Computer Science Fundamentals

A curriculum covering the foundational concepts of computer science, equivalent to an undergraduate CS degree.

Course Overview

This course is organized into 18 modules, progressing from mathematical foundations through advanced topics like distributed systems and machine learning. Each module builds upon previous concepts.

Estimated Study Time: 400-500 hours total

Curriculum

Module 1: Discrete Mathematics

The mathematical foundation for computer science

1. Logic and Proofs
2. Set Theory
3. Relations and Functions
4. Combinatorics
5. Graph Theory Fundamentals

Module 2: Programming Fundamentals

Core programming concepts and paradigms

1. Introduction to Programming
2. Data Types and Variables
3. Control Structures
4. Functions and Scope
5. Object-Oriented Programming
6. Error Handling and Debugging

Module 3: Data Structures

Organizing and storing data efficiently

1. Arrays and Dynamic Arrays
2. Linked Lists
3. Stacks and Queues
4. Hash Tables
5. Trees and Binary Search Trees
6. Heaps and Priority Queues
7. Graphs

Module 4: Algorithms

Solving problems efficiently

1. Algorithm Analysis and Big O
2. Searching Algorithms
3. Sorting Algorithms
4. Recursion and Divide-and-Conquer
5. Dynamic Programming
6. Greedy Algorithms
7. Graph Algorithms

Module 5: Computer Architecture

How computers work at the hardware level

1. Number Systems and Binary
2. Logic Gates and Circuits
3. CPU Architecture
4. Memory Hierarchy
5. Assembly Language Basics

Module 6: Operating Systems

Managing computer resources

1. OS Overview and Processes
2. Threads and Concurrency
3. Memory Management
4. File Systems
5. Synchronization and Deadlocks

Module 7: Databases

Storing and retrieving data

1. Introduction to Databases
2. Relational Model and SQL
3. Database Design and Normalization
4. Indexing and Query Optimization
5. Transactions and ACID

Module 8: Networking

How computers communicate

1. Network Fundamentals and OSI Model
2. TCP/IP Protocol Suite
3. Application Layer Protocols
4. Network Security Basics
5. Socket Programming

Module 9: Theory of Computation

The theoretical limits of computing

1. Finite Automata
2. Regular Languages and Expressions
3. Context-Free Grammars
4. Turing Machines and Computability

Module 10: Software Engineering

Building maintainable software

1. Version Control with Git
2. Software Development Lifecycle
3. Design Patterns
4. Testing Strategies
5. Clean Code Principles

Module 11: Security Fundamentals

Protecting systems and data

1. Security Principles
2. Cryptography Basics
3. Authentication and Authorization
4. Common Vulnerabilities

Module 12: Probability & Statistics for CS

Mathematical foundations for data analysis and algorithms

1. Probability Fundamentals
2. Random Variables and Distributions
3. Statistical Inference
4. Randomized Algorithms

Module 13: Linear Algebra for CS

Mathematical tools for graphics, ML, and data science

1. Vectors and Matrices
2. Linear Systems and Transformations
3. Eigenvalues and Applications

Module 14: Compilers & Interpreters

How programming languages are implemented

1. Lexical Analysis
2. Parsing
3. Semantic Analysis
4. Code Generation

Module 15: Distributed Systems

Building reliable systems across multiple machines

1. Distributed Systems Fundamentals
2. Consensus and Coordination
3. Replication and Consistency

Module 16: Parallel Computing

Harnessing multiple processors for performance

1. Parallel Computing Fundamentals
2. Threading and Synchronization
3. Concurrent Patterns
4. GPU and Parallel Hardware

Module 17: Functional Programming

A different paradigm for building software

1. Functional Programming Foundations
2. Higher-Order Functions
3. Advanced Functional Concepts

Module 18: Machine Learning Fundamentals

Teaching computers to learn from data

1. Machine Learning Fundamentals
2. Supervised Learning
3. Neural Networks

How to Use This Course

1. Sequential Learning: Modules are designed to be completed in order
2. Practice: Each reading includes exercises - complete them before moving on
3. Projects: Build small projects to reinforce concepts
4. Review: Revisit earlier modules as needed when concepts resurface

Prerequisites

• Basic computer literacy
• Ability to install software and use a terminal
• High school level mathematics

Recommended Tools

• A text editor (VS Code, Vim, etc.)
• Python 3.x (for code examples)
• Git
• A Unix-like terminal (Linux, macOS, or WSL on Windows)