Complete Computer Science Education

MIT + Stanford + Carnegie Mellon University

Format: 8 semesters / 4 years Reference universities: MIT, Stanford, Carnegie Mellon University Course codes: Actual university course numbers Purpose: A comprehensive undergraduate CS education covering programming, mathematics, algorithms, systems, software engineering, databases, networking, AI/ML, theory, security, graphics, HCI, distributed systems, compilers, and advanced specialization.

Important: This is a synthesized curriculum. The courses are real courses from MIT, Stanford, and CMU, but the semester-by-semester combination is not an official degree plan from any one university.

YEAR 1 — PROGRAMMING & MATHEMATICAL FOUNDATIONS

Semester 1 — Programming + Mathematics

Computer Science

MIT 6.1000 — Introduction to Programming and Computer Science
Stanford CS106A — Programming Methodology
CMU 15-122 — Principles of Imperative Computation

Mathematics

CMU 21-122 — Integration and Approximation
CMU 15-151 — Mathematical Foundations for Computer Science
Stanford MATH51 — Linear Algebra and Differential Calculus of Several Variables

General Education

CMU 07-128 — First Year Seminar
CMU 99-101 — Core@CMU
Humanities / Arts elective

Main concepts

Variables
Types
Functions
Control flow
Recursion
Data representation
Debugging
Testing
Algorithmic thinking
Mathematical proof
Logic
Sets
Functions
Linear algebra fundamentals
Calculus

Semester 2 — Abstraction + Computer Systems

Programming

MIT 6.1010 — Fundamentals of Programming
Stanford CS106B — Programming Abstractions
CMU 15-150 — Principles of Functional Programming
Stanford CS242 or CMU's Type Systems Courses - Modern systems increasingly rely on type safety, invariants, and formal methods (Rust, type systems, formal proofs).

Systems

Stanford CS107 — Computer Organization and Systems
CMU 15-213 — Introduction to Computer Systems
MIT 6.1910 — Computation Structures (true hardware-to-software depth)
CMU 18-447 or UC Berkeley's CS61C - rounds out digital logic and processor microarchitecture.

Mathematics

MIT 18.06 — Linear Algebra
CMU 21-259 — Calculus in Three Dimensions

General Education

Science / Engineering course
Humanities / Arts course

Main concepts

Object-oriented programming
Functional programming
Abstract data types
Recursion
Memory
Pointers
C
Assembly
Machine representation
CPU
Caches
Linking
Compilation
Processes
Basic systems programming

Stanford's current CS curriculum identifies CS106B as Programming Abstractions and CS107 as Computer Organization and Systems; CMU's curriculum similarly includes 15-150 and 15-213 in its core.

YEAR 2 — CORE COMPUTER SCIENCE

Semester 3 — Data Structures, Algorithms & Probability

Data Structures

CMU 15-210 — Parallel and Sequential Data Structures and Algorithms
Stanford CS161 — Design and Analysis of Algorithms

Theory

MIT 6.1200 — Mathematics for Computer Science
Stanford CS103 — Mathematical Foundations of Computing

Probability

Stanford CS109 — Introduction to Probability for Computer Scientists
MIT 6.3700 — Introduction to Probability

Systems

MIT 6.1910 — Computation Structures

General Education

Science / Engineering course
Humanities / Arts course

Main concepts

Arrays
Linked lists
Stacks
Queues
Trees
Heaps
Hash tables
Graphs
Sorting
Searching
Divide and conquer
Greedy algorithms
Dynamic programming
Complexity analysis
Probability
Combinatorics
Graph theory
Mathematical proofs
Digital logic
Computer architecture

MIT's current 6-3 curriculum explicitly includes Mathematics for Computer Science, Introduction to Algorithms, Computability and Complexity Theory, Computation Structures, and probability/inference options.

Semester 4 — Algorithms, OS, Databases & Theory

Algorithms

MIT 6.1210 — Introduction to Algorithms
CMU 15-451 — Algorithm Design and Analysis

Operating Systems

Stanford CS111 — Operating Systems Principles

Databases

Stanford CS145 — Data Management and Data Systems

Theory

Stanford CS154 — Introduction to the Theory of Computation
MIT 6.1400 — Computability and Complexity Theory

Software Engineering

MIT 6.1020 — Software Construction

Main concepts

Advanced algorithms
Graph algorithms
Shortest paths
Network flow
NP-completeness
Reductions
Automata
Formal languages
Computability
Processes
Threads
Synchronization
Virtual memory
File systems
SQL
Relational algebra
Transactions
Indexes
Query processing
Software architecture
Testing
Version control

MIT's current 6-3 core includes 6.1020, 6.1210, 6.1400/6.1220, and a systems choice among 6.1800, 6.1810, or 6.5831.

