cs-foundations

Included with Lifetime

$97 forever

Master discrete mathematics, logic, formal proofs, and computational thinking. Build the mathematical foundation for all computer science.

Generalscriptsassets

What this skill does


# CS Foundations Skill

## Skill Metadata

```yaml
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]
```

---

## Quick Start

Computer science is built on mathematics. Master these fundamentals:

### Core Topics

**Discrete Mathematics**
- Set theory and operations
- Logic and proof techniques
- Combinatorics and counting
- Number theory basics
- Relations and functions

**Computational Thinking**
- Problem decomposition
- Abstraction and generalization
- Pattern recognition
- Algorithmic thinking

**Formal Logic**
- Propositional logic
- Predicate logic
- Proof by induction
- Truth tables and logical equivalence

---

## Learning Path

**Week 1: Logic Basics**
- Boolean algebra
- Truth tables
- Logical operators
- Inference rules

**Week 2: Proof Techniques**
- Direct proof
- Proof by contradiction
- Mathematical induction
- Strong induction

**Week 3: Set Theory**
- Set operations (∪, ∩, complement)
- Cartesian product
- Relations
- Equivalence relations

**Week 4: Functions**
- Function notation
- Domain, codomain, range
- One-to-one and onto
- Function composition

**Week 5: Combinatorics**
- Counting principles
- Permutations
- Combinations
- Pigeonhole principle

**Week 6: Number Theory**
- Modular arithmetic
- Prime numbers
- GCD and Euclidean algorithm
- Congruence

---

## Practice Problems

1. Prove by induction that 1+2+...+n = n(n+1)/2
2. Prove √2 is irrational
3. Show A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
4. Count functions from {1,2,3} to {a,b}
5. Solve: x ≡ 5 (mod 12) and x ≡ 3 (mod 8)

---

## Troubleshooting

| 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 |

---

## Key Concepts

- **Axioms**: Statements we assume true
- **Theorems**: Statements we prove
- **Lemmas**: Helper theorems
- **Corollaries**: Results that follow easily

---

## Why It Matters

These foundations enable:
- Understanding algorithm correctness
- Analyzing computational complexity
- Designing new algorithms
- Proving algorithm properties
- Understanding what's computable

---

## Interview Prep

- Explain mathematical induction
- Prove that a function is injective
- Count permutations with constraints
- Solve modular equations
- Apply pigeonhole principle

Files: 5

Size: 15.3 KB

Complexity: 59/100

Category: General

Source: https://github.com/pluginagentmarketplace/custom-plugin-computer-science/tree/main/skills/foundations

Related in General

modeling-omnistudio-epc-catalog

Included

Salesforce Industries CME EPC product-modeling skill for Product2-based catalog creation. Use when creating EPC products, configuring product attributes, building offer bundles with Product Child Items, or reviewing EPC DataPack JSON metadata for product catalog changes. TRIGGER when: user creates or updates Product2 EPC records, AttributeAssignment payloads, AttributeMetadata/AttributeDefaultValues, Offer bundles, or ProductChildItem relationships. DO NOT TRIGGER when: designing OmniScripts/FlexCards/Integration Procedures (use building-omnistudio-omniscript, building-omnistudio-flexcard, or building-omnistudio-integration-procedure), implementing Apex business logic (use generating-apex), or troubleshooting deployment pipelines (use deploying-metadata).

Generalscripts

relationship-science-coach

Included

Use this skill for direct, practical adult relationship coaching: couples conflict, repair, trust, marriage, dating, flirting, attachment patterns, emotional connection, sex, desire differences, eroticism, kink negotiation, affection, love languages, breakups, and long-term passion. Draw on Gottman, EFT and Hold Me Tight, attachment science, modern sex research, Perel, Nagoski, Kerner, Schnarch, Love and Stosny, and flexible love-language tools. Be concrete and low-hedge. Redirect only for imminent danger, abuse, coercive control, minors, non-consent, self-harm, stalking, or medical/legal/psychiatric decisions.

Generalscripts

building-sf-integrations

Included

Salesforce integration architecture and runtime plumbing with 120-point scoring. Use this skill to set up Named Credentials, External Credentials, External Services, REST/SOAP callout patterns, Platform Events, and Change Data Capture. TRIGGER when: user sets up Named Credentials, External Services, REST/SOAP callouts, Platform Events, CDC, or touches .namedCredential-meta.xml files. DO NOT TRIGGER when: Connected App/OAuth config (use configuring-connected-apps), Apex-only logic (use generating-apex), or data import/export (use handling-sf-data).

Generalscripts

venue-templates

Included

Access comprehensive LaTeX templates, formatting requirements, and submission guidelines for major scientific publication venues (Nature, Science, PLOS, IEEE, ACM), academic conferences (NeurIPS, ICML, CVPR, CHI), research posters, and grant proposals (NSF, NIH, DOE, DARPA). This skill should be used when preparing manuscripts for journal submission, conference papers, research posters, or grant proposals and need venue-specific formatting requirements and templates.

Generalscripts

let-fate-decide

Included

Draws the 12 Houses of the Zodiac Tarot spread to inject entropy into planning when prompts are vague, ambiguous, or casually delegated. Interprets the spread to guide next steps. Use when the user says 'let fate decide', 'YOLO', 'whatever', 'idk', or other nonchalant phrases, makes Yu-Gi-Oh references, or when you are about to arbitrarily pick between multiple reasonable approaches. Prefer over ask-questions-if-underspecified when the user's tone is casual or playful rather than precision-seeking.

Generalscripts

net-ops

Included

Cross-platform network troubleshooting (Windows, macOS, Linux) via local or remote shell. Use for: DNS broken, can't resolve hostnames, nslookup/dig works but apps fail, NRPT, WFP, scutil, /etc/resolver, systemd-resolved, /etc/resolv.conf, NetworkManager, VPN DNS leak residue (ProtonVPN/Mullvad/WireGuard/AnyConnect), AV/firewall blocking DNS or DoH, Tailscale DNS interaction, intermittent connectivity, remote diagnostics over SSH.

Generalscripts