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Vault Linking Analysis Report

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Obsidian Vault Linking Structure Analysis Report

Generated: 2025-11-24 Vault: mi-quartz study notes Courses: MAT1610 Calculo I, MAT1203 Algebra Lineal, EYP1016 Introduccion a la Estadistica

Executive Summary

This vault contains 229 markdown files across three mathematics courses. While 115 files (50%) contain wikilinks, there are significant opportunities to improve the knowledge graph through:

  1. Linking 26 orphaned concept notes in MAT1203 to their corresponding class notes
  2. Creating cross-course connections between related mathematical concepts
  3. Reducing the 7 completely orphaned notes
  4. Establishing bidirectional links between concept definitions and class applications

Key Finding: The MAT1203 Algebra Lineal course has 26 concept files in the /Conceptos/ folder that contain no wikilinks, despite being referenced in class notes. This represents the biggest opportunity for immediate improvement.

Overall Statistics

MetricCountPercentage
Total markdown files229100%
Files with wikilinks11550.2%
Files without wikilinks4017.5%
Concept files (/Conceptos/)7432.3%
Truly orphaned notes73.1%

Linking Patterns by Course

MAT1610 Calculo I:

  • Strong linking culture in concept files (42 concept files, most well-linked)
  • Class notes have moderate linking to concept notes
  • Good use of bidirectional references
  • Top linked concepts: Derivada (10 links), Razon-de-Cambio (7 links)

MAT1203 Algebra Lineal:

  • ISSUE: 26 concept files have NO wikilinks despite being mentioned in class notes
  • Class notes use wikilinks but often to other class notes, not concept notes
  • Has a well-structured Cronograma with links to all classes
  • Moderate internal linking within class notes

EYP1016 Introduccion a la Estadistica:

  • Minimal concept file structure (only 1 concept file)
  • Class notes have good internal linking to each other
  • Heavy use of inline definitions rather than concept notes
  • Less modular than the other two courses

Most Referenced Notes

Top 10 most-linked notes in the vault:

  1. 23) Como Afecta Derivada Forma Grafica - 10 incoming links
  2. Derivada - 10 incoming links
  3. 21) Valores Maximos y Minimos - 9 incoming links
  4. Base (MAT1203) - 9 incoming links
  5. Numeros-Criticos - 8 incoming links
  6. 10) Recta Tangente, Velocidad y el Concepto de Derivada - 8 incoming links
  7. Razon-de-Cambio - 7 incoming links
  8. Limites-Infinitos - 7 incoming links
  9. 12) La Derivada como una Función - 6 incoming links
  10. Combinacion-Lineal - 6 incoming links

Completely Orphaned Files (7 total)

These files have ZERO wikilinks in or out:

MAT1610 Calculo I (2 files):

  • Clases/03 Aplicaciones de la derivada/24) Formas Indeterminadas y Regla de L'Hopital.md
  • Clases/03 Aplicaciones de la derivada/25) Mas Formas Indeterminadas, Productos, Diferencias y Potencias.md

Recommendation: These class notes on L’Hopital’s Rule should link to:

  • Limites-Infinitos.md
  • Derivada.md
  • 22) Teorema del Valor Medio.md (since L’Hopital uses derivatives)

MAT1203 Algebra Lineal (1 file):

  • Resumen Completo Clases 11-23.md

Recommendation: This summary should link to all class notes and concepts it covers (Classes 11-23).

Other (4 files):

  • Otros/Resumen 1 MUC872.md
  • Otros/Resumen 2 MUC872.md
  • Otros/Resumen 3 MUC872.md
  • Otros/Resumen 4 MUC872.md

Note: These appear to be from a different course (MUC872) and are currently staged for deletion in git.

Cross-Course Concept Overlaps

Analysis reveals these concepts appear in multiple courses but lack cross-references:

ConceptAppears InCurrent LinksOpportunity
IndependenciaMAT1203 (linear independence), EYP1016 (event independence)SeparateAdd conceptual comparison note
VariableMAT1203 (free variable), EYP1016 (random variable), MAT1610 (variable)NoneClarify different uses of “variable”
FunciónAll three coursesMinimalLink function concepts across contexts
TransformaciónMAT1203 (linear transform), MAT1610 (derivative as linear approx)NoneAdvanced connection
LinealMAT1203 (linear systems), MAT1610 (linear approximation)NoneConceptual bridge
VectorMAT1203 (geometric), EYP1016 (random vectors)NoneTerminology clarification
IntegralMAT1610 (single), MAT1203 (multiple)NoneExtension concept
Esperanza/PromedioEYP1016 (expected value), MAT1610 (average value)NoneStatistical vs analytical average

Specific Cross-Course Linking Opportunities

Priority 1: High-Value Connections

  1. Independencia Lineal ↔ Independencia (Probabilidad)

    • From: MAT1203/Conceptos/Independencia-Lineal.md
    • To: EYP1016/Clases/4) Probabilidad Condicional e Independencia.md
    • Type: Conceptual comparison
    • Add a note explaining: “In linear algebra, vectors are independent if no vector is a linear combination of others. In probability, events are independent if knowing one doesn’t affect the other. Different mathematical meanings of ‘independence’.”

