MAY
Tuesday, May 31th, 2011.
 Graphs  Lecture 16. Cost of a task, cost of a planning. Correctness of a planning. Download this video . "Size:1.5 GB" .
 Problems of Graphs  Lecture 16. Problem st: Exercise 23 and 26. Download this video . "Size:1.5 GB" .
Monday, May 30th, 2011.
 Graphs  Lecture 14. Digraphs. Oriented paths, cycles. Acyclic digraphs. Ordering induced by an acyclic graph. Review of partial and total orderings. Total orderings compatible with partial orderings. Topological sorting. Existence of minimal elements in finite partial relations. Download this video . "Size:2.05 GB" .
 Graphs  Lecture 15. Existence of minimal elements in finite partial relations. Download this video . "Size:1.94 GB" .
Friday, May 27th, 2011.
 Graphs  Lecture 13. Weighted graphs. Distances. Properties of distances. Dijkstra algorithm. Examples of this algorithm. Shortestpath trees. . Download this video . "Size:974 MB" .
 Problems of Graphs  Problem set: exercise 31. Download this video . "Size:1.7GB" .
Thursday, May 26th, 2011.
 Graphs  Lecture 10. Weighted graphs. Distances. Properties of distances. Dijkstra algorithm. Examples of this algorithm. Shortestpath trees. . Download this video . "Size:974 MB" .
 Characterization of trees. Rooted trees. Root, internal nodes, leaves. Relatives: father, siblings, ancestors, descendant. Isomorphic trees.
 Problem set: exercise 31.
 Graphs  Lecture 11. Undirected trees. Definition and characterization . Download this video . "Size:974 MB" .
Wednesday, May 25th, 2011.
 Graphs  Lecture 9. Hamiltonian circuit, Hamiltonian paths, Hamiltonian graphs. Necessary conditions. Sufficient conditions: Dirac's Theorem. Download this video . "Size:974 MB" .
 Problems of Graphs  Problem set: exercises 19 and 20. Download this video . "Size:1.7GB" .
Monday, May 23th, 2011.
 Graphs  Lecture 8. Connectivity in multigraphs: Eulerian circuits, Eulerian multigraphs, Eulerian paths, semiEulerian multigraphs. Sufficient and necessary conditions for a multigraph to be Eulerian. Sufficient conditions for a multigraph to be semiEulerian. Download this video . "Size:1.57 GB" .
 Problems of Graphs  Problem set: exercises 16 and 18. Download this video . "Size:414 MB" .
Tuesday, May 17th, 2011.
 Graphs  Lecture 7. Connectivity in simple graphs: paths, simple paths, circuits, simple circuits. Connectivity in directed graphs. Connectivity between pair of vertices. Cut vertices and cut edges. Download this video . "Size:974 MB" .
 Problems of Graphs  Problem set: exercises 13. Download this video . "Size:1.7GB" .
Monday, May 16th, 2011.
 Graphs  Lecture 6. Induced graphs. Adjacency lists and adjacency matrix for simple graphs, pseudographs, and directed graphs. Adjacency matrix and isomorphism. Download this video . "Size:974 MB" .
 Problems of Graphs  Lecture 6. Problem set: exercises 10 to 12. Download this video . "Size:1.7GB" .
Friday, May 13th, 2011.
 Graphs  Lecture 4. Regular graphs and degree sequence. New graphs from old: subgraphs, union of graphs and complementary of graphs. Download this video . "Size:1.7GB"
 Problems of Graphs  Lecture 4. Problem set: exercises 2 and 4. Download this video . "Size:1.7GB" .
 Graphs  Lecture 5. Isomorphisms of graphs. Examples of isomorphic graphs.Graph invariants. Examples of nonisomorphic graphs. Download this video . "Size:1.7GB" .
 Problems of Graphs  Lecture 5. Problem set: exercises 5, 6, and 7. Download this video . "Size:1.7GB" .
Wednesday, May 11th, 2011.
 Graphs  Lecture 3. Special graphs: complete graphs, cycles, paths, wheels, and hypercubes. Bipartite graphs. Download this video . "Size:1.7GB" .
 Magic Effect  A Fibonaccibased magical effect. Project 5.. Download this video . "Size:405MB" .
Tuesday, May 10th, 2011.
 Graphs  Lecture 2. Modeling with graphs (continued): acquaintanceship graphs and call graphs. Basic terminology: adjacency, incidence, connectivity. Degree of a vertex in an undirected graph. The handshaking theorem and related results. Degree of a vertex in a directed graph. The handshaking theorem and related results for directed graphs.Download this video . "Size:1.68GB" .
