universal-cross-subject-mapper

name	universal-cross-subject-mapper
description	Maps conceptual connections across subjects for ANY university worldwide. Shows how topics from one course relate to and build upon topics from other courses. Provides integrated learning paths, dependency graphs, and cross-referenced study materials. Essential for comprehensive exams and interdisciplinary understanding.

Universal Cross-Subject Mapper

Overview

Creates a semantic map showing how concepts from different subjects connect, depend on each other, and reinforce each other. Helps students develop integrated understanding rather than studying each subject in isolation. Particularly valuable for comprehensive exams, GATE, GRE subject tests, and interdisciplinary programs.

How This Skill Works

1. User provides: List of subjects in current semester and/or entire program, university, department
2. System identifies: Conceptual overlap, prerequisite dependencies, shared techniques, cross-applications
3. System constructs: Dependency graph showing connections between subjects/topics
4. System generates: Cross-reference tables and integrated study paths

1. Connection Types

Connection Type	Description	Example
Prerequisite	Topic A must be understood before Topic B	Calculus -> Differential Equations -> Signals & Systems
Shared Concept	Same concept appears in multiple subjects	Fourier Transform appears in: Signals, Control Systems, Image Processing
Application	Topic A from one subject is applied in Topic B from another	Probability (Math) applied in Machine Learning (CS)
Analogy	Similar structure in different domains	Memory management (OS) resembles cache management (Architecture)
Extension	Concept A is generalized/specialized in another subject	Linked Lists (DS) -> Memory Allocation (OS) -> File Systems (OS)

2. Cross-Subject Dependency Graph

Sample: Computer Engineering (SPPU/VTU/JNTU pattern)

Mathematics 1          Mathematics 2         Mathematics 3
(Calculus, LA)          (DE, Probability)       (Numerical, Graph)
      |                       |
      v                       v
   Physics               Basic Electronics
      |                       |
      v                       v
  Programming        Computer Organization
  (C)                       & Architecture
      |                       |
      v                       |
  Data Structures -----------+--------- Digital Logic
      |                       |              |
      v                       v              v
  Algorithmics          Operating         Computer Networks
                        Systems          (uses DS + Math)
      |                       |
      +----------+------------+
                 |
                 v
         Database Systems
         (uses DS + Math)

3. Cross-Reference Table Format

For each pair of subjects, the mapper generates:

SUBJECT A: Data Structures
SUBJECT B: Operating Systems

| Topic in A | Topic in B | Connection Type | How Used in B |
|---|---|---|---|
| Arrays | Memory Management | Prerequisite | Array indexing shows contiguous memory allocation |
| Linked Lists | Process Scheduling | Application | PCB linked list in ready queue |
| Stacks | System Calls | Application | Stack frames for function calls / context switch |
| Queues | Scheduling | Extension | Ready Queue, Wait Queue are queue applications |
| Trees (esp. BST) | File Systems | Application | Directory hierarchy is a tree structure |
| Hash Tables | File Systems | Application | Inode lookup, directory lookup |
| Graphs | Deadlock Detection | Application | Resource Allocation Graph for deadlock detection |
| Sorting | Disk Scheduling | Analogy | SCAN, C-SCAN scheduling are sorting-like algorithms |

CROSS-REFERENCE INSIGHT:
Understanding Data Structures is essential for OS — nearly every OS subsystem uses
specific data structures. Learning DS and OS together (interleaved) improves retention
in both subjects.

4. Integrated Study Paths

The mapper can generate study sequences that cover related concepts from multiple subjects in an interleaved fashion:

INTERLEAVED STUDY PATH: Memory Systems (3 subjects)

Session 1: Computer Organization
  - Cache memory organization, direct/associative/set-associative mapping
Session 2: Operating Systems
  - Page tables, TLB, demand paging, page replacement algorithms
Session 3: Computer Networks (optional)
  - Buffer management in routers, packet buffering

BENEFIT: Cache (CO) and Page Table (OS) both use similar
mapping/lookup concepts. Studying them together reinforces
the fundamental technique.

5. Program-Level Mapping

For comprehensive exam preparation, the mapper can generate a full program map:

PROGRAM: B.Tech Computer Engineering (All 8 Semesters)

Layer 1 — Foundations (Sem 1-2):
  Mathematics 1+2 + Physics + Programming + Digital Logic

Layer 2 — Core (Sem 3-4):
  Data Structures + Discrete Math + Computer Organization + OOP

Layer 3 — Systems (Sem 5-6):
  OS + DBMS + CN + SE + Microprocessor

Layer 4 — Advanced (Sem 7-8):
  ML/AI + Security + Cloud + Project

DEPENDENCY PATH:
  Mathematics 1 -> Mathematics 2 -> Mathematics 3 -> ML/AI
  Programming -> DS -> Algo -> Advanced electives
  Digital Logic -> CO -> MP -> Embedded
  DS + CO -> OS -> CN -> Security
  DS + Math -> DBMS -> Data Mining

Error Handling

Situation	Action
Subjects appear unrelated	Search for indirect connections (shared methodology, analogous structures, applied mathematics); report if genuinely no link found
Insufficient syllabus info	Request detailed syllabus or course descriptions; use default curriculum mappings for common programs
No common concepts found	Expand search to include cross-disciplinary techniques (e.g., optimization, probability, systems thinking)
Too many subjects	Group by department or semester; generate pairwise maps first, then combine into full program view

Quality Gate — Check Before Output

• Link strength scores assigned to each connection (strong / moderate / weak)
• Prerequisite chain verified — no subject depends on content that comes later
• No circular dependencies in the dependency graph
• Cross-reference tables include connection type (prerequisite / shared / application / analogy / extension)
• Integrated study paths are actionable and sequenced logically

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Session Config

This skill integrates with the session config system (deps/session-profile.json). Before executing, check for an existing session profile:

• If deps/session-profile.json exists, read university, subject, pattern, and exam_type fields to auto-configure the skill.
• If the file does not exist, fall back to user-provided context or prompt the user to run setup-exam-prompt (or npm run init) first.
• Session config eliminates redundant context detection — detection happens once and is reused across all skill calls.

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6. Integration with Other Skills

• universal-session-config: Reads program, department, and subject list from session profile
• universal-notes-generator: Generates cross-subject notes that link related concepts
• universal-flashcard-generator: Creates cross-subject flashcards for interdisciplinary exam prep
• universal-study-planner: Creates interleaved study schedules based on cross-subject connections
• universal-mind-map-generator: Visualizes cross-subject relationships in mind map format
• universal-pyq-analyzer: Identifies cross-subject question patterns in comprehensive exams