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Bài giảng Toán rời rạc - Phần 4: Hệ thức đệ quy (TS. Nguyễn Viết Đông)
Bài giảng Toán rời rạc - Phần 4: Hệ thức đệ quy (TS. Nguyễn Viết Đông) cung cấp cho học viên những kiến thức về định nghĩa hệ thức đệ quy, nghiệm tổng quát, nghiệm riêng, mục đích giải hệ thức đệ qui, hệ thức đề qui tuyến tính thuần nhất, hệ thức đề qui tuyến tính không thuần nhất,... Mời các bạn cùng tham khảo chi tiết nội dung bài giảng!
4/4/2023 11:14:13 PM +00:00
Bài giảng Toán rời rạc - Phần 3: Tập hợp, ánh xạ, phép đếm (TS. Nguyễn Viết Đông)
Bài giảng Toán rời rạc - Phần 3: Tập hợp, ánh xạ, phép đếm (TS. Nguyễn Viết Đông) cung cấp cho học viên những kiến thức về tập hợp và các phép toán trên tập hợp, tính chất của phép toán trên tập hợp, số phần tử của tập hợp hữu hạn; ánh xạ, ánh xạ bằng nhau, ảnh và ảnh ngược, song ánh và ánh xạ ngược; phép đếm, nguyên lý cộng và nguyên lý nhân;... Mời các bạn cùng tham khảo chi tiết nội dung bài giảng!
4/4/2023 11:14:03 PM +00:00
Bài giảng Toán rời rạc - Phần 2: Vị từ và lượng từ (TS. Nguyễn Viết Đông)
Bài giảng Toán rời rạc - Phần 2: Vị từ và lượng từ (TS. Nguyễn Viết Đông) cung cấp cho học viên những kiến thức về vị từ và lượng từ, phủ định của vị từ, phép nối liền (tương ứng nối rời, kéo theo), mệnh đề lượng từ hóa, hoán vị hai lượng từ,... Mời các bạn cùng tham khảo chi tiết nội dung bài giảng!
4/4/2023 11:13:56 PM +00:00
Bài giảng Toán rời rạc - Phần 1: Mệnh đề (TS. Nguyễn Viết Đông)
Bài giảng Toán rời rạc - Phần 1: Mệnh đề (TS. Nguyễn Viết Đông) cung cấp cho học viên những kiến thức về mệnh đề và chân trị, phép tính mệnh đề, dạng mệnh đề, quy tắc suy diễn, bài tập luyện tập,... Mời các bạn cùng tham khảo chi tiết nội dung bài giảng!
4/4/2023 11:13:48 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 22
Lecture Introduction to Stochastic Processes: Lesson 22 provide students with knowledge about limiting distribution, periodicity of the chain is causing the problem, a similar argument yields, aperiodic Markov chain, the limiting distribution of the chain,...
4/4/2023 11:04:30 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 21
Lecture Introduction to Stochastic Processes: Lesson 21 provide students with knowledge about SLLN for Markov chains, unique stationary distribution, the long run proportion, write the limit differently, the approximation using blocks, application of dissection principle,...
4/4/2023 11:04:23 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 20
Lecture Introduction to Stochastic Processes: Lesson 20 provide students with knowledge about suppose the Markov chain is irreducible and recurrent, unique stationary distribution, consequences of the theorem, positive recurrence and null recurrence are both class properties, symmetric transition probability matrix,...
4/4/2023 11:04:15 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 19
Lecture Introduction to Stochastic Processes: Lesson 19 provide students with knowledge about invariant measures and stationary distributions, stationary distribution of a Markov chain, how to obtain a stationaty distribution, proof of claim, invariant measure of the Markov chain,...
4/4/2023 11:04:05 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 18
Lecture Introduction to Stochastic Processes: Lesson 18 provide students with knowledge about recurrent classes are closed, application of the proposition, expected number of visits, n-step transition probabilities, if the state space is finite, then not all states are transient,...
4/4/2023 11:03:56 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 17
Lecture Introduction to Stochastic Processes: Lesson 17 provide students with knowledge about simple random walk on Z3, class property, solidarity property, recurrence and transience are class properties, period of a state, the canonical decomposition, closed sets,...
4/4/2023 11:03:49 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 16
Lecture Introduction to Stochastic Processes: Lesson 16 provide students with knowledge about simple random walk on Z, Stirling's approximation, nearest neighbour random walk on Z, direct product of two simple random walks on Z, one-dimensional estimate, two-dimensional case,...
4/4/2023 11:03:42 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 15
Lecture Introduction to Stochastic Processes: Lesson 15 provide students with knowledge about power series: a quick recap; Abel's limit theorem; corollary to establish extremely useful characterization of transience and recurrence; advantage of this charactarization;...
4/4/2023 11:03:35 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 14
Lecture Introduction to Stochastic Processes: Lesson 14 provide students with knowledge about the dissection principle, the blocks consist of the pieces of path between consecutive visits to a fixed state, the successive excursions between visits to the state, E-valued random variables,...
4/4/2023 11:03:24 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 13
Lecture Introduction to Stochastic Processes: Lesson 13 provide students with knowledge about communication classes, these equivalence classes are called communication classes or classes of the Markov chain, communication classes are fully determined by the transition matrix P, the dissection principle,...
