My Math Academy Learning Workflow
Aug 25, 2024 • 5 min read
Navigating complex Math Academy lessons can be challenging. Over time, I’ve developed a structured approach that has significantly improved my understanding and retention of mathematical concepts. Let me walk you through my process, and hopefully it’ll speed up your learning journey.
Here’s how I approach each new Math Academy lesson:

Topic Check: I start by asking, “Is this a new topic?”
 For new topics, I use an AI tool to generate initial notes.
 For familiar topics, I review my existing notes.

Quick Prep: I spend about 5 minutes reviewing the notes. This brief overview helps prime my brain for the lesson.

Math Academy Lesson: With this preparation, I find it easier to follow and engage with the actual lesson.

Note Refinement: After the lesson, I revisit my notes. I add new information, clarify points, and sometimes correct misunderstandings.

Practice Problems: Next, I tackle practice problems. When I make mistakes, I try to figure them out on my own before checking the solutions.

Repeat: I move on to the next topic and start the process again.
AI Prompt Preview:
Create concise mathematical notes (fenced markdown code block) on the topic "[INSERT TOPIC]" using the following structure:
# [Topic Name] ([Area] > [Subarea])
[e.g., "Mean (Mathematics > Statistics)" or "Complex Numbers (Mathematics > Algebra)"]
## Definition
Provide a clear, formal mathematical definition of the topic. Include:
 A concise verbal explanation of the concept
 The mathematical formula or representation, using LaTeX notation
Example: "For a dataset ${x_1, x_2, ..., x_n}$, the arithmetic mean $\bar{x}$ is defined as:
$$\large\bar{x} = \frac{1}{n}\sum_{i=1}^n x_i = \frac{x_1 + x_2 + ... + x_n}{n}$$"
## Key Concepts
 [List 34 fundamental ideas or principles related to the topic]
## Important Properties
1. [State a key property or characteristic]
2. [State another key property or characteristic]
3. [State a third key property or characteristic, if applicable]
## Essential Formulas
 [Present a crucial formula, using LaTeX notation]
 [Present another crucial formula, if applicable]
## Core Examples
1. [Provide a basic example demonstrating the concept]
2. [Provide a more advanced application or example]
## Related Theorems/Rules
[If applicable, state any important theorems or rules associated with the topic]
## Common Pitfalls
 [Mention a common mistake or misunderstanding]
 [Mention another common mistake or misunderstanding]
## Related Topics
 [List a closely related mathematical topic]
 [List another closely related mathematical topic]
## Quick Review Questions
1. [Pose a question that tests understanding of a key concept]
2. [Pose another question that encourages deeper thinking about the topic]
Ensure the notes are mathematically accurate, concise, and suitable for quick review. Use LaTeX notation for ALL mathematical expressions, including numbers (e.g., $2$, $\pi$). Use double dollar symbols ($$) for displaystyle equations or main expressions, and single dollar symbols ($) for inline expressions. The area and subarea in the title should reflect the topic's place in the broader mathematical hierarchy. Use double square brackets [[]] to link to related concepts, theorems, or topics, creating connections between different notes.
Example of AIGenerated Notes:
Complex Numbers (Mathematics > Algebra)
Definition
A complex number $z$ is a number of the form $a + bi$, where $a$ and $b$ are real numbers and $i$ is the imaginary unit defined by $i^2 = 1$. Formally:
Key Concepts
 Real and imaginary parts
 Complex plane representation
 Modulus and argument
 Complex conjugate
Important Properties
 Closure: The sum and product of two complex numbers is a complex number
 Commutativity: $z_1 + z_2 = z_2 + z_1$ and $z_1 \cdot z_2 = z_2 \cdot z_1$
 Every complex number has a unique complex conjugate
Essential Formulas
 Modulus: $z = \sqrt{a^2 + b^2}$
 Euler’s formula: $e^{i\theta} = \cos\theta + i\sin\theta$
Core Examples
 Simplify $(3 + 2i) + (1  5i)$
 Find the roots of $z^2 + 1 = 0$
Related Theorems/Rules
Fundamental Theorem of Algebra: Every nonconstant polynomial equation has at least one complex root
Common Pitfalls
 Forgetting that $i^2 = 1$ when simplifying expressions
 Incorrectly applying properties of real numbers to complex numbers
Related Topics
 [[Polar Form of Complex Numbers]]
 [[Complex Roots of Unity]]
Quick Review Questions
 What is the complex conjugate of $2  3i$?
 How does multiplication by $i$ affect a complex number geometrically in the complex plane?
Why This Method Works For Me
This approach is effective for several reasons:

Preparation: The initial AI notes provide context, making the main lesson easier to follow. It’s like getting a movie trailer for the math lesson.

Active Learning: When I update my notes after the lesson, I’m not just passively absorbing – I’m actively engaging with the material. It’s like teaching it to myself.

ProblemSolving Skills: Working through problems independently deepens my understanding, even after commiting a mistake.

Consistent Practice: The repetitive nature of the process aids longterm retention, and the learning process doesn’t get monotonous.
Closing Thoughts
This method has transformed my approach to learning math. It combines the structured lessons from Math Academy with the flexibility of AIgenerated notes, creating a personalized learning experience that keeps me engaged and helps me retain information better.
But remember, this is just what works for me. Learning is a personal journey, and what’s effective can vary from person to person. Maybe you have a completely different approach that works wonders for you, or perhaps you’re still searching for your ideal study method.
I’m curious to hear about your experiences. How do you tackle challenging math concepts? Have you experimented with any tech tools in your studies? Share your thoughts and strategies – who knows, we might all learn some new tricks to add to our mathematical toolboxes!
Keep exploring, keep learning, and most importantly, don’t be afraid to find your own path in the world of mathematics. After all, that’s what makes this journey so exciting ⭐