MIT OpenCourseWare Courses

Casework and Strong Induction - Lecture 3

Master advanced proof techniques including casework and strong induction to strengthen your mathematical reasoning skills in computer science applications.

• YouTube
• 1 hour 24 minutes
• Self-Paced
• Free Video

Relations and Counting - Lecture 15

Explore relations, equivalence relations, and partial orders on sets, then dive into fundamental counting principles for computer science applications.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

Connectivity and Trees - Lecture 13

Explore graph connectivity and tree structures through optimization problems like finding shortest and fastest routes in this MIT mathematics lecture.

• YouTube
• 1 hour 22 minutes
• Self-Paced
• Free Video

Divisibility - Number Theory and Applications Through GCD and Extended Euclidean Algorithm - Lecture 8

Explore number theory fundamentals through divisibility, greatest common divisor (GCD), and the Extended Euclidean Algorithm in this MIT mathematics lecture.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

Predicates, Sets, and Proofs - Lecture 1

Explore fundamental mathematical concepts including predicates, sets, and proof techniques essential for computer science applications and logical reasoning.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

More Counting Techniques - Pigeonhole Principle - Lecture 17

Explore advanced counting methods including the pigeonhole principle to tackle complex mathematical problems in computer science applications.

• YouTube
• 1 hour 21 minutes
• Self-Paced
• Free Video

Probability - Lecture 18

Discover rigorous probability analysis for computer science through step-by-step methods, moving beyond intuition to mathematical foundations in this MIT mathematics lecture.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Large Deviations - Chebyshev and Chernoff Bound, Wrap Up - Lecture 24

Explore large deviation theory through Chebyshev and Chernoff bounds in this comprehensive mathematics lecture for computer science applications.

• YouTube
• 1 hour 23 minutes
• Self-Paced
• Free Video

Graphs and Coloring - Lecture 11

Explore graph theory fundamentals and coloring techniques essential for computer science applications in scheduling, communications, and search engines.

• YouTube
• 1 hour 21 minutes
• Self-Paced
• Free Video

Random Variables - Lecture 21

Explore probability mass functions and cumulative distribution functions as equivalent methods for expressing random variable distributions in mathematics for computer science.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Sums - Approximation Methods for Recurrences and Algorithms - Lecture 5

Master sum approximation techniques including perturbation, ansatz method, and integral method for recurrences, counting, probability, and algorithm analysis.

• YouTube
• 1 hour 22 minutes
• Self-Paced
• Free Video

Cryptography - Lecture 10

Discover how GCDs and modular arithmetic form the mathematical foundation of computer security through practical cryptographic applications.

• YouTube
• 1 hour 21 minutes
• Self-Paced
• Free Video

Expectation and Variance - Lecture 23

Explore expectation and variance concepts in probability theory through advanced mathematical analysis for computer science applications.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Contradiction and Induction - Lecture 2

Master fundamental proof techniques including contradiction and mathematical induction essential for computer science mathematics.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

Digraphs and DAGs - Lecture 14

Explore directed graphs (digraphs), their walks, cycles, and connectivity, plus Directed Acyclic Graphs (DAGs) with no cycles in this MIT mathematics lecture.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video