CS-101: Advanced information, computation, communication I

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Lectures in this course (309)

Strong Induction: The Power of Mathematical Proof

Explores strong induction as a powerful proof method with advantages over mathematical induction, demonstrated through a theorem about expressing integers as sums of powers of two.

Recursively Defined Functions

Introduces recursively defined functions and demonstrates how to compute values and prove properties using mathematical induction.

Propositional Logic: Examples

Covers interesting facts about propositional logic and Sudoku solving strategies.

Recursively Defined Sets and Structures

Explores recursively defined sets, natural numbers, strings, functions, string concatenation, and well-formed formulae.

Structural Induction

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

Recursive Algorithms: Factorial, Exponentiation, Search

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

Recursion and Induction: Proving Algorithms Correctly

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

Recursive Sorting: Merge Sort

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

Number Theory: Division, Remainder, Congruence

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

Number Theory: Quiz

Covers fundamental concepts in number theory with examples and quizzes.

Number Theory: Modular Exponentiation Examples

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

Number Theory: Division

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

Number Theory: Congruence

Explains congruence modulo m and its applications in arithmetic operations.

Introduction & Propositional Logic

Covers the basics of propositional logic, logical connectives, truth tables, and compound propositions.

Propositional Logic: Translations and Equivalences

Covers translating natural language to propositional logic and proving tautologies.

Counting: Permutations and Combinations

Covers permutation, combination, and the pigeonhole principle in counting problems.

Discrete Mathematics: Logic, Structures, Algorithms

Covers the basics of discrete mathematics, including logic, structures, and algorithms.

Predicate Logic: Quantifiers, CNF, DNF

Covers Predicate Logic, focusing on Quantifiers, CNF, and DNF.

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