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I will try to record my math plan as i am studying differnet math branches, reading new books , papers , persons ISA , I will start with this plan This plan is organized to build mathematical foundations progressively, starting with fundamental reasoning skills and advancing to specialized topics relevant to AI engineering.

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1. General Courses

I will start by Investigating different math branches with general courses
  1. Probability (Ross)
  2. Statistics (Wackerly)
  3. Algebra (Strang)
  4. Optimization (Boyd & Vandenberghe)
  5. Calculus
  6. Analysis
  7. Proof
  8. Logic
  9. Other Branches

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Phase 1: Foundations (Weeks 1-16)

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1. Logic & Mathematical Reasoning

Book: Discrete Mathematics with Applications by Susanna Epp Why this book: Establishes the foundation for mathematical thinking, including propositional logic, predicate logic, and proof techniques. Essential before moving to formal proofs. Focus areas:
  • Logic and proof techniques
  • Sets and functions
  • Mathematical reasoning
Duration: 4 weeks

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2. Proof Techniques

Book: An Introduction to Abstract Mathematics by Robert J. Bond and William J. Keane Why this book: Bridges computational mathematics and abstract reasoning. Teaches you how to read, write, and construct rigorous mathematical proofs. Focus areas:
  • Direct and indirect proofs
  • Mathematical induction
  • Proof by contradiction
Duration: 3 weeks

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Phase 2: Core Mathematics (Weeks 17-44)

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3. Calculus

Book: Calculus by James Stewart Why this book: Industry-standard text with excellent balance of theory and applications. Comprehensive coverage of single and multivariable calculus essential for ML/AI. Focus areas:
  • Limits and continuity
  • Differentiation and integration
  • Multivariable calculus
  • Vector calculus
Duration: 8 weeks

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4. Linear Algebra

Book: Linear Algebra and Its Applications by Gilbert Strang Why this book: Written specifically with applications in mind. Strang’s approach emphasizes geometric intuition and computational aspects crucial for AI/ML. This is THE book for AI practitioners. Focus areas:
  • Vector spaces and linear transformations
  • Eigenvalues and eigenvectors
  • Matrix decompositions (SVD, QR, etc.)
  • Applications to data science
Duration: 6 weeks

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5. Probability

Book: A First Course in Probability by Sheldon Ross Why this book: Clear, rigorous treatment with excellent examples. Builds the foundation for statistics and probabilistic machine learning. Focus areas:
  • Probability axioms and combinatorics
  • Random variables and distributions
  • Expectation and variance
  • Limit theorems
Duration: 5 weeks

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6. Statistics

Book: Mathematical Statistics with Applications by Dennis Wackerly Why this book: Rigorous yet accessible treatment connecting probability theory to statistical inference. Essential for understanding ML algorithms. Focus areas:
  • Statistical inference
  • Hypothesis testing
  • Estimation theory
  • Sampling distributions
Duration: 6 weeks

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Phase 3: Advanced Topics (Weeks 45-68)

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7. Real Analysis

Book: Analysis I by Terence Tao Why this book: Modern, clear exposition by a Fields Medalist. Builds rigorous foundations for calculus and provides intuition essential for optimization theory. Focus areas:
  • Real number system
  • Sequences and series
  • Continuity and differentiability
  • Riemann integration
Duration: 8 weeks

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8. Optimization

Book: Convex Optimization by Stephen Boyd and Lieven Vandenberghe Why this book: THE definitive text for convex optimization. Directly applicable to machine learning. Free online version available. Essential for deep learning and modern AI. Focus areas:
  • Convex sets and functions
  • Optimization problems
  • Duality theory
  • Applications to ML/AI
Duration: 8 weeks

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Phase 4: Specialized Topics (Weeks 69-88)

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9. Abstract Algebra

Book: Algebra by Michael Artin Why this book: More accessible than Dummit & Foote while maintaining rigor. Excellent for understanding symmetries, transformations, and algebraic structures in AI. Focus areas:
  • Group theory
  • Ring theory
  • Linear algebra from abstract perspective
  • Applications
Duration: 6 weeks

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10. Additional Branches

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Topology

Book: Introduction to Topology by Robert Everist Greene (assuming “robert everist” refers to Greene) Why: Provides foundations for understanding manifolds and topological data analysis. Duration: 4 weeks

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Combinatorics

Book: Applied Combinatorics by Alan Tucker Why: Essential for algorithm analysis and discrete optimization in AI. Duration: 4 weeks

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Complex Analysis

Book: Fundamentals of Complex Analysis with Applications to Engineering and Science by Saff & Snider Why: Important for signal processing and certain advanced ML topics. Duration: 4 weeks

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Graph Theory

Book: Graph Theory by Ronald Gould Why: Critical for network analysis, graph neural networks, and algorithm design. Duration: 2 weeks

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Study Strategy

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Prerequisites Flow

Logic → Proof → Calculus → Analysis
              ↓           ↓
         Linear Algebra   Optimization
              ↓           ↓
         Probability → Statistics
              ↓
         Abstract Algebra

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Priority Ranking for AI Engineering

Tier 1 (Critical - Master these):
  1. Linear Algebra (Strang)
  2. Probability (Ross)
  3. Calculus (Stewart)
  4. Optimization (Boyd & Vandenberghe)
Tier 2 (Very Important): 5. Statistics (Wackerly) 6. Analysis (Tao) 7. Logic (Epp) Tier 3 (Useful for specialization): 8. Proof (Bond & Keane) 9. Abstract Algebra (Artin) 10. Specialized topics based on research area

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Notes for AI Engineering Focus

  • Deep Learning: Emphasize Linear Algebra, Calculus, Optimization
  • Probabilistic ML: Emphasize Probability, Statistics, Analysis
  • Reinforcement Learning: Add optimization, graph theory
  • NLP: Abstract algebra (group theory for embeddings)
  • Computer Vision: Topology, geometry, linear algebra

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Estimated Timeline

  • Total duration: ~88 weeks (~21 months)
  • Intensive study: Can be compressed to 12-15 months
  • Part-time study: May extend to 24-30 months

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Additional Resources

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Free Online Supplements

  • Linear Algebra: Gilbert Strang’s MIT OpenCourseWare lectures
  • Optimization: Boyd’s Stanford lectures (freely available)
  • Probability: MIT 6.041/6.431 materials