YEAR 3 — SYSTEMS, SOFTWARE & INTELLIGENCE

Semester 5 — Operating Systems, Networks & AI

Operating Systems

MIT 6.1810 — Operating System Engineering
CMU 15-410 — Operating System Design and Implementation

Networking

CMU 15-441 — Networking and the Internet

Artificial Intelligence

Stanford CS221 — Artificial Intelligence: Principles and Techniques

Machine Learning

Stanford CS229 — Machine Learning

Security

Stanford CS155 — Computer and Network Security
Applied Cryptography / Hardware Security: Beyond general web security (CS155), ensure concepts like public-key cryptosystems, zero-knowledge fundamentals, side-channel attacks, and enclave computing (TEE/SGX) are represented.

Main concepts

Operating Systems

Processes
Threads
Scheduling
Synchronization
Locks
Deadlocks
Virtual memory
Paging
File systems
System calls
Kernel design

Networking

TCP/IP
Ethernet
Routing
Congestion control
Flow control
DNS
HTTP
Network security
Distributed communication

AI

Search
Planning
Knowledge representation
Reasoning
Decision making
Probabilistic models

Machine Learning

Linear regression
Logistic regression
Classification
Regularization
Optimization
Neural networks
Model evaluation

Security

Cryptography
Authentication
Authorization
Network attacks
Secure systems
Web security

CMU currently lists 15-410, 15-411, 15-418, 15-440, 15-441 and 15-445 as its systems-elective family, while Stanford's current course schedule includes CS111, CS155, CS221 and CS229.

Semester 6 — Distributed Systems, Databases, Compilers & AI

Distributed Systems

MIT 6.5840 — Distributed Systems (widely considered the best distributed systems course)
CMU 15-440 — Distributed Systems

Database Systems

CMU 15-445 — Database Systems
MIT 6.5831 — Database Systems

Compilers

CMU 15-411 — Compiler Design
Stanford CS143 — Compilers

Programming Languages

Stanford CS242 — Programming Languages

Machine Learning / AI

CMU 10-301 — Introduction to Machine Learning
Stanford CS236 — Deep Generative Models

Main concepts

Distributed systems

RPC
Concurrency
Distributed state
Replication
Fault tolerance
Consensus
Distributed storage
Failure handling
Monitoring

Databases

Storage engines
B-trees
Hash indexes
Query optimization
Transactions
ACID
Concurrency control
Recovery
Logging
Distributed databases
Parallel query execution

Compilers

Lexical analysis
Parsing
AST
Type checking
Semantic analysis
Intermediate representation
Optimization
Code generation
Runtime systems

Programming languages

Type systems
Lambda calculus
Functional programming
Language semantics
Interpreters
Static analysis

CMU describes 15-445 as a course in the design and implementation of database systems, covering storage, indexing, transactions, recovery, query processing and parallel architectures. Its 15-411 course covers compiler and runtime-system design.

YEAR 4 — ADVANCED COMPUTER SCIENCE

Semester 7 — Advanced Systems + Specialization

Advanced Systems

Choose from:

CMU 15-418 — Parallel Computer Architecture and Programming
MIT 6.5840 — Distributed Systems (widely considered the best distributed systems course)
CMU 15-440 — Distributed Systems
CMU 15-441 — Networking and the Internet
CMU 15-445 — Database Systems

Advanced Theory

Stanford CS166 — Advanced Data Structures
Stanford CS154 — Introduction to the Theory of Computation
MIT 6.1220 — Design and Analysis of Algorithms

Advanced Security

MIT 6.1600 — Foundations of Computer Security
CMU 15-330 — Introduction to Computer Security

Software Engineering

MIT 6.1040 — Software Design
CMU 17-313 — Foundations of Software Engineering

AI / ML specialization

Choose one or more:

Stanford CS224R — Deep Reinforcement Learning
Stanford CS231N — Deep Learning for Computer Vision
Stanford CS224W — Machine Learning with Graphs
MIT 6.3900 — Introduction to Machine Learning
CMU 15-442 — Machine Learning Systems

CMU's current catalog explicitly permits SCS electives from Computer Science, Computational Biology, HCI, Machine Learning, Language Technologies, Robotics, and Software & Societal Systems.