  2. Valor Promedio ↔ Esperanza

    • From: MAT1610/Conceptos/Valor-Promedio.md
    • To: EYP1016/Clases/6) Variables Aleatorias Discretas.md (section on Esperanza)
    • Type: Conceptual analogy
    • Note: “The expected value in statistics is analogous to the average value of a function in calculus. For continuous random variables, esperanza uses integrals similar to average value.”

  3. Combinación Lineal ↔ Aproximación Lineal

    • From: MAT1203/Conceptos/Combinacion-Lineal.md
    • To: MAT1610/Conceptos/Aproximacion-Lineal.md
    • Type: Conceptual link
    • Note: “Linear approximation represents a function locally as a linear combination of basis functions.”

Priority 2: Advanced Connections

  1. Transformaciones Lineales ↔ Derivada

    • From: MAT1203/Conceptos/Transformaciones-Lineales.md
    • To: MAT1610/Conceptos/Derivada.md
    • Type: Advanced connection
    • Note: “The derivative is the best linear approximation to a function at a point. In multivariable calculus, this becomes a linear transformation (the Jacobian matrix).”

  2. Determinante ↔ Integrales Múltiples

    • From: MAT1203/Conceptos/Determinante.md
    • To: MAT1203/Conceptos/Integrales-Múltiples.md
    • Type: Advanced application
    • Note: “Determinants appear in change of variables for multiple integrals (Jacobian determinant).”

  3. Sistema Homogéneo ↔ Ecuaciones Diferenciales

    • From: MAT1203/Conceptos/Sistema-Homogeneo.md
    • To: MAT1610/Conceptos/Ecuaciones-Diferenciales.md
    • Type: Applied connection
    • Note: “Systems of homogeneous linear differential equations can be solved using linear algebra techniques.”

Priority 3: Terminology Clarifications

  1. Vector (Geométrico) ↔ Vector Aleatorio

    • From: MAT1203/Conceptos/Vector.md
    • To: EYP1016/Clases/8) Vectores Aleatorios Discretos.md
    • Type: Terminology clarification
    • Note: “Both use the term ‘vector’ but in different contexts: geometric vectors in R^n vs random vectors (tuples of random variables).”

  2. Matriz (Álgebra) ↔ Matriz de Covarianza

    • From: MAT1203/Conceptos/Matriz.md
    • To: References in EYP1016 if/when covered
    • Type: Application
    • Note: “Matrices in statistics (covariance matrices) use the same algebraic structure from linear algebra.”

4. Suggested New Connections

A. Link Concept Notes to Class Notes (MAT1203 - HIGHEST PRIORITY)

The following concept files exist but have NO wikilinks. They should be populated with content and linked from relevant class notes:

Concept FileStatusShould Link ToPriority
Vector.mdEmpty (“En desarrollo :P”)Clase 1, 2HIGH
Matriz.mdEmptyClase 7, 15HIGH
Independencia-Lineal.mdNo linksClase 12, 23HIGH
Base.mdNo linksClase 23HIGH
Determinante.mdNo linksClases 18-21HIGH
Transformaciones-Lineales.mdNo linksClases 13-14, 32HIGH
Valores-Propios.mdNo linksClases 29-33HIGH
Dimension.mdNo linksClase 26MEDIUM
Rango.mdNo linksClase 27MEDIUM
Subespacio-Vectorial.mdNo linksClase 22MEDIUM
Espacio-Nulo.mdNo linksClase 24MEDIUM
Producto-Punto.mdNo linksClase 2MEDIUM
Producto-Cruz.mdNo linksFuture topicLOW
Vectores-Ortogonales.mdNo linksFuture topic (Ch. 7)LOW
Vectores-Unitarios.mdNo linksClase 1MEDIUM

Recommendation: Create a systematic linking pattern where:

  1. Each class note links to relevant concept notes in a “Conceptos Relacionados” section
  2. Each concept note links back to class notes where it’s introduced and applied
  3. Concept notes should have at minimum: definition, examples, and related concepts

B. Create Cross-Reference Sections

Add “See Also” or “Related Concepts” sections to connect ideas:

In MAT1610 Derivada.md:

## Conexiones con Otros Cursos
 
- En [[MAT1203 Algebra Lineal/Conceptos/Transformaciones-Lineales|álgebra lineal]],
  la derivada representa la mejor aproximación lineal a una función
- Ver también [[Aproximacion-Lineal]] para la aplicación práctica

