:28
P13 Math 221 Lecture 13
40:45
P14 Math 221 Lecture 14
36:10
P15 Math 221 Lecture 15
53:23
P16 Math 221 Lecture 16
21:52
P17 Math 221 Lecture 17
47:00
P18 Math 221 Lecture 18
44:16
P19 Math 221 Lecture 19
50:52
P20 Math 221 Lecture 20
48:34
P21 Math 221 Lecture 21
47:01
P22 Math 221 Lecture 22
48:38
P23 Math 221 Lecture 23
40:06
P24 Math 221 Lecture 24
38:06
P25 Math 221 Lecture 25
37:05
P26 Math 221 Lecture 26
42:33
P27 Math 221 Lecture 27
45:35
P28 Math 221 Lecture 28
46:24
P29 Math 221 Lecture 29
46:55
P30 Math 221 Lecture 30
48:57
P31 Math 221 Lecture 31
43:09
P32 Math 221 Lecture 32
41:36
P33 Math 221 Lecture 33
36:11
P34 Math 221 Lecture 34
42:35
P35 Math 221 Lecture 35
42:11
P36 Math 221 Lecture 36
44:42
P37 Math 221 Lecture 37
01:00:49
P38 Math 221 Lecture 38
34:18
P39 Math 221 Lecture 39
38:14
【佩珀代因大学 - 中英】形式化方法 Formal Methods
P01 Formal Methods, Lecture 1
50:15
P02 Formal Methods, Lecture 1 Recap
10:43
P03 Formal Methods, Lecture 2
52:41
P04 Formal Methods, Lecture 2 Recap
18:22
P05 Formal Methods, Lecture 3
51:50
P06 Formal Methods, Lecture 3 Recap
28:55
P07 Formal Methods, Lecture 4
50:21
P08 Formal Methods, Lecture 4 Recap
23:28
P09 Formal Methods, Lecture 5
47:01
P10 Formal Methods, Lecture 5 Recap
29:20
P11 Formal Methods, Lecture 6
51:22
P12 Formal Methods, Lecture 6 Recap
20:08
P13 Formal Methods, Lecture 7
50:56
P14 Formal Methods, Lecture 7 Recap
25:14
P15 Formal Methods, Lecture 8
51:23
P16 Formal Methods, Lecture 8 Recap
23:53
P17 Formal Methods, Lecture 9
50:00
P18 Formal Methods, Lecture 9 Recap
20:13
P19 Formal Methods, Lecture 10
49:58
P20 Formal Methods, Lecture 10 Recap
18:10
P21 Formal Methods, Lecture 11
53:05
P22 Formal Methods, Lecture 11 Recap
15:17
P23 Formal Methods, Lecture 12
51:21
P24 Formal Methods, Lecture 13
41:44
P25 Formal Methods, Lecture 14
51:45
P26 Formal Methods, Lecture 14 Recap
26:28
P27 Formal Methods, Lecture 15
49:29
P28 Formal Methods, Lecture 15 Recap
25:20
P29 Formal Methods, Lecture 16
52:12
P30 Formal Methods, Lecture 17
43:53
P31 Formal Methods, Lecture 18
49:39
P32 Formal Methods, Lecture 19
48:48
P33 Formal Methods, Lecture 20
48:41
P34 Formal Methods, Lecture 21
51:22
P35 Formal Methods, Lecture 22
51:35
P36 Formal Methods, Lecture 23
44:56
P37 Formal Methods, Lecture 24
47:33
P38 Formal Methods, Lecture 25
30:37
P39 Formal Methods, Lecture 26
47:28
P40 Formal Methods, Lecture 27
45:52
P41 Math 220 Lecture 28
40:12
P42 Math 220 Lecture 29
48:40
P43 Math 220 Lecture 30
52:08
P44 Math 220 Lecture 31
49:23
P45 Math 220 Lecture 32
51:20
P46 Math 220 Lecture 33
48:54
P47 Math 220 Lecture 34
50:07
P48 Math 220 Lecture 35
47:22
P49 Math 220 Lecture 36
48:26
P50 Math 220 Lecture 37
50:15
P51 Math 220 Lecture 38
46:43
P52 Math 220 Lecture 39
44:55
P53 Math 220 Lecture 40
44:34
python实现大学微积分，完整课程
06:56:45
泛函分析 | IMPA
P01 Lecture 1 - Linear spaces - definition, examples and
39:18
P02 Lecture 2 - Linear spaces - quotient spaces and convex
56:57
P03 Lecture 3 - Normed linear spaces - definition and basic
43:34
P04 Lecture 4 - Completing a normed linear space
01:07:12
P05 Lecture 5 - Finite dimensional linear spaces
46:07
P06 Lecture 6 - Examples of normed linear spaces
43:16
P07 Lecture 7 - In infinite dimensions the unit ball is not
42:58
P08 Lecture 8 - Zorns lemma
35:05
P09 Lecture 9 - The Hahn-Banach theorem
46:06
P10 Lecture 10 - Convex sets and gauge functions
47:52
P11 Lecure 11 - Geometric Hanh-Banach theorems
01:02:50
P12 Lecture 12 - Dual o a normed linear space
34:00
P13 Lecture 13 - Extension of bounded linear functionals
01:25:39
P14 Lecture 14 - Reflexive spaces
01:06:57
P15 Lecture 14A - The dual space of C([a,b])
01:05:59
P16 Lecture 14B -An application of the Hahn-Banach theorem
01:02:22
P17 Lecture 14C - A dual variational problem in optimal control
32:20
P18 Lecture 14D - An application of the Hahn-Banach theorem
58:23
P19 Lecture 15 - Hilbert spaces
01:03:14
P20 Lecture 16 - Closed convex subsets of a Hilbert space