Monday, May 9th, 2011.
 Graphs  Lecture 1. Introduction to graph theory. Definition of a graph. Vertex set, edge set. Types of graphs: simple graphs, multigraphs, pseudographs, directed graphs. Examples of those graphs. Modeling with graphs. Precedence graphs.Download this video . "Size:1.37GB" .
Wednesday, May 4th, 2011.
There was a review class and it was not recorded.
Tuesday, May 3th, 2011.
 Induction and Recursion  Lecture 12. Problem set: exercises 24 to and 26..Download this video . "Size:1.7GB" .
APRIL
Friday, April 29th, 2011.
 Induction and Recursion  Lecture 10. Problem set: exercises 9 .Download this video . "Size:1.34GB" .
 Induction and Recursion  Lecture 11.Problem set: exercise 19 .Download this video . "Size:5 GB".
Wednesday, April 27th, 2011.
 Induction and Recursion  Lecture 9. Problem set: exercises 9 and 11. Review of lists: definition of a list, length of a list, rest of a list, head of a list, concatenation of lists. Structural tree of a list. Depth of a list.Download this video . "Size:1.5GB" .
 Propositional Logic. Lecture 20. Problem set: exercise 19 .Download this video . "Size:441 MB"
Tuesday, April 26th, 2011.
 Induction and Recursion  Lecture 8. Problem set: exercises 6 to 8. Download this video . "Size:1.41GB" .
 Propositional Logic. Lecture 19. Problem set: exercise 18 (f).Download this video . "Size:605 MB" Warning: due to technical reasons, some parts of this video are not properly recorded. We apologize for the inconveniences.
Wednesday, April 13th, 2011.
 Induction and Recursion .Lecture 7. Distinction between recursion and induction. Problem set: exercises 2 to 5.Download this video . "Size:1.41GB" .
 Propositional Logic . Lecture 18. Problem set: exercise 18..Download this video . "Size:605 MB"
Tuesday, April 12th, 2011.
 Induction and Recursion. Lecture 6. Dependency trees and initial examples. Types of recursive functions to be dealt with. Formal definition of dependency trees. More examples.Download this video . "Size:1.29 GB" .
 Propositional Logic. Lecture 17. Problem set: exercise 17.Download this video . "Size:397 MB"
Monday, April 11, 2011.
 Induction and Recursion. Lecture 5. Recursive definition of sets. Examples: numerical sets, lists. Formal definition of lists. Functions on lists: LONG, REST, CAB, the set of LIST_p.Download this video . "Size:3.01 GB" .
 Propositional Logic . Lecture 16. Problem set: exercises 15 and 16.Download this video . "Size:474 MB"
Friday, April 8th, 2011.
 Induction and Recursion  Lecture 3 and Lecture 4. Recursive definitions of sets, sequences and maps/functions. Examples. Recursive correspondences. Welldefined recursive maps. Fibonacci numbers. More examples of induction proofs. Errors in inductive proofs. Examples.Download this video . "Size: GB" .
 Propositional Logic  Lecture 14. Continue problem 15.Download this video . "Size: MB" .
 Explanation of the Magic Effect about Riffle Shuffle. Additional clues to solve the magic effect for project 4. .Download this video . "Size: MB" .
Wednesday, April 6th, 2011.
 Induction and recursion  Lecture 2. WellOrdering Property. Proof of the equivalence between the WellOrdering Property and the Induction Principle. Other forms of induction. Strong induction. Examples.Download this video . "Size: 642MB" .
 Propositional Logic  Lecture 14. Continue problem 15.Download this video . "Size: 2.35GB" .
Tuesday, April 5th, 2011.
 Induction and recursion  Lecture 1. Properties depending on natural numbers. Inductive proofs: basis step and inductive step. Examples: summation and inequalities.Download this video . "Size: 2.35GB"
 Propositional Logic  Lecture 13. Problem 15. Download this video . "Size: 2.35GB" .
Monday, April 4th, 2011.
 Propositional Logic . Lecture 12. Problem set: exercises 11 a15. Download this video . "Size: 2.35GB" .
Friday, April 1st, 2011.
 Propositional Logic . Lecture 10. Replacement theorem. Further elaboration of tableaux rules (implication and biconditional). More on closed trees and unsatisfiable formulae. Deductive argument: hypotheses and conclusion. Correct and incorrect deductive arguments. Relation between argument correctness and unsatisfiable formulae.Download this video . "Size: 2.35GB" .