In EYP1016 Variables Aleatorias Discretas:

## Nota sobre Terminología
 
- El término "variable" aquí se refiere a variables aleatorias (funciones del espacio
  muestral a los reales)
- Esto difiere del uso en [[MAT1203 Algebra Lineal/Conceptos/Variable-Libre|álgebra
  lineal]] donde "variable libre" se refiere a incógnitas en sistemas de ecuaciones

C. Build a Concepts Map of Content (MOC)

Create a Map of Content for each course in a central location:

Create: MAT1610 Calculo I/MOC - Mapa de Conceptos.md

# Mapa de Conceptos - Cálculo I
 
## Conceptos Fundamentales
- [[Limite-de-una-funcion]]
- [[Derivada]]
- [[Integral]]
 
## Por Capítulo
### Cap 1: Límites
- [[Limite-de-una-funcion]]
- [[Limites-Laterales]]
- [[Limites-Infinitos]]
- [[Continuidad-y-Derivabilidad]]
 
### Cap 2: Derivadas
- [[Derivada]]
- [[Regla-de-la-Cadena]]
- [[Derivacion-Implicita]]
 
[etc.]
 
## Conexiones con Otros Cursos
- [[MAT1203 Algebra Lineal/Conceptos/Transformaciones-Lineales]] - La derivada como transformación lineal
- [[EYP1016 Introduccion a la Estadistica/Conceptos/Fórmulas y Conceptos]] - Integrales en esperanza continua

Create: MAT1203 Algebra Lineal/MOC - Mapa de Conceptos.md

Similar structure for linear algebra concepts.

For well-developed concept notes that already link to class notes, ensure class notes link back:

Example:

  • Derivada.md links to 10) Recta Tangente, Velocidad y el Concepto de Derivada
  • But does that class note link back to Derivada.md? (Check and add if missing)

Pattern to implement:

## Concepto Principal
 
Este tema introduce [[Derivada|el concepto de derivada]].
 
[Class content...]
 
## Referencias y Conceptos
 
- [[Derivada]] - Definición formal y propiedades
- [[Limite-de-una-funcion]] - Prerequisito

5. Concept Notes Existing But Not Linked from Class Notes

MAT1203 Algebra Lineal - Complete List

These 26 concept files exist in /Conceptos/ but are NOT linked from class notes:

  1. Base.md
  2. Bases-Dimension.md
  3. Determinante.md
  4. Dimension.md
  5. Ecuaciones-Parametricas.md
  6. Espacio-Nulo.md
  7. Factorizacion-LU.md
  8. Hiperplanos.md
  9. Independencia-Lineal.md
  10. Integrales-Múltiples.md
  11. Matriz-Adjunta.md
  12. Matriz.md
  13. Producto-Cruz.md
  14. Producto-Punto.md
  15. Rango.md
  16. Sistema-Equivalente.md
  17. Sistema-Homogeneo.md
  18. Sistemas-Lineales.md
  19. Subespacio-Vectorial.md
  20. Teorema-Matriz-Invertible.md
  21. Transformaciones-Lineales.md
  22. Valores-Propios.md
  23. Variable-Libre.md
  24. Vector.md
  25. Vectores-Ortogonales.md
  26. Vectores-Unitarios.md

Phase 1: Populate Empty Concept Notes (Week 1)

  1. Add content to Vector.md and Matriz.md (currently just say “En desarrollo :P”)
  2. These are foundational - should be done first

Phase 2: Link Existing Concept Notes to Classes (Week 2-3) For each concept note that has no links:

  1. Identify which class notes introduce or use the concept
  2. Add wikilink from class note to concept note
  3. Add backlink from concept note to class notes

Phase 3: Add Cross-Course Links (Week 4)

  1. Implement the 8 cross-course connections identified in Section 3
  2. Add explanatory notes about how concepts relate across courses

Phase 4: Create MOCs (Week 5)

  1. Build a Map of Content for each course
  2. Create a master “Mathematics Concepts” MOC linking all three courses

6. Specific Recommendations by Course

MAT1610 Calculo I

Strengths:

  • Good concept note coverage (42 concept files)
  • Strong bidirectional linking in well-developed notes
  • Clear hierarchy (Clases → Conceptos)

Improvements Needed:

  1. Link orphaned class notes (24, 25) about L’Hopital’s Rule
  2. Add cross-references to MAT1203 for advanced topics
  3. Create a comprehensive MOC

Quick Wins:

  • Add links from Classes 24-25 to existing limit and derivative concepts
  • Link Valor-Promedio.md to EYP1016 esperanza concept

MAT1203 Algebra Lineal

Strengths:

  • Well-organized directory structure
  • Excellent Cronograma.md that links to all classes
  • Good internal class note linking

Critical Issues:

  1. 26 concept files have no wikilinks (highest priority to fix)
  2. Two foundational concept files are empty (Vector.md, Matriz.md)
  3. Class notes don’t consistently link to concept notes

Improvements Needed:

  1. Populate empty concept notes
  2. Add systematic linking from classes to concepts
  3. Add backlinks from concepts to classes
  4. Create cross-course connections to MAT1610 and EYP1016

Quick Wins:

  • Start with most-used concepts: Vector, Matriz, Independencia-Lineal, Base, Determinante
  • Add “Conceptos Relacionados” section to each class note

EYP1016 Introduccion a la Estadistica

Strengths:

  • Class notes are well-developed with good internal linking
  • Clear examples and explanations
  • Good use of callouts and formatting

Improvements Needed:

  1. Create more concept notes (currently only 1)
  2. Extract common concepts into separate notes (e.g., Esperanza, Varianza, Probabilidad)
  3. Link to MAT1610 for integral-based concepts
  4. Link to MAT1203 for random vectors

Recommended New Concept Notes:

  • Esperanza.md
  • Varianza.md
  • Probabilidad.md
  • Variable-Aleatoria.md
  • Distribucion-Probabilidad.md
  • Independencia-Eventos.md

Quick Wins:

  • Create Esperanza.md and link from Classes 6, 7
  • Add note in Class 8 (Vectores Aleatorios) linking to MAT1203 Vector concept

7. Implementation Checklist

Immediate Actions (This Week)

  • Fix 7 completely orphaned notes

    • Link MAT1610 Classes 24-25 to limit/derivative concepts
    • Link MAT1203 summary to all covered classes
    • Delete or integrate Otros/Resumen files

  • Populate 2 empty concept notes in MAT1203

    • Add content to Vector.md
    • Add content to Matriz.md

  • Create top 5 missing concept notes for MAT1203

    • Independencia-Lineal.md
    • Base.md
    • Determinante.md
    • Transformaciones-Lineales.md
    • Valores-Propios.md

Short-term Actions (Next 2 Weeks)

  • Add systematic class → concept links in MAT1203

    • Review each class note
    • Add “Conceptos Relacionados” section
    • Link to relevant concept notes

  • Implement top 3 cross-course connections

    • Independencia: MAT1203 ↔ EYP1016
    • Valor Promedio ↔ Esperanza: MAT1610 ↔ EYP1016
    • Combinación Lineal ↔ Aproximación Lineal: MAT1203 ↔ MAT1610

  • Create concept notes for EYP1016

    • Esperanza.md
    • Varianza.md
    • Variable-Aleatoria.md

Medium-term Actions (Next Month)

  • Complete all MAT1203 concept notes (remaining 21 files)
  • Implement all 8 cross-course connections
  • Create MOC (Map of Content) for each course
  • Add bidirectional links throughout
  • Create master “Mathematics Concepts” MOC

Long-term Maintenance

  • When adding new notes, always link to related concepts
  • Review orphaned notes monthly
  • Update MOCs as new topics are added
  • Add cross-references when seeing connections during study

8. Tools and Automation Suggestions

Manual Review Tasks

  • Use Obsidian Graph View to visualize orphaned clusters
  • Use “Outgoing Links” and “Backlinks” panes to verify bidirectional links
  • Search for concept keywords in class notes to find missing links

Potential Automation

  • Create a script to:

    • Find all mentions of concept file names in class notes
    • Report which mentions are not wikilinked
    • Suggest wikilink additions

  • Use Dataview plugin to:

    • Create dynamic lists of “Notes without links”
    • Generate automatic backlink sections
    • Build dynamic MOCs

Obsidian Plugins to Consider

  • Dataview: Query-based note organization
  • Graph Analysis: Better visualization of link structure
  • Link Converter: Bulk convert text to wikilinks
  • Consistent Attachments and Links: Maintain link integrity

Conclusion

This vault has a strong foundation with good content and structure. The primary improvement opportunity is in linking existing content, particularly:

  1. 26 orphaned concept notes in MAT1203 represent the biggest quick win
  2. Cross-course connections will create a richer knowledge graph for interdisciplinary understanding
  3. Systematic bidirectional linking between class notes and concept notes will improve navigation

Estimated Effort:

  • High-priority fixes: 4-6 hours
  • Complete MAT1203 concept linking: 10-15 hours
  • Full implementation: 25-30 hours over 4-6 weeks

Expected Benefits:

  • Easier navigation during study and review
  • Better understanding of concept relationships
  • Reduced cognitive load (concepts defined once, linked everywhere)
  • Foundation for future advanced connections (e.g., multivariable calculus, linear models in statistics)

Next Steps: Review this report and prioritize actions based on upcoming exams and study needs. Consider starting with the course you’re currently studying to see immediate benefits.

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