31:21
P21 Lecure 17 - Riesz and Lax-Milgram representation theorems
50:39
P22 Lecture 18 - Orthonormal sets and closed linear spans
01:00:01
P23 Lecture 19 - Orthonormal bases
44:51
P24 Lecture 19A - A quadratic variational problem
38:34
P25 Lecture 19B The Dirichlet principle
21:41
P26 Lecture 19C - Generalized derivatives and Sobolev spaces
53:42
P27 Lecture 20 - Uniform boundedness principle
32:05
P28 Lecture 21 - Weak convergence
31:16
P29 Lecture 22 - Uniform boundedness of weak converging
42:39
P30 Lecture 23 - Weak sequentially compactness
37:48
P31 Lecture 24 - Weak topology
46:57
P32 Lecture 25 - Applications of weak convergence
01:01:22
P33 Lecture 26 - Bounded linear operators
01:18:36
P34 Lecture 27 - Transpose of Bounded linear operators
46:41
P35 Lecture 28 - Strong and weak convergence of operators
51:19
P36 Lecture 29 - Principle of uniform boundedness for maps
20:25
P37 Lecture 30 - Open map principle.
46:36
P38 Lecture 31 - The closed graph theorem.
40:00
P39 Lecture 32. Examples of bounded linear maps - Integral
29:12
P40 Lecture 33 - Symmetric operators
42:44
P41 Lecture 34 - Eigenvalues of compact symmetric operators
01:27:55
P42 Lecture 35 - The Fredholm alternative
01:19:08
P43 Lecture 36 - An application to integral operators
52:50
概率论 | Probability Theory | IMPA
P01 Lecture 1 - Introduction
52:33
P02 Lecture 2 - Independence
01:03:28
P03 Lecture 3 - Applications of independence
58:45
P04 Lecture 3A - Large deviations for i.i.d. random variables, ...
01:05:59
P05 Lecture 3B - Large deviations lower bound
43:07
P06 Lecture 3C - The Galton-Watson branching process.
53:07
P07 Lecture 4 - Convergence of random variables
48:14
P08 Lecture 5 - Borel-Cantelli lemma
52:11
P09 Lecture 6 - Weak convergence - Hellys selection theorem and...
01:25:53
P10 Lecture 7 - Weak convergence - Helly-Brays theorem
01:01:29
P11 Lecture 8 - Characteristic functions
01:04:08
P12 Lecture 9 - The Lévy continuity theorem
45:26
P13 Lecture 10 - Weak law of large numbers
59:24
P14 Lecture 10A - Phase transition in the Ising model, Introduction
01:01:43
P15 Lecture 10B - The one-dimensional Ising model
51:06
P16 Lecture 10C - Phase transition of the two-dimensional Ising...
01:12:00
P17 Lecture 10D - The two-dimensional Ising model at high...
01:33:46
P18 Lecture 11 - Convergence of series
01:17:26
P19 Lecture 12 - Kolmogorovs three series theorem
01:32:56
P20 Lecture 13 - The strong law of large numbers
56:55
P21 Lecture 14 - Law of large Numbers II
01:08:35
P22 Lecture 15 - Applications of the Law of large Numbers
01:30:10
P23 Lecture 16 - Central Limit Theorem
54:13
P24 Lecture 17 - Central Limit Theorem, II
54:05
P25 Lecture 18 - Infinitely Divisible Laws
01:06:03
P26 Lecture 19 - Accompanying laws
43:22
P27 Lecture 20, Part 1 - Proof of the Accompanying Laws theorem
49:17
P28 Lecture 20, Part 2 - Proof of the Accompanying Laws theorem
51:27
P29 Lecture 21 - The Lévy--Khintchine theorem
01:05:14
P30 Lecture 22A - The one-dimensional central limit problem, Part 1
41:07
P31 Lecture 22B - The one-dimensional central limit problem, Part 2
01:08:21
P32 Lecture 23 - Applications
01:26:15
P33 Lecture 24 - Conditional expectation
01:19:31
P34 Lecture 25 - Properties of conditional expectation
01:20:25
P35 Lecture 26 - Regular conditional probability
01:02:42
概率论与数理统计
P01 Probability and Statistics - Overview
29:43
P02 Gentle Introduction to Probability - Counting Coin Flips and Dice
20:05
P03 Counting Probabilities with Combinatorics and the Factorial
17:50
P04 Set Theory in Probability - Sample Spaces and Events
24:13
P05 The Birthday Problem in Probability - P(A) = 1 - P(not A)
20:21
P06 Quality Control, Non-Destructive Inspection, and the Multinomial Distributio
13:30
P07 The Binomial Distribution and the Multinomial Distribution
16:32
P08 Conditional Probabilities
13:11
P09 The Law of Total Probability
10:14
P10 Bayes Theorem (with Example!)