 Propositional Logic . Lecture 11. Types of proofs. Direct proof. Rules of inference. Proof by contradiction. Proof by contrapositive.Download this video . "Size: 819MB" .
 Magic Effect. Explanation of Magic Effect about Riffle Shuffle. Additional clues to solve the magic effect for project 4. .Download this video . "Size: 631 MB" .
MARCH
Wednesday, March 30th, 2011.
 Lecture 8. Problem set: exercises 7 to 10. Sets of formulae. Generalization of the satisfiable formula, tautology and contradiction to sets of formulae. Download this video . "Size: 2.32GB" .
Tuesday, March 29th, 2011.
 Lecture 7. Analytic tableaux. Simplifiable, developable, disjunctive and conjunctive formulae. Description of the construction of an analytic tableaux. Halting conditions. Obtaining the models from the tree. Determining whether a formula is tautology or contradiction. Examples. Download this video . "Size: 2.32GB" .
Monday, March 28th, 2011.
 Lecture 6. Logical equivalences as a equivalence relation. The class of the constant true and constant false. Results on equivalence relations. Download this video . "Size: 2.32GB" .
 Problem Set: exercises 1 to 6. Download this video . "Size: 2.32GB"
 Lecture 6. Logical equivalences as a equivalence relation. The class of the constant true and constant false. Results on equivalence relations. Download this video . "Size: 2.32GB" .
 Problem Set: exercises 1 to 6. Download this video . "Size: 2.32GB"
Friday, March 24th, 2011.
 Propositional Logic . Lecture 4. Semantics. Valuations. Meaningful valuations. Models of formulae. Nonmodels. Tautologies, contradictions and contingencies. Download this video . "Size: 2.32GB" .
 Propositional Logic . Lecture 5. Satisfiable formulae. Unsatisfiable formulae. Results relating tautology and satisfiable formulae, and contradiction and unsatisfiable formulae. Download this video . "Size: 964MB" .
 Magic Effect Magic Riffle Shuffle . On colours, suits and card values. Download this video . "Size: 397MB" .
Wednesday, March 23th, 2011.
 Propositional Logic  Lecture 3. Structural Recursion Principle (continued). Several examples including functions that transform formulae into formulae. Structural tree. Examples.Download this video . "Size: 2.07GB" .
Tuesday, March 22nd, 2011.
 Propositional Logic . Lecture 2. Logic Syntax. Primitive symbols. Propositional variables. Logical constants. Literal. Main connective. Formation rules for formulae. Order of precedence. Formula simplification. Structural Recursion Principle. Examples.Download this video . "Size: 2.19GB" .
Monday, March 21st, 2011.
 Propositional Logic . The purpose of logic. Propositions. Declarative sentences. Formal languages. Formalization. Simple and compound statements. Connectives: negation, disjunction, exclusive or, conjunction, implication and biconditional connectives. Table truth of connectives. Converse, contrapositive and inverse of an implication. Translating English sentences to a formal language. Necessary and sufficient conditions.Download this video . "Size: 1.8GB" .
 Magic Effect. Explanation of Magic Effect .Download this video . "Size: 651 MB" .
Wednesday, March 16th, 2011.
 Combinatorics 11. Problems .Download this video . "Size: 2.5GB" .
Tuesday, March 15th, 2011.
 Combinatorics 10. Problems from the Moodle platform. Problem set: problems 10, 16, and 17.Download this video . "Size: 861 MB" .
 Magic Effect Combinatorics. A probabilistic magic effect. Download this video . "Size: 651 MB" .
Friday, March 11th, 2011.
 Combinatorics 9 . Discrete probability. Random experiments. Outcomes. Sample space. Probability functions. Elementary events. Event operations in terms of set operations. Properties of events. Laplace's rule. Examples. Problem set: problems 15  17 Download this video . "Size: 2.26GB" .
Wednesday, March 9th, 2011.
 Combinatorics 8 . Problems on permutation with repetitions, rpermutations with repetitions and combinations with repetitions. Counting the number of natural solutions of a linear equation. Problems 1014. Download this video. "Size: 2.20GB"
Tuesday, March 8th, 2011.
 Combinatorics 7 . Review of counting techniques. Counting with repetitions. rPermutations with repetitions. Permutations with repetitions. Solving an integer equation. Combinations with repetitions. Download this video. "Size: 1.70GB"
Monday, March 7th, 2011.
