CS-101: Advanced information, computation, communication I

Lectures in this course (220)

Covers set equality, subsets, proper subsets, and techniques for showing equality of sets.

Covers the time complexity of algorithms and includes a quiz.

Explains constructing sets and determining set cardinality.

Explores examples of algorithm complexity, sorting, and polynomial computations.

Covers set operations and their relations to propositional logic, including cardinality.

Analyzes the growth of functions to understand algorithm complexity and efficiency.

Covers set identities and different approaches to prove them, including set builder notation and membership tables.

Explains Big-O notation for algorithm complexity and polynomial growth rates.

Covers the basics of functions, including domain, codomain, image, and range, as well as injections, surjections, and bijections.

Explores advanced big-O facts for powers, logarithms, factorials, and function combinations.

Explains Big-Omega, Big-Theta, and Little-o notations for functions and polynomials.

Covers inverse functions, function composition, partial functions, and graphical representation of functions.

Introduces time complexity and worst-case analysis of algorithms, abstracting computational complexity from implementation details.

Covers binary relations, functions, set operations, composition, and n-ary relations.

Covers the complexity analyses of search and sorting algorithms.

Explains binary relations on a set and their properties with illustrative examples.

Covers equivalence relations, classes, and partitions of a set.

Covers matrix notation, arithmetic, multiplication algorithms, and complexity analysis.

Explores partial orderings, divisibility relations, lattices, lexicographic ordering, comparability, and total orderings.

Covers complexity classes, tractable problems, the class NP, NP-complete problems, and summarizes the concept of tractable problems.

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