17:43
P11 Bayes Theorem Example - Drug Testing
12:32
P12 Independence in Probability
13:00
P13 Random Variables and Probability Distributions
21:57
P14 Bernoulli and Binomial Random Variables
24:41
P15 The Normal Distribution - The Limit of Binomial Distribution for Large n
17:15
P16 The Standard Unit Normal and Probability Computations
17:12
P17 The Poisson Distribution - The Rare Event Limit of a Binomial Distribution
13:01
P18 The Geometric Distribution - The First Success of a Bernoulli Distribution
12:56
P19 The Exponential Distribution - Time Between Poisson Events
18:46
P20 The Hazard Rate and Memoryless Property of the Exponential Distribution
07:11
P21 The Connection Between the Exponential Distribution and the Poisson Process
10:13
P22 The Gamma Distribution
12:30
P23 Functions of a Random Variable
13:36
P24 Rescaling the Normal Distribution to Mean Zero and Variance One
09:16
P25 The Chi Squared Distribution - The Square of the Normal Distribution
13:09
P26 Joint Probability Distributions
14:34
P27 Joint Probability Distributions - Marginal and Conditional Densities
09:36
P28 The Expected Value (Mean) of a Probability Distribution
15:24
P29 Properties of the Expected Value
10:18
P30 Variance and Standard Deviation
12:59
P31 Example of Computing the Expectation and Variance of an Exponential Distribu
11:58
P32 Two Examples of Expected Values & Functions - Temperature in C vs F, and the
15:26
P33 Markovs Inequality in Probability - First Order Estimates
08:09
P34 Chebyshevs Inequality in Probability - Second Order Estimates
09:44
P35 The Law of Large Numbers
12:44
P36 The Central Limit Theorem
10:57
P37 The Moment Generating Function
21:57
P38 Example of The Moment Generating Function
09:48
P39 The Lebesque Measure in Probability
06:21
P40 Additive Property of the Moment Generating Function
06:18
P41 Covariance and Correlation in Probability
19:34
P42 Covariance and Correlation - Example with Gaussian Distributions
05:29
P43 The Tail Sum Formula in Probability
09:04
P44 Proof of the Central Limit Theorem
26:25
【东爱达荷学院 (CEI)】逻辑导论 Introduction to Logic（Fall 2020）
P01 Introduction to Logic - Welcome Video
14:15
P02 Introduction to Logic, Week 1 - Arguments
02:15:44
P03 Introduction to Logic, Week 2 - Introduction to Propositional Logic
02:46:42
P04 Week 3 - Truth Tables for Propositions and Arguments (Validity)
01:44:57
P05 Natural Deduction Proof Method for Propositional Logic - Rules of Implicatio
01:02:52
P06 Week 5 - Natural Deduction Proof Method - Rules of Implication II
01:30:47
P07 Week 6 - Rules of Replacement I, Instructor - Zachary Fruhling
01:35:51
P08 Week 7 - Rules of Replacement II (Natural Deduction)
43:32
P09 Week 8 - Conditional Proof and Indirect Proof
02:26:20
P10 Week 9 - Proving Logical Truths
01:20:46
P11 Week 10 - Predicate Logic Symbols & Translation
59:29
P12 Week 11 - Predicate Logic Natural Deduction Rules
01:24:09
P13 Week 12 - Quantifier Negation (QN)
32:26
P14 Week 13 - Conditional Proof & Indirect Proof in Predicate Logic
24:45
P15 Week 14 - Relational Predicates and Overlapping Quantifiers
47:56
P16 Week 15 - Identity Statements in Predicate Logic
38:45
【普渡大学】计算优化 ChE-597（Computational Optimization，Spring 2025）
P26 Lecture 1 Introduction to Computational Optimization
01:10:18
P25 Recitation Linear Algebra and Calculus Review
01:11:20
P24 Lecture 2 Convex Sets and Functions
01:21:08
P23 Lecture 3 Unconstrained Optimization
01:11:05
P22 Lecture 4 Linear Programming Applications
01:10:38
P21 Lecture 5 Polyhedron Theory
01:17:36
P20 Lecture 6 Simplex Algorithm
01:15:37
P19 Lecture 7 Linear Programming Duality
01:17:07
P18 Lecture 8 Conic Programming
01:21:48
P17 Lecture 9 Langrangian Dual and Optimality Conditions
01:15:53
P16 Lecture 10 Nonlinear Programming Algorithms
01:08:01
P15 Lecture 11 Modeling of Discrete and Continuous Decisions
01:20:06
P14 Lecture 12 Formulating Mixed Integer Linear Programming Models
