If you're looking for a consistent and beginner-friendly pathway to prepare for studying advanced concepts like calculus, real analysis, and dynamical systems, it's great that you already have some basics in algebra, linear algebra, geometry, and trigonometry! Here’s a step-by-step guide tailored to your current level:

1. Strengthen Basic Arithmetic and Algebra

• Why? Algebra is the foundation of almost every advanced math topic.

• Topics to Cover:

  • Solving linear equations.
  • Understanding polynomials and factoring.
  • Simplifying expressions.
  • Working with exponents and roots.
  • Inequalities and absolute values.

• Resources:

  • Book: Algebra for Dummies by Mary Jane Sterling (great for beginners).
  • Free Course: Khan Academy - Algebra Basics.

2. Dive Deeper into Geometry and Trigonometry

• Why? You need a solid understanding of shapes, angles, and trigonometric functions for calculus and linear algebra.

• Topics to Cover:

  • Geometry: Properties of triangles, circles, and polygons.
  • Trigonometry: Sine, cosine, tangent, unit circle, and trigonometric identities.
  • Graphs of trigonometric functions.

• Resources:

  • Book: Geometry for Enjoyment and Challenge by Richard Rhoad (accessible and structured).
  • Free Course: Khan Academy - Geometry and Trigonometry.

3. Learn Pre-Calculus Concepts

• Why? Pre-calculus bridges the gap between basic algebra/trigonometry and calculus.

• Topics to Cover:

  • Functions: Domain, range, transformations, and inverses.
  • Exponential and logarithmic functions.
  • Sequences and series.
  • Intro to limits.

• Resources:

  • Book: Precalculus: Mathematics for Calculus by James Stewart et al. (clear explanations).
  • Free Course: Khan Academy - Precalculus.

4. Start with Calculus

• Why? It’s essential for understanding changes, motion, and areas under curves.

• Topics to Cover:

  • Limits and continuity.
  • Differentiation: Rules, applications, and graphing.
  • Integration: Techniques and applications.
  • Basic differential equations (optional for now).

• Resources:

  • Book: Calculus Made Easy by Silvanus P. Thompson (classic, simple explanations).
  • Free Course: Paul’s Online Math Notes - Calculus.

5. Explore Linear Algebra

• Why? Linear algebra is heavily used in machine learning, graphics programming, and dynamical systems.

• Topics to Cover:

  • Matrix operations and properties.
  • Vector spaces and transformations.
  • Eigenvalues and eigenvectors.

• Resources:

  • Book: Introduction to Linear Algebra by Gilbert Strang (widely recommended).
  • Free Course: MIT OpenCourseWare - Linear Algebra.

6. Begin Exploring Real Analysis

• Why? Real analysis provides the rigorous foundation for calculus.

• Topics to Cover:

  • Proofs in mathematics.
  • Limits and sequences in depth.
  • Continuity, differentiation, and integration.

• Resources:

  • Book: Understanding Analysis by Stephen Abbott (beginner-friendly and insightful).
  • Free Course: YouTube - Real Analysis by Dr. Tadashi Tokieda.

Recommended Pathway Summary

1. Master algebra → geometry → trigonometry.
2. Build on pre-calculus.
3. Dive into calculus and linear algebra.
4. Transition to real analysis and advanced topics.

General Tips

• Practice, Practice, Practice: Use problems and exercises from the books or online platforms like Khan Academy.
• Consistency is Key: Dedicate small but consistent amounts of time daily or weekly.
• Community Support: Join forums like Math Stack Exchange if you get stuck.
• Focus on Concepts, Not Memorization: Aim to understand why something works, not just how.

Start with the resources above, and feel free to ask if you need more guidance. You've got this! 🚀