Semester 8 — Research, Capstone & Advanced Specialization

Capstone / Research

Senior Capstone / Independent Research
Stanford CS191W — Writing Intensive Senior Capstone
Stanford CS194W — Senior Project
Stanford CS210B — Senior Project

Advanced AI

Choose:

Stanford CS229 — Machine Learning
Stanford CS236 — Deep Generative Models
Stanford CS237A — Principles of Robot Autonomy I
Stanford CS238 — Decision Making under Uncertainty
Stanford CS224R — Deep Reinforcement Learning
CMU 10-301 — Introduction to Machine Learning
CMU 15-442 — Machine Learning Systems
MIT 6.3900 — Introduction to Machine Learning

Advanced Systems

Choose:

CMU 15-410 — Operating System Design and Implementation
CMU 15-411 — Compiler Design
CMU 15-418 — Parallel Computer Architecture and Programming
MIT 6.5840 — Distributed Systems (widely considered the best distributed systems course)
CMU 15-440 — Distributed Systems
CMU 15-441 — Networking and the Internet
CMU 15-445 — Database Systems

Advanced HCI

Choose:

Stanford CS147 — Introduction to Human-Computer Interaction Design
Stanford CS247A — Design for Artificial Intelligence
CMU 05-391 — Designing Human Centered Software

Advanced Graphics

Choose:

Stanford CS148 — Introduction to Computer Graphics and Imaging
Stanford CS248A — Computer Graphics: Rendering, Geometry, and Image Manipulation
Stanford CS248B — Fundamentals of Computer Graphics: Animation and Simulation
CMU 15-362 — Computer Graphics

COMPLETE KNOWLEDGE MAP

A student completing this curriculum should cover the following areas.

1. Programming

Programming fundamentals
Procedural programming
Object-oriented programming
Functional programming
Generic programming
C
C++
Python
Java
Assembly
Memory management
Debugging
Testing
Software construction

Representative courses:

MIT 6.1000
MIT 6.1010
MIT 6.1020
Stanford CS106A
Stanford CS106B
Stanford CS106L
CMU 15-122
CMU 15-150
Stanford CS242
CMU's Type System Courses

2. Data Structures

Arrays
Linked lists
Stacks
Queues
Hash tables
Trees
Binary search trees
Balanced trees
Heaps
Graphs
Tries
Union-find
Advanced data structures
Persistent data structures
Amortized analysis

Representative courses:

CMU 15-210
Stanford CS161
Stanford CS166
MIT 6.1210
MIT 6.1220

3. Algorithms

Complexity
Sorting
Searching
Divide and conquer
Greedy algorithms
Dynamic programming
Graph algorithms
Shortest paths
Minimum spanning trees
Network flow
Matching
Randomized algorithms
Approximation algorithms
Online algorithms
Parameterized algorithms
NP-completeness

Representative courses:

Stanford CS161
CMU 15-451
MIT 6.1210
MIT 6.1220
MIT 6.1420

4. Mathematics

Discrete Mathematics

Logic
Sets
Relations
Functions
Graph theory
Combinatorics
Induction
Proofs

Courses:

MIT 6.1200
CMU 15-151
Stanford CS103

Calculus

Differential calculus
Integral calculus
Multivariable calculus
Vector calculus

Courses:

CMU 21-122
CMU 21-259
Stanford MATH51

Linear Algebra

Vectors
Matrices
Linear transformations
Eigenvalues
Eigenvectors
Orthogonality
Optimization

Courses:

MIT 18.06
Stanford MATH51
CMU 21-241

Probability & Statistics

Probability
Random variables
Distributions
Expectation
Variance
Bayesian reasoning
Statistical inference

Courses:

MIT 6.3700
MIT 6.3800
MIT 18.05
Stanford CS109

5. Computer Architecture

Digital logic
Boolean algebra
CPU design
Instruction sets
Assembly
Pipelining
Caches
Memory hierarchy
Virtual memory
Parallel architecture
Multicore systems
GPU concepts

Courses:

MIT 6.1910
MIT 6.1903
Stanford CS107
CMU 15-213
MIT 6.1910
CMU 18-447
UC Berkeley's CS61C
CMU 15-418

6. Operating Systems

Processes
Threads
Scheduling
Synchronization
Concurrency
Deadlocks
Virtual memory
Paging
File systems
Storage
System calls
Kernel architecture
Security

Courses:

MIT 6.1810
Stanford CS111
Stanford CS112
CMU 15-410

7. Networking

OSI model
TCP/IP
Ethernet
Routing
Switching
Congestion control
Flow control
DNS
HTTP
Web architecture
Network security
Distributed networking

Courses:

CMU 15-441
Stanford CS155
Stanford CS111

8. Databases

Relational model
SQL
Relational algebra
Transactions
ACID
Indexing
B-trees
Hash indexes
Query optimization
Storage engines
Concurrency control
Recovery
Distributed databases
NoSQL
Parallel databases

Courses:

MIT 6.5831
Stanford CS145
CMU 15-445

9. Distributed Systems

RPC
Distributed state
Logical clocks
Replication
Consensus
Leader election
Fault tolerance
Distributed storage
Consistency
Partitioning
Failure detection
Distributed transactions

Courses:

MIT 6.5840 (widely considered the best distributed systems course)
CMU 15-440
CMU 15-441
Stanford advanced systems courses

10. Software Engineering

Requirements
Architecture
Design
Modularity
Testing
Debugging
Version control
CI/CD
Refactoring
Software maintenance
Code review
Large-scale software development

Courses:

MIT 6.1020
MIT 6.1040
CMU 17-313

11. Programming Languages

Language paradigms
Functional programming
Type systems
Static typing
Dynamic typing
Lambda calculus
Semantics
Interpreters
Runtime systems
Program analysis

Courses:

Stanford CS242
CMU 15-150
CMU 15-312
CMU 17-363
Stanford CS242
CMU's Type Systems Courses

12. Compilers

Lexing
Parsing
ASTs
Semantic analysis
Type checking
Intermediate representations
Optimization
Code generation
Runtime systems
Memory management

Courses:

Stanford CS143
CMU 15-411
MIT 6.1100
MIT 6.1120

13. Theory of Computation

Finite automata
Regular languages
Context-free grammars
Pushdown automata
Turing machines
Decidability
Computability
Complexity
P
NP
NP-completeness
Reductions

Courses:

Stanford CS154
MIT 6.1400
CMU 15-251
CMU 15-455

14. Artificial Intelligence

Search
Planning
Knowledge representation
Constraint satisfaction
Probabilistic reasoning
Decision theory
Game playing
Reinforcement learning
Machine learning

Courses:

Stanford CS221
CMU 07-280
CMU 10-301
MIT 6.3900

15. Machine Learning

Linear regression
Logistic regression
Classification
Decision trees
Clustering
Dimensionality reduction
Optimization
Neural networks
Deep learning
Generative models
Reinforcement learning
Graph learning
ML systems

Courses:

Stanford CS229
Stanford CS236
Stanford CS224W
Stanford CS224R
Stanford CS231N
CMU 10-301
CMU 15-442
MIT 6.3900

16. Computer Security

Cryptography
Authentication
Authorization
Access control
Network security
Operating-system security
Web security
Privacy
Secure software
Threat modeling
Vulnerability analysis

Courses:

Stanford CS155
MIT 6.1600
CMU 15-330
CMU 15-316

17. Computer Graphics

Rendering
Rasterization
Geometry
Transformations
Lighting
Shading
Animation
Simulation
Image processing
GPU programming

Courses:

Stanford CS148
Stanford CS248A
Stanford CS248B
CMU 15-362

18. Human-Computer Interaction

User research
Interaction design
Prototyping
Usability
User interfaces
Human-centered design
Product design
AI + HCI

Courses:

Stanford CS147
Stanford CS247A
CMU 05-391

19. Information & Language

Information retrieval
Natural language processing
Search
Text processing
Language models
Information extraction
Conversational AI

Courses:

Stanford CS124
Stanford CS224V
Stanford CS224R
CMU 11-324

20. Parallel & High-Performance Computing

Parallel algorithms
Multicore processors
GPU computing
Synchronization
Performance optimization
Distributed computation
Parallel architecture

Courses:

CMU 15-418
Stanford CS149
MIT advanced systems courses

21. Robotics & Autonomous Systems

Robot perception
Planning
Control
Localization
Decision making
Reinforcement learning
Autonomous systems

Courses:

Stanford CS237A
Stanford CS238
Stanford CS224R
CMU robotics courses

22. Research & Professional Skills

Technical writing
Research methodology
Scientific communication
Presentations
Teamwork
Ethics
Social impact
Legal considerations
Capstone development

Examples:

CMU 07-128
CMU technical communication requirement
Stanford senior project
MIT CI-M / communication-intensive subjects

ACTUAL UNIVERSITY CORE COMPARISON

Area	MIT	Stanford	CMU
Programming	6.1000 / 6.1010	CS106A / CS106B	15-122 / 15-150
Math for CS	6.1200	CS103	15-151
Probability	6.3700 / 6.3800 / 18.05	CS109	Probability requirement
Systems	6.1910 / 6.1800 / 6.1810	CS107 / CS111	15-213
Algorithms	6.1210 / 6.1220	CS161	15-210 / 15-451
Theory	6.1400	CS103 / CS154	15-251 / 15-455
Databases	6.5831	CS145	15-445
Networks	Advanced systems options	Systems depth	15-441
Distributed Systems	Systems track	Systems depth	15-440
Compilers	6.1100 / 6.1120	CS143	15-411
Security	6.1600	CS155	15-330 / 15-316
AI	6.3900 / AI track	CS221	07-280 / AI electives
ML	6.3900	CS229	10-301
Graphics	CS/EECS track	CS148 / CS248	15-362
HCI	6.4500 and related	CS147	05-391
Software Engineering	6.1020 / 6.1040	CS104 and related	17-313
Parallel Computing	Systems track	CS149	15-418
Advanced Data Structures	6.1220 / advanced electives	CS166	15-210
Programming Languages	6.1100 / 6.1120	CS242	15-312 / 17-363

THE EDUCATION IN ONE LINE

Programming
    ↓
Data Structures
    ↓
Discrete Mathematics
    ↓
Computer Organization
    ↓
Algorithms
    ↓
Probability + Linear Algebra
    ↓
Operating Systems
    ↓
Databases
    ↓
Networks
    ↓
Software Engineering
    ↓
Theory of Computation
    ↓
Programming Languages
    ↓
Compilers
    ↓
Distributed Systems
    ↓
Security
    ↓
Artificial Intelligence
    ↓
Machine Learning
    ↓
Advanced Systems
    ↓
Specialization
    ↓
Research / Capstone

MINIMUM CORE TO MASTER

If the goal is to reproduce the intellectual core of a top U.S. CS undergraduate education, the following should not be skipped:

Programming
Data Structures
Algorithms
Discrete Mathematics
Probability
Linear Algebra
Calculus
Computer Organization
Computer Architecture
Operating Systems
Databases
Computer Networks
Software Engineering
Programming Languages
Theory of Computation
Compilers
Distributed Systems
Computer Security
Artificial Intelligence
Machine Learning
Human-Computer Interaction
Computer Graphics
Parallel Computing
Technical Communication
Research
Ethics / Social Impact
Senior Capstone

WHAT THE REAL DEGREES LOOK LIKE

MIT — Computer Science & Engineering, Course 6-3

MIT's current 6-3 degree requires programming, software construction, mathematics for CS, algorithms, computability/complexity, computer systems, low-level programming, computation structures, probability/inference or linear algebra, plus upper-level track courses and electives. The degree also includes MIT's General Institute Requirements: science, HASS, restricted science/technology electives, laboratory, communication, and physical education requirements.

Stanford — Computer Science B.S.

Stanford's CS B.S. requires mathematics, science, engineering fundamentals, Technology in Society, CS core, depth coursework, and senior-project coursework. Its core includes programming, mathematical foundations, computer organization/systems, probability and algorithms, while its depth areas span AI, systems, theory, HCI, visual computing, information, computer engineering and computational biology.

Carnegie Mellon — Computer Science B.S.

CMU's Fall 2026 CS B.S. requires 15-122, 15-150, 15-210, 15-213, 15-251 and 15-451, plus AI, logic/languages, systems and SCS electives. It also requires mathematics, technical communication, science/engineering, humanities/arts, free/minor/concentration requirements, First Year Seminar and Core@CMU.

FINAL 4-YEAR STRUCTURE

Year	Primary Focus
Year 1	Programming + Mathematics + Computer Organization
Year 2	Data Structures + Algorithms + OS + Databases + Theory
Year 3	Networks + Distributed Systems + Compilers + AI + ML + Security
Year 4	Advanced Systems + Specialization + Research + Capstone

This is much closer to the breadth and depth of a top-tier U.S. CS education than the earlier 48-course simplified list. The actual universities intentionally give students substantial freedom in the upper years, so the final two semesters are naturally specialization-heavy rather than a fixed identical set of courses for everyone.