01:20:27
P13 Lecture 13 Mixed Integer Linear Programming Applications
01:01:47
P12 Lecture 14 Branch and Bound
01:12:20
P11 Lecture 15 Cutting Planes
01:03:34
P10 Lecture 16 MIP Solvers
01:08:14
P09 Lecture 17 Nonconvex Optimization Applications
01:17:07
P08 Lecture 18 Convex Relaxation
01:15:31
P07 Lecture 19 Branch and Reduce
01:19:59
P06 Lecture 20 Decomposition Algorithms for MINLP
01:11:15
P05 Lecture 21 Stochastic Programming and Benders Decomposition
01:16:21
P04 Lecture 22 Column Generation and Dantzig Wolfe Decomposition
01:10:01
P03 Lecture 23 Lagrangian Relaxation and Decomposition
01:21:15
P02 Lecture 24 Augmented Lagrangian and ADMM
51:01
P01 Lecture 25 Bilevel Optimization
01:14:01
离散数学与概率论 CS70（2015）
P01 Computer Science 70 2015-01-20
01:20:47
P02 Computer Science 70 2015-01-22
01:19:42
P03 Computer Science 70 2015-01-27
01:18:57
P04 Computer Science 70 2015-01-29
01:17:55
P05 Computer Science 70 2015-02-03
01:19:18
P06 Computer Science 70 2015-02-05
01:19:05
P07 Computer Science 70 2015-02-10
01:20:54
P08 Computer Science 70 2015-02-12
01:11:34
P09 Computer Science 70 2015-02-19
01:19:33
P10 Computer Science 70 2015-02-24
01:19:14
P11 Computer Science 70 2015-02-26
01:18:04
P12 Computer Science 70 2015-03-03
01:19:36
P13 Computer Science 70 2015-03-05
01:15:21
P14 Computer Science 70 2015-03-10
01:14:10
P15 Computer Science 70 2015-03-12
01:19:23
P16 Computer Science 70 2015-03-17
01:20:00
P17 Computer Science 70 2015-03-19
01:21:49
P18 Computer Science 70 2015-04-02
01:22:12
P19 Computer Science 70 2015-04-07
01:21:44
P20 Computer Science 70 2015-04-09
01:20:05
P21 Computer Science 70 2015-04-14
01:20:53
P22 Computer Science 70 2015-04-16
01:20:24
P23 Computer Science 70 2015-04-21
59:40
P24 Computer Science 70 2015-04-23
01:16:45
P25 Computer Science 70 2015-04-28
01:19:30
P26 Computer Science 70 2015-04-30
59:26
P27 Computer Science 70 2015-05-05
01:53:44
P28 Computer Science 70 2015-05-07
01:48:40
【斯坦福大学】超越最坏情况分析 | Beyond Worst-Case Analysis
P01 (Lecture 1 - Three Motivating Examples)
55:55
P02 (Lecture 2 - Instance-Optimal Geometric Algorithms)
01:11:16
P03 (Lecture 3 - Online Paging and Resource Augmentation)
01:18:48
P04 (Lecture 4 - Parameterized Analysis of Online Paging)
01:19:15
P05 (Lecture 5 - Computing Independent Sets -A Parameterized Analysis)
01:14:49
P06 (Lecture 6 - Clustering in Approximation-Stable Instances)
01:19:05
P07 (Lecture 7 - Perturbation Stability and Single-Link++)
01:13:38
P08 (Lecture 8 - Exact Recovery in Stable Cut Instances)
01:17:08
P09 (Lecture 9 - A Taste of Compressive Sensing)
57:22
P10 (Lecture 10 - Planted and Semi-Random Graph Models)
01:10:15
P11 (Lecture 11 - LP Decoding)
01:13:05
P12 (Lecture 12 - LP Decoding Introduction to Smoothed Analysis)
01:16:53
P13 (Lecture 13 - Smoothed Analysis of Local Search)
01:16:24
P14 (Lecture 14 - Smoothed Analysis of Pareto Curves)
01:08:47
P15 (Lecture 15 - Smoothed Complexity and Pseudopolynomial-Time Algorithms)
01:22:34
P16 (Lecture 16 - Pseudorandom Data and Universal Hashing)
01:18:26
P17 (Lecture 17 - Self-Improving Algorithms)
01:25:12
P18 (Lecture 18 - Pricing with an Unknown Distribution)
01:12:06
P19 (Lecture 19 - Online Algorithms and Random Permutations)
01:17:26
P20 (Lecture 20 - From Unknown Input Distributions to Instance Optimality)
01:16:44
【ICTP】偏微分方程 Partial Differential Equations (MTH-PDE) 2021
P01 Lecture 1
01:38:29
P02 Lecture 2
01:31:08
P03 Lecture 3
01:31:22
P04 Lecture 4
01:30:13
P05 Lecture 5
01:31:05
P06 Lecture 6
01:32:00
P07 Lecture 8
01:29:04
P08 Lecture 7
01:28:36
P09 Lecture 9
01:29:24
P10 Lecture 10
01:30:30
P11 Lecture 11
01:29:19
P12 Lecture 12
01:29:10
P13 Lecture 13
01:29:53
P14 Lecture 14
01:29:38
P15 Lecture 15
01:30:09
微积分 | Calculus | Professor Leonard
P01 Calculus 1 Lecture 0.1 - Lines, Angle of Inclination, and the Distance Form
48:58
P02 Calculus 1 Lecture 0.2 - Introduction to Functions.
