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learning_plans/linear_algebra/02_INITIAL_ASSESSMENT.md
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learning_plans/linear_algebra/02_INITIAL_ASSESSMENT.md
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# Linear Algebra Initial Assessment
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## 🎯 Purpose
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This assessment will help determine your current Linear Algebra proficiency level and create a personalized learning path.
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## 📋 Assessment Structure
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### Part 1: Self-Assessment Questionnaire
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### Part 2: Computational Problems
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### Part 3: Knowledge Gap Analysis
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---
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## Part 1: Self-Assessment Questionnaire
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Rate yourself honestly (0-4):
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- **Level 0:** Never heard of it
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- **Level 1:** Basic awareness
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- **Level 2:** Can use with reference
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- **Level 3:** Proficient, confident
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- **Level 4:** Expert, can teach
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### Vectors
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| Topic | Level (0-4) | Notes |
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|-------|-------------|-------|
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| Vector definition & notation | | |
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| Vector addition/subtraction | | |
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| Scalar multiplication | | |
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| Dot product | | |
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| Cross product (3D) | | |
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| Vector magnitude/norm | | |
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| Unit vectors | | |
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| Orthogonal vectors | | |
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| Vector projection | | |
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| Linear combinations | | |
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### Matrices
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| Topic | Level (0-4) | Notes |
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|-------|-------------|-------|
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| Matrix definition | | |
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| Matrix addition/subtraction | | |
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| Matrix multiplication | | |
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| Transpose | | |
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| Identity matrix | | |
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| Inverse matrix | | |
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| Determinants | | |
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| Special matrices (diagonal, symmetric) | | |
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### Linear Systems
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| Topic | Level (0-4) | Notes |
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|-------|-------------|-------|
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| Systems of linear equations | | |
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| Gaussian elimination | | |
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| Row echelon form | | |
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| RREF | | |
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| Solution types (unique, infinite, none) | | |
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| Homogeneous systems | | |
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| Augmented matrices | | |
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### Vector Spaces
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| Topic | Level (0-4) | Notes |
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|-------|-------------|-------|
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| Vector space definition | | |
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| Subspaces | | |
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| Span | | |
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| Linear independence | | |
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| Basis | | |
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| Dimension | | |
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| Null space | | |
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| Column space | | |
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| Rank | | |
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### Eigenvalues & Decompositions
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| Topic | Level (0-4) | Notes |
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|-------|-------------|-------|
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| Eigenvalues | | |
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| Eigenvectors | | |
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| Characteristic polynomial | | |
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| Diagonalization | | |
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| LU decomposition | | |
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| QR decomposition | | |
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| SVD | | |
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| Orthogonalization (Gram-Schmidt) | | |
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### Applications
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| Topic | Level (0-4) | Notes |
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|-------|-------------|-------|
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| Linear regression | | |
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| PCA | | |
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| Graphics transformations | | |
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| Least squares | | |
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| Optimization | | |
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---
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## Part 2: Computational Problems
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### Problem 1: Vector Operations (Beginner)
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Given vectors u = [2, -1, 3] and v = [1, 4, -2]:
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a) Compute u + v
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b) Compute 3u - 2v
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c) Compute ||u|| (magnitude)
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d) Compute u · v (dot product)
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e) Are u and v orthogonal?
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**Can you solve this?** ☐ Yes ☐ No ☐ Partially
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---
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### Problem 2: Matrix Multiplication (Beginner)
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Compute AB where:
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```
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A = [1 2] B = [5 6]
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[3 4] [7 8]
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```
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**Can you solve this?** ☐ Yes ☐ No ☐ With formula
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---
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### Problem 3: Solve Linear System (Intermediate)
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Solve using Gaussian elimination:
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```
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x + 2y - z = 3
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2x - y + z = 1
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3x + y + 2z = 11
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```
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**Can you solve this?** ☐ Yes ☐ No ☐ With steps
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---
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### Problem 4: Matrix Inverse (Intermediate)
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Find the inverse of:
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```
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A = [2 1]
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[5 3]
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```
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**Can you solve this?** ☐ Yes ☐ No ☐ With formula
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---
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### Problem 5: Eigenvalues (Advanced)
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Find eigenvalues and eigenvectors of:
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```
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A = [3 1]
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[1 3]
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```
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**Can you solve this?** ☐ Yes ☐ No ☐ With steps
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---
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### Problem 6: Application - Linear Regression (Advanced)
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Given data points: (1,2), (2,4), (3,5), (4,6)
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Set up and solve the least squares problem to find the best-fit line y = mx + b using matrix methods.
