Study the mathematics behind computer science through a structured learning path and practice problems. Covers logic, proofs, sets, functions, counting, and number theory, connecting these foundations to algorithm correctness and computational thinking.
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Master discrete mathematics, logic, formal proofs, and computational thinking. Build the mathematical foundation for all computer science.
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skill_config:
version: "1.0.0"
category: theoretical
prerequisites: []
estimated_time: "6-8 weeks"
difficulty: intermediate
parameter_validation:
topic:
type: string
enum: [logic, proofs, sets, functions, combinatorics, number-theory, graphs]
required: true
depth:
type: string
enum: [intro, standard, advanced]
default: standard
retry_config:
max_attempts: 3
backoff_strategy: exponential
initial_delay_ms: 500
observability:
log_level: INFO
metrics: [topic_usage, proof_verification_rate, exercise_completion]
Computer science is built on mathematics. Master these fundamentals:
Discrete Mathematics
Computational Thinking
Formal Logic
Week 1: Logic Basics
Week 2: Proof Techniques
Week 3: Set Theory
Week 4: Functions
Week 5: Combinatorics
Week 6: Number Theory
| Issue | Root Cause | Resolution |
|---|---|---|
| Proof stuck | Missing case or wrong direction | Check base case, verify induction step |
| Set operation confusion | ∪ vs ∩ mix-up | Draw Venn diagram |
| Counting error | Overcounting duplicates | Distinguish P(n,r) vs C(n,r) |
| Modular arithmetic error | Forgot wraparound | Work with remainders explicitly |
These foundations enable:
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Support experimental validation of designed proteins through a cloud laboratory. Prepare and optimize sequences, submit tests for binding, expression, thermal stability, or enzyme activity, track experiment progress, and retrieve results through the API.
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Analyze time series, observations ordered over time, using aeon in Python. Build classification, prediction, and clustering workflows, detect unusual patterns or changes, and compare methods through an interface compatible with scikit-learn.
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Create original generative art with p5.js, using code to produce patterns and motion. Receive a written artistic concept and an interactive HTML viewer with adjustable parameters, reproducible random variations, seed navigation, and PNG downloads.
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Retrieve stock prices, exchange rates, cryptocurrency prices, company financial statements, and economic indicators through the Alpha Vantage API. It also covers historical data, news sentiment, and technical indicators, which summarize price and trading patterns.
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Design backend systems with clear boundaries between business rules, databases, and external services. Use Clean Architecture, Hexagonal Architecture, and Domain-Driven Design to organize new applications, refactor existing code, and make core logic easier to test.
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Helps process astronomical data in Python by converting coordinates, units, and time scales, working with FITS observation files, matching object catalogs, and calculating distances using cosmological models.
中文简介正在准备中。当前显示英语简介。