01:37:06
P03 Calculus 1 Lecture 0.3 - Review of Trigonometry and Graphing Trigonometric
01:20:15
P04 Calculus 1 Lecture 0.4 - Combining and Composition of Functions
15:53
P05 Calculus 1 Lecture 1.1 - An Introduction to Limits
01:27:26
P06 Calculus 1 Lecture 1.2 - Properties of Limits. Techniques of Limit Computa
03:00:15
P07 Calculus 1 Lecture 1.4 - Continuity of Functions
01:26:51
P08 Calculus 1 Lecture 1.5 - Slope of a Curve, Velocity, and Rates of Change
01:50:43
P09 Calculus 1 Lecture 2.1 - Introduction to the Derivative of a Function
01:16:01
P10 Calculus 1 Lecture 2.2 - Techniques of Differentiation (Finding Derivatives
01:12:31
P11 Calculus 1 Lecture 2.3 - The Product and Quotient Rules for Derivatives of
01:02:22
P12 Calculus 1 Lecture 2.4 - Applications of the Derivative
40:39
P13 Calculus 1 Lecture 2.5 - Finding Derivatives of Trigonometric Functions
48:43
P14 Calculus 1 Lecture 2.6 - Discussion of the Chain Rule for Derivatives of Fu
01:34:01
P15 Calculus 1 Lecture 2.7 - Implicit Differentiation
01:08:11
P16 Calculus 1 Lecture 2.8 - Related Rates
53:52
P17 Calculus 1 Lecture 3.1 - Increasing Decreasing and Concavity of Functions
01:34:07
P18 Calculus 1 Lecture 3.2 - A BRIEF Discussion of Rolles Theorem and Mean-Valu
06:36
P19 Calculus 1 Lecture 3.3 - The First Derivative Test for Increasing and Decre
26:10
P20 Calculus 1 Lecture 3.4 - The Second Derivative Test for Concavity of Functi
36:50
P21 Calculus 1 Lecture 3.5 - Limits of Functions at Infinity
01:23:49
P22 Calculus 1 Lecture 3.6 - How to Sketch Graphs of Functions
01:32:36
P23 Calculus 1 Lecture 3.7 - Optimization Max Min Application Problems
01:34:43
P24 Calculus 1 Lecture 4.1 - An Introduction to the Indefinite Integral
02:45:37
P25 Calculus 1 Lecture 4.2 - Integration by Substitution
01:33:58
P26 Calculus 1 Lecture 4.3 - Area Under a Curve, Limit Approach, Riemann Sums
02:07:03
P27 Calculus 1 Lecture 4.4 - The Evaluation of Definite Integrals
30:55
P28 Calculus 1 Lecture 4.5 - The Fundamental Theorem of Calculus
02:46:09
P29 Calculus 1 Lecture 5.1 - Finding Area Between Two Curves
01:33:47
P30 Calculus 1 Lecture 5.2 - Volume of Solids By Disks and Washers Method
02:47:49
P31 Calculus 1 Lecture 5.3 - Volume of Solids By Cylindrical Shells Method
54:56
P32 Calculus 1 Lecture 5.4 - Finding the Length of a Curve on a Plane
02:17:58
P33 Calculus 2 Lecture 6.1 - The Natural Log Function
02:22:47
P34 Calculus 2 Lecture 6.2 - Derivatives of Inverse Functions
44:09
P35 Calculus 2 Lecture 6.3 - Derivatives and Integrals of Exponential Functions
01:30:52
P36 Calculus 2 Lecture 6.4 - Derivatives and Integrals of General Exponential F
01:15:21
P37 Calculus 2 Lecture 6.5 - Calculus of Inverse Trigonometric Functions
01:52:50
P38 Calculus 2 Lecture 6.6 - A Discussion of Hyperbolic Functions
01:16:06
P39 Calculus 2 Lecture 6.7 - Evaluating Limits of Indeterminate Forms
01:40:42
P40 Calculus 2 Lecture 7.1 - Integration By Parts
01:54:37
P41 Calculus 2 Lecture 7.2 - Techniques For Trigonometric Integrals
02:21:10
P42 Calculus 2 Lecture 7.3 - Integrals By Trigonometric Substitution
02:09:24
P43 Calculus 2 Lecture 7.4 - Integration By Partial Fractions
02:55:43
P44 Calculus 2 Lecture 7.6 - Improper Integrals
02:48:31
P45 Calculus 2 Lecture 8.1 - Solving First Order Differential Equations By Separ
02:49:22
P46 Calculus 2 Lecture 9.1 - Convergence and Divergence of Sequences
02:27:29
P47 Calculus 2 Lecture 9.2 - Series, Geometric Series, Harmonic Series, and Div
02:01:40
P48 Calculus 2 Lecture 9.3 - Using the Integral Test for Convergence Divergence
01:11:52
P49 Calculus 2 Lecture 9.4 - The Comparison Test for Series and The Limit Compa
01:34:42
P50 Calculus 2 Lecture 9.5 - Showing Convergence With the Alternating Series Te
01:19:45
P51 Calculus 2 Lecture 9.6 - Absolute Convergence, Ratio Test and Root Test For
01:46:22
P52 Calculus 2 Lecture 9.7 - Power Series, Calculus of Power Series, Ratio Test