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**Can you solve this?** ☐ Yes ☐ No ☐ Know concept only
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---
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## Part 3: Knowledge Gap Analysis
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### Based on Self-Assessment
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**Count your scores:**
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- Topics at Level 0: ___
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- Topics at Level 1: ___
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- Topics at Level 2: ___
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- Topics at Level 3: ___
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- Topics at Level 4: ___
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**Total topics:** ___
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### Based on Problems
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**Problems solved:**
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- Problem 1 (Vectors): ☐
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- Problem 2 (Matrix Mult): ☐
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- Problem 3 (Systems): ☐
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- Problem 4 (Inverse): ☐
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- Problem 5 (Eigenvalues): ☐
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- Problem 6 (Application): ☐
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**Total solved:** ___ / 6
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---
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## 📊 Proficiency Level Determination
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### Absolute Beginner (0-20% Level 2+, 0-1 problems)
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- **Start:** Phase 1 from Module 1.1
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- **Timeline:** 10-12 months to applications
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- **Focus:** Build from scratch, emphasize geometric intuition
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- **Resources:** 3Blue1Brown, Khan Academy, "Linear Algebra Done Right"
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### Beginner (20-40% Level 2+, 1-2 problems)
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- **Start:** Phase 1 with quick review, focus on Phase 2
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- **Timeline:** 8-10 months to applications
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- **Focus:** Strengthen basics, master systems and inverses
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- **Resources:** Gilbert Strang lectures, "Linear Algebra and Its Applications"
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### Intermediate (40-60% Level 2+, 3-4 problems)
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- **Start:** Phase 2, review Phase 1 as needed
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- **Timeline:** 6-8 months to applications
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- **Focus:** Vector spaces, eigenvalues, decompositions
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- **Resources:** Strang's book, MIT OCW
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### Advanced (60-80% Level 2+, 5 problems)
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- **Start:** Phase 3, skim Phase 1-2
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- **Timeline:** 4-6 months to specialization
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- **Focus:** Advanced theory and applications
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- **Resources:** "Matrix Analysis", research papers
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### Expert (80%+ Level 3+, 6 problems)
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- **Start:** Phase 4-5 (Applications & Specialization)
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- **Timeline:** 2-4 months to deep specialization
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- **Focus:** Specialized applications, cutting-edge topics
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- **Resources:** Research papers, advanced texts
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---
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## 🎯 Personalized Learning Path
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### Your Starting Point
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**Based on assessment:** _______________
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### Recommended Phase
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**Start at Phase:** _______________
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### Topics to Review First
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1. _______________
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2. _______________
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3. _______________
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### Topics to Skip (Already Mastered)
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1. _______________
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2. _______________
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### Weak Areas to Focus On
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1. _______________
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2. _______________
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### Estimated Timeline to Advanced
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**From your starting point:** ___ months
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---
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## 📝 Action Items
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### Immediate (This Week)
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1. ☐ Complete this assessment
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2. ☐ Set up Python + NumPy or MATLAB
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3. ☐ Watch 3Blue1Brown: "Essence of Linear Algebra" (video 1)
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4. ☐ Review recommended phase in Master Plan
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5. ☐ Join math communities (r/learnmath, Math Stack Exchange)
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### First Month
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1. ☐ Complete ____ modules
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2. ☐ Solve 100+ practice problems
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3. ☐ Watch all 3Blue1Brown videos (11 total)
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4. ☐ Implement basic operations in code
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5. ☐ Take first monthly exam
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---
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## 🔄 Reassessment Schedule
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- **Week 4:** Quick progress check
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- **Month 3:** Comprehensive reassessment
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- **Month 6:** Mid-journey assessment
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- **Month 9:** Full reassessment
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- **Month 12:** Expert level check
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---
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## 📚 Additional Resources
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### Video Series
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- **3Blue1Brown:** "Essence of Linear Algebra" (MUST WATCH)
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- **MIT OCW:** Gilbert Strang's 18.06
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- **Khan Academy:** Linear Algebra playlist
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### Interactive Tools
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- **GeoGebra:** Visualize vectors and transformations
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- **WolframAlpha:** Compute anything
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- **MATLAB/Octave:** Numerical experiments
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- **Python + NumPy:** Programming practice
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### Problem Sources
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- MIT OCW problem sets
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- Gilbert Strang's textbook exercises
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- Linear Algebra Done Right exercises
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- Math Stack Exchange
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---
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**Date Completed:** _______________
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**Next Reassessment:** _______________
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**Notes:**
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_______________________________________________
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_______________________________________________
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