CS-101: Advanced information, computation, communication I

Lectures in this course (220)

Introduces structural induction, a method to prove properties of elements in recursively defined sets.

Analyzes the growth of functions to understand algorithm efficiency and uses Big-O notation for characterization.

Explains recursive algorithms for factorial, exponentiation, and search problems.

Explains Big-O notation for algorithm complexity analysis through polynomial examples and growth rate identification.

Covers big-O estimates for factorial function and combinations of functions.

Explains recursion, induction, and proving algorithm correctness through mathematical induction.

Covers the concept of Merge Sort, a highly efficient recursive sorting algorithm.

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

Covers number theory, division, remainder, congruence, prime numbers, integer representation, and the Euclidean algorithm.

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

Covers the complexity analyses of algorithms and their worst-case time complexities.

Covers fundamental concepts in number theory with examples and quizzes.

Covers examples of modular exponentiation, complexities, Lame's Theorem, Collatz Conjecture, and prime numbers.

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

Explores the concept of division in number theory, including properties, algorithms, and examples.

Covers complexity classes, effect on computer time, tractable problems, class NP, and NP-complete problems.

Explains mathematical induction for proving propositions true for all positive integers.

Explains congruence modulo m and its applications in arithmetic operations.

Explains modular arithmetic operations and properties, including commutative rings and multiplicative inverses.

Covers mathematical proofs by induction, inequalities, divisibility, and subsets.

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