FREE COMPUTER SCIENCE ROADMAP · 14 LAYERS · 56 LESSONS

Computer Science Roadmap

Follow the complete Bits Stack Trace from mathematics and silicon through software, data systems, distributed systems, AI, and agents.

• Mathematics & logic
  • The map is not the territory — Representation is the first engineering decision
  • Claims, counterexamples, and invariants — How software earns a guarantee
  • Four lenses for discrete problems — Sets, graphs, matrices, and probability
  • Foundation mastery: specify before you build — Prove the model survives a changed assumption
• Physics & signals
  • A bit is a physical agreement — Stable distinctions in a noisy world
  • Sampling a continuous world — What measurement keeps—and loses
  • Signals must arrive in time — Bandwidth, latency, energy, and synchronization
  • Signal mastery: protect meaning — Detect corruption and locate the broken boundary
• Semiconductors & electronics
  • From material to controllable path — Why semiconductors make switching possible
  • The CMOS inverter — Complementary devices restore a bit
  • Timing, heat, and fabrication — Why billions of switches are a systems problem
  • Electronics mastery: find the real bottleneck — Reason across logic, timing, power, and yield
• Digital logic
  • From truth table to circuit — Composition turns switches into decisions
  • Addition is a chain of local facts — Build arithmetic and see the carry path
  • Memory begins with feedback — Registers, clocks, and state over time
  • Logic mastery: design a state machine — Make control explicit and test every transition
• Architecture & memory
  • The stored-program contract — Instructions and data share an organized machine
  • The memory hierarchy — Locality turns a speed gap into a workable illusion
  • Devices, interrupts, and DMA — The processor is not the whole computer
  • Architecture mastery: performance is a budget — Reason with bottlenecks, parallelism, and measurement
• Machine code & execution
  • State changes one instruction at a time — Registers, addresses, and control flow
  • Calls are negotiated protocols — Calling conventions and stack frames
  • From object file to running image — Symbols, relocation, linking, and loading
  • Execution mastery: overlap without lying — Pipelines, hazards, prediction, and precise state
• Operating systems & runtimes
  • Processes, threads, and the scheduler — Many streams of work share finite processors
  • Virtual memory is controlled indirection — Isolation, translation, paging, and faults
  • System calls and durable names — Files, descriptors, buffering, and persistence
  • OS mastery: concurrency without corruption — Atomicity, waiting, deadlock, and isolation
• Languages & compilers
  • Source becomes structure — Lexing, parsing, grammars, and syntax trees
  • Types make impossible states harder to express — Static constraints and runtime meaning
  • Many roads to execution — Compilers, interpreters, VMs, and JITs
  • Language mastery: who owns memory? — Lifetime, allocation, garbage collection, and boundaries
• Algorithms & data structures
  • A data structure is a bet — Choose for operations, constraints, and evidence
  • Correctness and cost — Invariants, growth rates, and honest analysis
  • Explore without getting lost — Search, sort, and graph traversal patterns
  • Algorithm mastery: design from structure — Greedy choices, dynamic programming, and proof
• Applications & software architecture
  • Architecture is change made legible — Cohesion, coupling, and domain boundaries
  • An API is a promise over time — Contracts, identity, errors, and idempotency
  • Evidence across the lifecycle — Tests, telemetry, and debugging
  • Application mastery: design for failure and change — Security, migration, and evolutionary architecture
• Databases & data systems
  • Records live in pages, not tables — Storage layout and indexes from first principles
  • A query is an algorithm choice — Plans, cardinality, joins, and execution
  • Transactions control interleavings — Isolation, locking, MVCC, and invariants
  • Database mastery: a commit is a promise — Logging, recovery, replication, and failure boundaries
• Networks & distributed systems
  • One request crosses many protocols — DNS, IP, transport, TLS, and HTTP
  • Failure is partial and ambiguous — Timeouts, retries, backoff, and overload
  • Copies must agree enough — Replication, consistency, ordering, and consensus
  • Distributed mastery: shape and observe load — Load balancers, caches, queues, and graceful degradation
• AI & machine learning
  • Start with the decision, not the model — Targets, data, baselines, and leakage
  • Training is guided search — Models, loss, gradients, and regularization
  • Evaluation is an argument about the future — Generalization, metrics, calibration, and uncertainty
  • ML mastery: the model lives inside a system — Deployment, drift, feedback, safety, and human judgment
• LLMs & agents
  • A transformer predicts one token at a time — Tokens, embeddings, attention, and residual computation
  • Training creates capability, not a truth guarantee — Pretraining, adaptation, inference, and limits
  • Ground language in evidence and tools — Retrieval, tool contracts, and untrusted content
  • Agent mastery: close the loop safely — State, planning, permissions, evaluation, and stop conditions