Learning objectives:

In education, learning objectives are brief statements that describe precisely what students will be expected to learn.

This section will be updated as we move along the material. With this information you can prepare for the midterm and final exams.

NEW: Here are the learning objectives for the all the sections of the course.

Lectures:

Lecture 1, Jan 7th: Introduction to the course. See the slides
Lecture 2, Jan 11th: Propositional Logic: Propositions, logical operators and truth tables. (Section 1.1 in textbook)
Lecture 3, Jan 12th: Propositional Logic: Conditional and Biconditional Statements; logical equivalence. (Section 1.1 and 1.3 in textbook)
Lecture 4, Jan 14th: Propositional Logic: Tautologies and Important logical equivalences (e.g. De Morgan's laws). See Table.
(Section 1.3 in textbook, Table and Examples 7-8)
Lecture 5, Jan 18th: Applications to Propositional Logic: Circuits. (Section 1.2 in textbook)
Lecture 6, Jan 19th: Predicate Logic. (Sections 1.4-1.5 in textbook)
Lecture 7, Jan 21st: Predicate Logic and Applications to Propositional Logic: Final remarks on the logic circuit examples and negating statements with quantifiers.
Lecture 8, Jan 25th: Proof Methods: Rules of inference and Introduction to proofs. (Sections 1.6-1.7 in textbook)
Lecture 9, Jan 26th: Proof Methods: Direct Proof, Proof by contradiction, proof by cases. (Section 1.8 in textbook)
Lecture 10, Jan 28th: Proof Methods: Mathematical Induction, Strong Induction and Pigeonhole principle. (Sections 5.1-5.2 and 6.2 in textbook)
Lecture 11, Feb 1st: Sets and functions: Sets operations, Venn Diagrams and Computer representation of sets. See the slides (Section 2.1-2.2 in textbook)
Lecture 12, Feb 2nd: Sets and functions: Functions, cardinality of sets, sums and sequences. See the slides (Section 2.3-2.5 in textbook)
Lecture 13, Feb 4th: Algorithms: Comparing Algorithm properties with functions. Growth of functions.(Section 3.2-3.3 in textbook)
Lecture 14, Feb 8th: Algorithms: Growth of functions. (Section 3.2-3.3 in textbook)
Lecture 15, Feb 9th: Number Theory: The division algorithm. Modular arithmetic (applications) and GCD as linear combinations (Section 4.1 and 4.3 in textbook)
Lecture 16, Feb 11th: Number Theory: Prime decomposition (gcd and lcm) and applications to modular arithmetic. Fermat's Little Theorem(Section 4.3-4.5 in textbook)
Lecture 17, Feb 15th: Number Theory: Cryptology: Caesars cipher, Vigenere's cipher and RSA Encryption (Section 4.4 and 4.6 in textbook)
Lecture 18, Feb 16th: Reivew: Methods of evalution. Guidelines to submit assignment 6.
Lecture 19, Feb 18th: Recursive structures: Recursive sequences, recursive and iterative algorithm, correctness of recursive algorithms
See the slides (Sections 5.3,5.4 in textbook)
Lecture 20, Feb 22nd: Recursive structures: Divide and conquer algorithms, asymptotic upper bounds for its time complexity. Solving linear (homogeneous) recurrences.
See the slides (Sections 8.1-8.3 in textbook)
Lecture 21, Feb 23rd: Reivew: Practice Exam
Exam, Feb 25th: Midterm.

Lectures after reading week:

Lecture 1, March 7th: Combinatorics: Counting rules, permutations and combinations.
See the slides and exercises (Sections 6.1, 6.3 in textbook)
Lecture 2, March 8th: Combinatorics: Binomial coeffients and combinatorial proofs. (Section 6.4 in textbook)
Lecture 3, March 10th: Combinatorics: Advanced combinatorics, introduction to discrete probability. (Sections 6.5,7.1 in textbook)
Lecture 4, March 14th: Probability: Basic properties, conditional probability. (Section 7.2 in textbook)
Lecture 5, March 15th: Probability: Conditional probabilities and Bayes theorem.(Section 7.3 in textbook)
Lecture 6, March 17th: Probability: Basic properties of mean, examples and basic random variables. (Section 7.4 in textbook)
Lecture 7, March 21th: Relations: Definitions, representation with matrices and digraphs. (Section 9.1, 9.3 in textbook)
Lecture 8, March 22nd: Relations: Properties and equivalence relations. Definitions of paths in graphs and digraphs (Section 9.5 and 10.2 in textbook)
Lecture 9, March 24th: Relations Warshall's algorithm for the transitive closure of relations (Section 9.4 in textbook)
Lecture 10, March 29th: Graph Theory: Connectivity, connected components, degree of vertices etc. (Section 10.4 in textbook)
Lecture 11, March 31st: Graph Theory: Euler and Hamiltonian paths/circuits, complete matching problem (Section 10.2,10.5 in textbook)
Lecture 12, April 4th: Graph Theory : Planarity and Colouring. (Sections 10.7-8 in textbook)
Lecture 13, April 5th: Trees: Definitions and m-ary trees (Section 11.1 in textbook)
Lecture 14, April 7th: Trees: Spanning trees and minimum spanning trees: BFS,DFS and Kruskal's algorithm (Section 11.4-5 in textbook)
Lecture 15, April 11th: Trees: Minimum spanning trees: Prim's algorithm (Section 11.5 in textbook)
Lectures 16, April 12th: Probability Review . See the slides .
Lectures 17, April 14th: Relations/Graphs/Tree Review : See the slides . And a See the brief overview about the final exam