CS-101: Advanced information, computation, communication I

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Lectures in this course (220)

Equivalence Relations: Classes, Partitions

Explains equivalence relations, classes, and partitions in sets.

Inference Rules in Propositional Logic

Covers inference rules in propositional logic and common logical fallacies.

Partial Ordering: Relations, Sequences, Summation

Introduces partial orderings, lattices, and lexicographic orderings on Cartesian products.

Counting: Bit Strings and Committees

Explores counting bit strings, committees, balls distribution, poker hands, and coefficients, with examples of the Pigeonhole Principle and card selection.

Sequences: Relations, Summation, Strings

Covers arithmetic and geometric progressions, strings, and recurrence relations in sequences.

Counting with Recurrence Relations

Covers counting with recurrence relations, focusing on bit strings and the Tower of Hanoi problem.

Number Sequences: Guessing, Modeling, and Solving Recurrence Relations

Covers the identification of number sequences, modeling population growth, and solving recurrence relations.

Linear Recurrence Relations: Solving Techniques

Explores linear homogeneous recurrence relations, solving techniques, characteristic equations, and examples like Fibonacci numbers.

Summation and Sequences: Notation and Formulas

Covers summation notation, product notation, and geometric series formulas.

Advanced Counting: Linear Homogeneous Recurrence Relations and Generating Functions

Explores solving linear homogeneous recurrence relations and generating functions for sequence formulas.

Proofs: Arguments in Predicate Logic

Covers rules of inference for quantified statements and constructing valid arguments using predicate logic.

Cardinality of Sets: Countable and Uncountable

Explores countable and uncountable sets, demonstrating how to determine the cardinality of different sets through listing elements in a sequence.

Algorithms: Organisational Questions

Covers organizational issues, exercise content, COVID regulations, mock exam plans, and a mid-semester survey.

Advanced Counting: Generating Functions and Recurrence Relations

Explores generating functions, recurrence relations, and advanced counting techniques.

Extended Binomial Theorem

Explores the Extended Binomial Theorem and counting problems using generating functions.

Algorithms: Summary of the week

Covers algorithms for searching, sorting, optimization, and the Halting Problem.

Probability: Short History and Basic Concepts

Explores the short history of probability and basic concepts like sample space and event.

Algorithms: Halting Problem Quiz

Explores the Halting Problem, efficient list element positioning, and the cashier's algorithm.

Marriage Problem: Gale Shapley Algorithm

Covers the Marriage Problem and the Gale Shapley Algorithm to find stable matches.

Conditional Probability: Understanding Independence

Explores conditional probability and independence between events, using dice roll examples to illustrate fundamental probability concepts.

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