4/4/2023 11:03:16 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 12
Lecture Introduction to Stochastic Processes: Lesson 12 provide students with knowledge about Chapman-Kolmogorov equation, decomposition of state space, hitting time, a very useful criterion for accessibility, deterministically monotone Markov chain,...
4/4/2023 11:03:09 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 11
Lecture Introduction to Stochastic Processes: Lesson 11 provide students with knowledge about simple random walk, on-off process, choose a lamp at random and switch it on, choose another lamp at random (independently of the previous choice and the configuration of the lamps), random walks on groups,...
4/4/2023 11:02:58 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 10
Lecture Introduction to Stochastic Processes: Lesson 10 provide students with knowledge about proof of (MC) ⇒ (MP), Markov chain, discrete parameter stochastic process, time-homogeneous Markov chain, the Markov property, a trivial example: an iid sequence, the deterministically monotone Markov chain,...
4/4/2023 11:02:51 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 9
Lecture Introduction to Stochastic Processes: Lesson 9 provide students with knowledge about discrete parameter Markov chain on a countable state space, simple random walk on integers, mathematical description, transition probabilities, define a stochastic process with initial distribution,...
4/4/2023 11:02:44 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 8
Lecture Introduction to Stochastic Processes: Lesson 8 provide students with knowledge about domestic and international passengers, thinning of a homogeneous poisson processes, quick review of probability generating functions, computation of probability generating functions,...
4/4/2023 11:02:37 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 7
Lecture Introduction to Stochastic Processes: Lesson 7 provide students with knowledge about the order statistics property, an application of order statistics property, how to establish the order statistics property, further properties of homogeneous poisson processes,...
4/4/2023 11:02:27 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 6
Lecture Introduction to Stochastic Processes: Lesson 6 provide students with knowledge about a small digression; third step: the verification; extensions that finish the proof of theorem; properties of homogeneous poisson processes; probability density function;...
4/4/2023 11:02:16 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 5
Lecture Introduction to Stochastic Processes: Lesson 5 provide students with knowledge about homogeneous Poisson process, poissonian increments, the converse of the previous theorem also holds, inhomogeneous Poisson process, towards the proof of theorem,...
4/4/2023 11:02:08 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 4
Lecture Introduction to Stochastic Processes: Lesson 4 provide students with knowledge about consequence of theorem, proof of the claim, what does the claim mean, disjoint time-intervals, the stochastic process, homogeneous Poisson proces,...
4/4/2023 11:02:02 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 3
Lecture Introduction to Stochastic Processes: Lesson 3 provide students with knowledge about positive random variables; the proof modulo (A) and (B); the Poisson process of phonecalls observed by you is independent of the number of phonecalls before you joined;...
4/4/2023 11:01:55 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 2
Lecture Introduction to Stochastic Processes: Lesson 2 provide students with knowledge about poisson process: an easy observation; poisson process: another easy observation; heuristic justification; rigorous justification; more general question; proof of the first proposition;...
4/4/2023 11:01:49 PM +00:00
Lecture Introduction to Stochastic Processes: Lesson 1
Lecture Introduction to Stochastic Processes: Lesson 1 provide students with knowledge about Homogeneous Poisson process on the positive real numbers; Discrete Markov chains with countable state space; classification of states - recurrence, transience, periodicity; stationary distributions, reversible chains; several illustrations;...
4/4/2023 11:01:38 PM +00:00
Lecture Discrete Mathematics I - Chapter 10: Trees (Tran Vinh Tan)
Lecture Discrete Mathematics I - Chapter 10: Trees (Tran Vinh Tan) provide students with knowledge about introduction to properties of trees; tree traversal; applications of trees - binary search trees, decision trees; spanning trees; minimum spanning trees, Prim’s algorithm, Kruskal’s algorithm;...
4/4/2023 10:59:02 PM +00:00
Lecture Discrete Mathematics I - Chapter 9: More about graphs (Tran Vinh Tan)
Lecture Discrete Mathematics I - Chapter 9: More about graphs (Tran Vinh Tan) provide students with knowledge about connectivity, paths and circuits; euler and hamilton paths, euler paths and circuits, hamilton paths and circuits; shortest path problem, Dijkstra’s algorithm, Bellman-Ford algorithm, Floyd-Warshall algorithm, traveling salesman problem;...
4/4/2023 10:58:52 PM +00:00
Lecture Discrete Mathematics I - Chapter 8: Introduction to Graphs (Tran Vinh Tan)
Lecture Discrete Mathematics I - Chapter 8: Introduction to Graphs (Tran Vinh Tan) provide students with knowledge about graph definitions, terminology, special simple graphs; representing graphs and graph isomorphism, representing graphs, graph isomorphism; exercise, graph, bipartie graph, isomorphism;...
4/4/2023 10:58:44 PM +00:00
Lecture Discrete Mathematics I - Chapter 7: Discrete Probability (Tran Vinh Tan)
Lecture Discrete Mathematics I - Chapter 7: Discrete Probability (Tran Vinh Tan) provide students with knowledge about introduction, randomness, probability, probability rules, random variables, probability models, geometric model, binomial model,...
4/4/2023 10:58:35 PM +00:00