02:29:49
P53 Calculus 2 Lecture 9.8 - Representation of Functions by Taylor Series and M
03:01:45
P54 Calculus 2 Lecture 9.9 - Approximation of Functions by Taylor Polynomials
01:34:10
P55 Calculus 2 Lecture 10.2 - Introduction to Parametric Equations
01:38:26
P56 Calculus 2 Lecture 10.3 - Calculus of Parametric Equations
01:34:19
P57 Calculus 2 Lecture 10.4 - Using Polar Coordinates and Polar Equations
02:01:36
P58 Calculus 2 Lecture 10.5 - Calculus of Polar Equations
01:12:46
P59 Numerical Integration With Trapezoidal and Simpsons Rule
27:08
P60 Calculus 3 Lecture 11.1 - An Introduction to Vectors
02:37:48
P61 Calculus 3 Lecture 11.2 - Vectors in 3-D Coordinate System
01:10:51
P62 Calculus 3 Lecture 11.3 - Using the Dot Product
02:29:04
P63 Calculus 3 Lecture 11.4 - The Cross Product
02:11:12
P64 Calculus 3 Lecture 11.5 - Lines and Planes in 3-D
03:21:03
P65 Calculus 3 Lecture 11.6 - Cylinders and Surfaces in 3-D
02:32:27
P66 Calculus 3 Lecture 11.7 - Using Cylindrical and Spherical Coordinates
01:40:16
P67 Calculus 3 Lecture 12.1 - An Introduction To Vector Functions
02:04:56
P68 Calculus 3 Lecture 12.2 - Derivatives and Integrals of Vector Functions
02:42:19
P69 Calculus 3 Lecture 12.3 - Arc Length Parameterization, TNB (Frenet-Serret)
02:12:46
P70 Calculus 3 Lecture 12.3 12.5 - TNB (Frenet-Serret) Frames, Curvature, Torsi
02:37:28
P71 Calculus 3 Lecture 12.4 - Velocity and Acceleration of Vector Functions
01:02:04
P72 Calculus 3 Lecture 13.1 - Intro to Multivariable Functions (Domain, Sketchi
01:49:07
P73 Calculus 3 Lecture 13.2 - Limits and Continuity of Multivariable Functions
02:14:36
P74 Calculus 3 Lecture 13.3 - Partial Derivatives (Derivatives of Multivariable
02:28:53
P75 Calculus 3 Lecture 13.4 - Finding Differentials of Multivariable Functions
01:51:04
P76 Calculus 3 Lecture 13.5 - The Chain Rule for Multivariable Functions
02:11:52
P77 Calculus 3 Lecture 13.6 - Finding Directional Derivatives and Gradients
02:37:18
P78 Calculus 3 Lecture 13.7 - Finding Tangent Planes and Normal Lines to Surfac
01:41:47
P79 Calculus 3 Lecture 13.8 - Finding Extrema of Functions of 2 Variables (Max
03:38:16
P80 Calculus 3 Lecture 13.9 - Constrained Optimization with LaGrange Multiplier
58:33
P81 Calculus 3 Lecture 14.1 - INTRODUCTION to Double Integrals (Background Info
51:58
P82 Calculus 3 Lecture 14.2 - How to Solve Double Repeated Iterated Integrals
03:23:48
P83 Calculus 3 Lecture 14.3 - Double Integrals over POLAR REGIONS
03:25:15
P84 Calculus 3 Lecture 14.4 - Center of Mass (and Moments of Mass and Inertia)
01:16:44
P85 Calculus 3 Lecture 14.6 - How to Solve TRIPLE INTEGRALS (Along with Center
03:33:32
P86 Calculus 3 Lecture 14.7 - TRIPLE Integrals Over Regions with CYLINDRICAL or
03:20:10
P87 Calculus 3 Lecture 14.8 - How to Change Variables in Multiple Integrals (Us
01:40:05
P88 Calculus 3 Lecture 15.1 - INTRODUCTION to Vector Fields (and what makes the
58:15
P89 Calculus 3 Lecture 15.2 - How to Find Divergence and Curl of Vector Fields
01:11:50
P90 Calculus 3 Lecture 15.3 - How to Compute Line Integrals (Over Non-Conservat
02:17:24
P91 Line Integrals on CONSERVATIVE Vector Fields (Independence of Path) - Calcu
01:53:58
P92 Greens Theorem - Calculus 3 Lecture 15.5
01:45:54
P93 Surface And Flux Integrals, Parametric Surf., Divergence Stokes Theorem - Ca
03:31:35
【加州大学伯克利】线性系统理论 EECS 221a
P01 Module 1- Introduction and Functions
22:23
P02 Module 2-Fields and Vector Spaces
19:24
P03 Module 3- Subspaces and Bases
18:21
P04 EECS-Module 4 - Linear Maps
16:55
P05 EECS-Module 5 - Matrix Representation Of lLinear Maps
16:42
P06 EECS-Module 6- Change of Basis
18:49
P07 EECS- Module 7- Norms
18:08
P08 Module 8 - Induced Norms
22:20
P09 Module 9 - Inner Products
18:26
P10 Module 10 - Adjoints
18:23
P11 Module 11 - Hermitian Matrices
14:38
P12 EECS- Module 12 -Singular Value Decomposition
12:57
P13 EECS- Module 13 -Fundamental Theorum of Ordinary Differential Equations