 Combinatorics 6 . The damned problem 9, solved in two ways: by using the complement and by computing directly the desired cardinality. Binomial Theorem. Proof of the Binomial Theorem. Properties that can be proved through the Binomial Theorem. Download this video. "Size: 1.76GB"
Friday, March 4th, 2011.
 Combinatorics 4  Lecture 1/2 Problem on combinatorics: problem 5. Counting set by removing the order a list. Combinations. Binomial coefficients. Combinatorial proof. Pascal's identity. Pascal triangle. Download this video. "Size: 1.43GB"
 Combinatorics 4  Lecture 2/2 Problem on combinatorics: problem 6, 7, 8.Download this video. "Size: 527MB"
 Magic Effect: A 5card magic effect (project 3).Download this video. "Size: 759MB"
Tuesday, March 1st, 2011.
 Combinatorics 3  The Pigeon Principle. The Generalized Pigeon Principle. Ordered selections of elements. Permutations. rPermutations. Examples Download this video. "Size: 1.8GB"
FEBRUARY
Monday, February 28th, 2011.
 Solution to Project 2. Solution to Project 2.Download this video. "Size: 811MB"
 Problems on combinatorics 1. Problems on the sum rule and the product rule.Download this video. "Size: 1.0GB"
Friday, February 25th, 2011.
 Combinatorics  Class 1: the art of counting, sum rule, product rule, general strategy to solve combinatorics problems. Examples: counting divisors, bit strings, maps, injective maps Download this video. "Size: 1.78GB"

Combinatorics  Class 2: inclusionexclusion principle. Examples of this principle using divisibility. Download this video. "Size: 1.43GB"
 Explanation Magic Prediction by Piling. 2. Further explanation of Project 2: function g(x), f2(x), relation between x and k. Download this video. "Size: 1.67GB"
Wednesday, February 23rd, 2011.
 Problems on Order Relations  5. Problems on Order Relations  class 5: quotient sets and Hasse diagrams. Download this video. "Size: 1.67GB"
 Work on Project 2. Work on Project 2: how to define the required functions. Download this video. "Size: 303MB "
Tuesday, February 22nd, 2011.
 Order Relations  4. Ordering Relations: posets, comparable elements, total ordering, Hasse diagrams, maximal elements, minimal elements, maximum element, and minimum element. Download this video. Size: 1.26GB.
 Problems on Order Relations. Problems on order relations. Download this video. Size: 520MB.
Monday, February 21st, 2011.
 Equivalence Relations and Partitions  3. Equivalence relations, Theorem 1 (on page 560) on how an equivalence relation induces a partition, definition of partition, relation between equivalence relations and partitions. Problems on relations. Download this video.
Friday, February 18th, 2011.
The class consisted of group work and there was no recording of the class that day.
Wednesday, February 16th, 2011.
 Relations  2. Relations class 2. Download this video.
 Problems Relations class 1. Download this video.
Tuesday, February 15th, 2011.
 Relations class 1: general definition of relation. Graphical representation of relations: sagittal diagrams. Relations on a set. Reflexive, symmetric, antisymmetric and transitive relations. Equivalence and order relations. Download this video.
 Explanation Magic Prediction by Piling. Clarification of some points about the project Magic Prediction by Piling. Download this video.
Monday, February 14th, 2011.
 Functions class 2: invertible functions, function composition, the floor function. Download this video.
 Magic Effect: Prediction by Piling. Download this video.
Friday, February 10th, 2011.
 Sets and Functions  3. Set operations: union, intersection, complement, difference. Functions: correspondence, maps, functions; injective, surjective and bijective functions. Download this video.
 Magic Effect. Explanation of the 1089 magic effect. Download this video.
Wednesday, February 9th, 2011.
 English Phonectics 3. Review of vowels, consonants, semiconsonants, pronunciation of plurals, pronunciation of possessives, pronunciation of the third person of singular of Present Simple.
 Sets  2: power set, number of elements of the power set, questions from the problem set. Download this video.
Tuesday, February 8th, 2011.
 English Phonetics  2.
 Sets  1: definition of a set, set membership, set equality, set inclusion, important sets. Download this video.
Monday, February 7th, 2011.
 Presentation  1/1. Course Information. Download this video.
 Presentation  1/2. English Phonetics  1. Download this video.
 Presentation  1/3. A Magic Effect. Download this video.