CS-101: Advanced information, computation, communication I

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Lectures in this course (220)

Sequences: Arithmetic and Geometric Progressions

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

Induction and Recursion: Mathematical and Strong Induction - An Example

Covers the concepts of mathematical and strong induction through an example.

Induction and Recursion: Organizational Questions

Covers updates on course materials, a questionnaire, and additional videos.

Number Sequences: Guessing, Fibonacci, Recurrence Relations

Covers the identification of number sequences and solving recurrence relations.

Induction and Recursion: Summary

Covers mathematical induction, recursively defined functions, and iterative algorithms for problem-solving.

Summation and Sequences: Notations and Formulas

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

Cardinality of Sets: Countable and Uncountable

Explores cardinality, countable sets, and examples of countable and uncountable sets.

Induction and Recursion: Quiz

Covers topics related to induction and recursion, including mathematical induction proofs and recursive definitions.

Induction and Recursion: Examples + Q&A

Covers examples and a Q&A session on induction and recursion.

Algorithms: Finding Maximum Value in a Sequence

Covers algorithm specification and finding maximum value in a sequence of integers.

Mathematical Recursion: Induction and Recursion

Covers the principle of mathematical induction for proving propositions true for all positive integers.

Searching Algorithms: Linear and Binary Search

Covers linear and binary search algorithms for locating items in lists.

Sorting Algorithms: Bubble and Insertion Sort

Covers the basic sorting algorithms Bubble Sort and Insertion Sort.

Mathematical Induction: Proofs and Subsets

Covers proofs by mathematical induction and the number of subsets of a finite set.

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.

Optimization Algorithms: Greedy Approach

Explores optimization problems, greedy algorithms, and the Cashier's Algorithm for finding the least total number of coins.

Recursively Defined Functions

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

Algorithms: Stable Matchings

Covers the concept of stable matchings and the Gale-Shapley algorithm.

Recursively Defined Sets and Structures

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

Halting Problem: Unsolvable Problems

Explores the unsolvability of the halting problem in algorithms and the limitations of procedures in determining program halting.

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