28:55
P14 EECS-Module 14 -Bellman-Gronwall Lemma
20:22
P15 Module 15 -Dynamical Systems
26:09
P16 Module 16 - Linearity and Time Invariance
19:38
P17 Module 17 - Linear Time Varying Systems
13:57
P18 Module 18 - State Transition Matrix
14:47
P19 Module 19 - Solutions to Linear Time Varying Systems
13:25
P20 Module 20- Jacobian Linearization
19:25
P21 Module 21 - The Matrix Exponetial
20:14
P22 Module 22 - Cayley Hamilton Theorem
19:44
P23 Module 23 -Eigenvalues and Eigenvectors
17:16
P24 Module 24 - Diagonalization
13:03
P25 Module 25 - A-invariant Subspaces
11:48
P26 Module 26 - 2nd Representation Theorem
10:59
P27 Module 27 - Minimum Polynomial
11:12
P28 Module 28 - Jordan Form
24:45
P29 Module 29 - Spectral Mapping Theorem
08:13
P30 Module 30 - Bibo Stability
16:42
P31 Module 31 - State Space Stability
16:08
P32 Module 32 - Exponential Stabilitity of x = AX
17:13
【剑桥大学】基于低维模型的高维数据分析：原理、计算和应用
P01 lec02_Aug31
01:16:56
P01 lec03
01:16:44
P02 lec04_Sep07
01:25:10
P03 lec05_Sep09
01:17:06
P04 lec06_Sep14
01:24:35
P05 lec07_Sep16
01:22:59
P06 lec08_Sep21
01:21:55
P07 lec09_Sep23
01:22:23
P08 lec10_Sep28
01:11:49
P09 lec11_Sep30
54:45
P10 lec12_Oct05
01:00:58
P11 lec14_Oct12
01:14:28
P12 lec16_Oct21
01:24:37
P13 lec17_Oct26
01:19:45
P14 lec18_Oct28
01:18:06
P15 lec19_Nov02
01:17:32
P16 lec20_Nov04
01:21:28
P17 lec21_Nov09
01:27:19
P18 lec22_Nov16
01:25:38
P19 lec23_Nov18
01:17:02
P20 lec24_Nov30
01:26:04
P21 lec25_Dec02(John Wright)
01:33:35
P22 lec26_Dec03(Mert Pilanci)
53:34
【克莱姆森大学】高等线性代数 | Math 8530, Spring 2021
P01 Lecture 1.1 - Vector spaces and linearity
36:25
P02 Lecture 1.2 - Spanning, independence, and bases
39:25
P03 Lecture 1.3 - Direct sums and products
19:24
P04 Lecture 1.4 - Quotient spaces
43:57
P05 Lecture 1.5 - Dual vector spaces
23:36
P06 Lecture 1.6 - Annihilators
29:07
P07 Lecture 2.1 - Rank and nullity
31:31
P08 Lecture 2.2 - Applications of the rank-nullity theorem
38:40
P09 Lecture 2.3 - Algebra of linear mappings
35:24
P10 Lecture 2.4 - The four subspaces
43:09
P11 Lecture 2.5 - The transpose of a linear map
41:07
P12 Lecture 2.6 - Matrices
41:51
P13 Lecture 2.7 - Change of basis
21:08
P14 Lecture 3.1 - Determinant prerequisites
27:11
P15 Lecture 3.2 - Symmetric and skew-symmetric multilinear forms
30:52
P16 Lecture 3.3 - Alternating multilinear forms
41:57
P17 Lecture 3.4 - The determinant of a linear map
33:30
P18 Lecture 3.5 - The determinant and trace of a matrix
33:38
P19 Lecture 3.6 - Minors and cofactors
31:34
P20 Lecture 3.7 - Tensors
56:25
P21 Lecture 4.1 - Eigenvalues and eigenvectors
39:44
P22 Lecture 4.2 - The Cayley-Hamilton theorem
49:20
P23 Lecture 4.3 - Generalized eigenvectors
29:29
P24 Lecture 4.4 - Invariant subspaces
41:31
P25 Lecture 4.5 - The spectral theorem
32:59
P26 Lecture 4.6 - Generalized eigenspaces
26:41
P27 Lecture 4.7 - Jordan canonical form
31:50
P28 Lecture 5.1 - Inner products and Euclidean structure
41:52
P29 Lecture 5.2 - Orthogonality
48:14
P30 Lecture 5.3 - Gram-Schmidt and orthogonal projection
52:30
P31 Lecture 5.4 - Adjoints
20:18
P32 Lecture 5.5 - Projection and Least Squares
36:31
P33 Lecture 5.6 - Isometries
32:19
P34 Lecture 5.7 - The norm of a linear map
47:07
P35 Lecture 5.9 - Complex inner product spaces
29:54
P36 Lecture 6.1 - Quadratic forms
36:12
P37 Lecture 6.2 - Spectral resolutions
38:56
P38 Lecture 6.3 - Normal linear maps
35:08
P39 Lecture 6.4 - The Rayleigh quotient
53:09
P40 Lecture 6.5 - Self-adjoint differential operators
44:50
P41 Lecture 7.1 - Definiteness and indefiniteness
34:42
P42 Lecture 7.2 - Nonstandard inner products and Gram matrices
40:49
信息论
P01 (IC 1.1) Information theory and Coding - Outline of topics
14:40
P02 (IC 1.2) Applications of Compression codes
11:39
P03 (IC 1.3) Applications of Error-correcting codes
29:11
P04 (IC 1.4) Source-channel separation
12:33
P05 (IC 1.5) Examples of source-encoder-channel pipelines
15:46
