Core Theory
This section covers the theoretical foundations of computer science, focusing on algorithms, data structures, and computational complexity. These concepts are essential for solving problems efficiently and understanding the limits of computation.
Topics Covered
- Divide and conquer
- Sorting and searching
- Randomized algorithms
- Graph search
- Shortest paths
- Data structures
- Greedy algorithms
- Minimum spanning trees
- Dynamic programming
- NP-completeness
- And more
Course Sequence
| Course | Duration | Effort | Prerequisites |
|---|---|---|---|
| Divide and Conquer, Sorting and Searching, and Randomized Algorithms | 4 weeks | 4-8 hours/week | Any programming language, Mathematics for Computer Science |
| Graph Search, Shortest Paths, and Data Structures | 4 weeks | 4-8 hours/week | Divide and Conquer, Sorting and Searching, and Randomized Algorithms |
| Greedy Algorithms, Minimum Spanning Trees, and Dynamic Programming | 4 weeks | 4-8 hours/week | Graph Search, Shortest Paths, and Data Structures |
| Shortest Paths Revisited, NP-Complete Problems and What To Do About Them | 4 weeks | 4-8 hours/week | Greedy Algorithms, Minimum Spanning Trees, and Dynamic Programming |
Why These Courses?
This sequence, taught by Tim Roughgarden of Stanford University, provides a comprehensive introduction to algorithms and theoretical computer science:
- Divide and Conquer introduces fundamental algorithm design paradigms and analysis techniques
- Graph Search and Data Structures covers graph algorithms and efficient data organization
- Greedy Algorithms and Dynamic Programming teaches powerful problem-solving approaches
- NP-Complete Problems explores computational complexity and the limits of efficient computation
Learning Outcomes
After completing the Core Theory sequence, you will be able to:
- Analyze algorithm efficiency using asymptotic notation
- Design efficient algorithms using various paradigms (divide-and-conquer, greedy, dynamic programming)
- Choose appropriate data structures for different problems
- Understand computational complexity classes
- Recognize NP-complete problems and approaches for handling them
- Apply algorithmic thinking to solve new problems efficiently
Importance for Computer Science
Algorithmic thinking is central to computer science because:
- It enables you to solve problems efficiently, saving computational resources
- It provides a language for reasoning about problem difficulty
- It gives you tools to recognize when problems might be inherently hard to solve
- It forms the foundation for fields like artificial intelligence, cryptography, and optimization
- It helps you write code that scales to large inputs
The theoretical concepts from this section underpin virtually every area of computer science and are essential for technical interviews at leading technology companies.