P06 (IC 1.6) A different notion of information
18:12
P07 (IC 2.1) A puzzle on weighing coins
05:28
P08 (IC 2.2) Symbol codes - terminology and notation
13:52
P09 (IC 2.3) Symbol codes - definition and examples
14:37
P10 (IC 2.4) Decoding - prefix versus non-prefix
16:00
P11 (IC 2.5) Prefix codes
15:50
P12 (IC 2.6) Prefix codes - remarks and whats next
05:37
P13 (IC 2.7) Expected codeword length
13:14
P14 (IC 2.8) Kraft-McMillan inequality - statement
13:46
P15 (IC 2.9) Kraft-McMillan - proof of (a)
18:20
P16 (IC 2.10) Kraft-McMillan - examples for (b)
20:53
P17 (IC 2.11) Kraft-McMillan - proof sketch for (b)
12:32
P18 (IC 3.1) Entropy as a lower bound on expected length (part 1)
15:20
P19 (IC 3.2) Entropy as a lower bound on expected length (part 2)
13:06
P20 (IC 3.3) Entropy as a lower bound on expected length (part 3)
17:49
P21 (IC 3.4) Remark - an alternate proof
01:44
P22 (IC 3.5) Bounds on optimal expected length
13:57
P23 (IC 3.6) Example - entropy as a lower bound
03:57
P24 (IC 3.7) Block codes for compression
13:25
P25 (IC 3.8) Entropy of i.i.d. random variables
08:30
P26 (IC 3.9) Source coding theorem (optimal lossless compression)
15:49
P27 (IC 3.10) Relative entropy as the mismatch inefficiency
15:36
P28 (IC 4.1) Huffman coding - introduction and example
12:31
P29 (IC 4.2) Huffman coding - more examples
13:43
P30 (IC 4.3) B-ary Huffman codes
12:23
P31 (IC 4.4) Weighted minimization with Huffman coding
06:32
P32 (IC 4.5) An issue with Huffman coding
11:57
P33 (IC 4.6) Optimality of Huffman codes (part 1) - inverse ordering
14:37
P34 (IC 4.7) Optimality of Huffman codes (part 2) - weak siblings
21:51
P35 (IC 4.8) Optimality of Huffman codes (part 3) - sibling codes
08:01
P36 (IC 4.9) Optimality of Huffman codes (part 4) - extension and contraction
18:18
P37 (IC 4.10) Optimality of Huffman codes (part 5) - extension lemma
22:19
P38 (IC 4.11) Optimality of Huffman codes (part 6) - induction
14:09
P39 (IC 4.12) Optimality of Huffman codes (part 7) - existence
23:46
P40 (IC 4.13) Not every optimal prefix code is Huffman
09:07
P41 (IC 5.1) Arithmetic coding - introduction
06:48
P42 (IC 5.2) Arithmetic coding - Example #1
29:05
P43 (IC 5.3) Arithmetic coding - Example #2
26:58
P44 (IC 5.4) Why the interval needs to be completely contained
25:03
P45 (IC 5.5) Rescaling operations for arithmetic coding
23:23
P46 (IC 5.6) Encoder for arithmetic coding (infinite-precision)
16:29
P47 (IC 5.7) Decoder for arithmetic coding (infinite-precision)
19:37
P48 (IC 5.8) Near optimality of arithmetic coding
32:18
P49 (IC 5.9) Computational complexity of arithmetic coding
19:08
P50 (IC 5.10) Generalizing arithmetic coding to non-i.i.d. models
24:20
P51 (IC 5.11) Finite-precision arithmetic coding - Rescaling
31:38
P52 (IC 5.12) Finite-precision arithmetic coding - Setup
07:52
P53 (IC 5.13) Finite-precision arithmetic coding - Encoder
17:37
P54 (IC 5.14) Finite-precision arithmetic coding - Decoder
24:22
流形入门
P01 Lesson 1 - Point Set Topology and Topological Spaces
29:57
P02 Lesson 2 - Elementary Definitions
38:41
P03 Lesson 3 - Separation
42:00
P04 Lesson 4 - Countability and Continuity
49:06
P05 Lesson 5 - Compactness, Connectedness, and Topological Properties
39:00
P06 Lesson 6 - Topological Manifolds
51:32
P07 Lesson 7 - Differentiable Manifolds
45:07
P08 Lesson 8 - Diffeomorphisms
45:04
P09 What is General Relativity Special Lecture - Tangent Spaces and Coordinate B
02:37:49
P10 Lesson 9 - The Tangent Space-Definition
01:23:35
P11 Lesson 10 - Tangent Space - Basis Vectors
56:11
P12 Lesson 11 - The Cotangent Space
31:31
P13 Lesson 12 - Fiber Bundles - Formal Description
01:06:25
P14 Lesson 13 - The tangent bundle - an illustration.
01:03:01
P15 Lesson 14 - Quotient Spaces
01:18:00
P16 What_is_a_Manifold_Lesson_16 - The Mobius strip
01:13:27
P17 Lesson 17 - Metric spaces (an aside)
59:49
P18 Lesson 18 - Homotopy
01:17:21
P19 Lesson 15 - The cylinder as a quotient space
59:09
展开