i used chatgpt to put together this list for learning all the math you need using only Khan Academy video tutorials for free, i hope you find it useful👇🏻

The recommended order is:

1. Get Ready for Algebra 1 — diagnostic only

2. Algebra 1

3. Geometry — selective topics

4. Algebra 2

5. Trigonometry

6. Precalculus

7. Linear Algebra

8. Calculus 1

9. Multivariable Calculus — selective topics

10. AP/College Statistics

You do NOT need to take every math course Khan Academy offers.

---

# 0. Get Ready for Algebra 1

Start here with the course challenge/assessment.

If you already know basic algebra, don't spend weeks going through material you already understand.

Use it to find gaps.

If you struggle with something, study that topic and move on.

---

# 1. Algebra 1

Do essentially the whole course.

Important topics:

- Linear equations and inequalities

- Systems of equations

- Ratios and proportions

- Functions

- Graphing

- Exponents

- Radicals

- Polynomials

- Quadratics

- Exponential relationships

The goal is to make basic algebra automatic.

You should be able to manipulate equations and formulas without constantly having to think about the mechanics.

---

# 2. Geometry — selective

You do NOT need the entire Geometry course for ML.

Focus on:

- Coordinate geometry

- Coordinate planes

- Distance between points

- Midpoint

- Slope

- Equations of lines

- Basic transformations

- Translations

- Reflections

- Rotations

- Scaling

- Basic geometric/vector intuition

Lower priority for ML:

- Long geometric proofs

- Congruence proofs

- Similarity proofs

- Circle theorems

- Geometric constructions

- Detailed Euclidean geometry

The purpose of geometry here is mainly to strengthen spatial and coordinate intuition.

---

# 3. Algebra 2

Do essentially the whole course.

Pay particular attention to:

- Functions

- Domain and range

- Function transformations

- Polynomial functions

- Rational functions

- Exponential functions

- Logarithms

- Sequences

- Systems of equations

- Complex numbers

Exponents and logarithms are particularly important later in statistics, probability, optimization and ML.

---

# 4. Trigonometry

Do most/all of the course, but don't obsess over difficult identities.

Focus on:

- Angles

- Radians

- Unit circle

- Sine, cosine and tangent

- Graphs of trig functions

- Inverse trig functions

- Fundamental identities

- Basic trig equations

The main purpose is to prepare for calculus and mathematical modeling.

---

# 5. Precalculus

Do most of the course, but prioritize the ML-relevant material.

### High priority

- Composite functions

- Inverse functions

- Trigonometry

- Rational functions

- Vectors

- Matrices

- Limits and continuity

### Especially important

## Vectors

Learn:

- Vector addition/subtraction

- Scalar multiplication

- Components

- Magnitude

- Direction

- Basic geometric interpretation

## Matrices

Learn:

- Matrix representation

- Matrix addition/subtraction

- Scalar multiplication

- Matrix multiplication

- Systems of equations

- Matrix inverses

- Basic transformations

These topics are a bridge into linear algebra.

### Lower priority

- Complex numbers — understand the basics, but don't spend excessive time here

- Conic sections — learn the basics, but not a major ML priority

- Series — useful mathematical knowledge, but lower priority for starting ML

---

# 6. Linear Algebra

This is one of the CORE subjects for ML.

I would study this thoroughly.

Focus on:

### Vectors

- Vector operations

- Magnitude/norm

- Dot product

- Geometric interpretation

- Linear combinations

### Matrices

- Matrix multiplication

- Transpose

- Inverse

- Determinant

- Systems of equations

### Linear algebra concepts

- Span

- Linear independence

- Basis

- Linear transformations

- Orthogonality

- Projections

- Eigenvalues

- Eigenvectors

You should eventually be comfortable seeing something like:

y = Xw

and understanding what the matrix/vector operation actually represents.

For this subject, 3Blue1Brown's "Essence of Linear Algebra" is also extremely useful for visual intuition. Khan Academy can remain the main source for structured learning and exercises.

---

# 7. Calculus 1

Study this thoroughly.

Focus on:

- Limits

- Continuity

- Derivatives

- Derivative rules

- Chain rule

- Implicit differentiation

- Applications of derivatives

- Optimization

- Integrals

- Fundamental theorem of calculus

For ML, the most important parts are:

1. Derivatives

2. Chain rule

3. Optimization

4. Understanding what a derivative represents

The chain rule becomes particularly important when you eventually study neural networks and backpropagation.

---

# 8. Multivariable Calculus

You do NOT need every topic in the course before starting ML.

## Unit 1 — Multivariable functions

Study:

- Functions of multiple variables

- Multidimensional graphs

- Contour maps

- Basic vector fields

- Geometric interpretation

## Unit 2 — Derivatives of multivariable functions

HIGH PRIORITY.

Study thoroughly:

- Partial derivatives

- Higher-order partial derivatives

- Gradients

- Directional derivatives

- Multivariable chain rule

The gradient is especially important.

You should eventually understand what something like:

∇f

means, rather than just knowing how to calculate it.

## Unit 3 — Applications of multivariable derivatives

Study:

- Critical points

- Maxima/minima

- Saddle points

- Optimization

- Hessian / second-derivative ideas

These concepts connect directly to optimization in ML.

## Unit 4 — Multivariable integration

Lower priority for initial ML.

You can study it later.

## Unit 5 — Green's theorem, Stokes' theorem, divergence theorem

Skip these initially.

They're useful mathematics, but they're not necessary for the ML foundation we're trying to build.

---

# 9. Statistics & Probability

This is where Khan Academy's catalog gets particularly confusing.

You may see courses such as:

- Statistics and Probability

- AP/College Statistics

- College Probability

- Normal Probability and Statistics

- High School Statistics

You do NOT need to take all of them.

## Recommended choice

Use:

**AP/College Statistics**

(or Khan Academy's current equivalent Statistics and Probability curriculum).

You do NOT need to separately take College Probability and Normal Probability and Statistics first.

Those topics are already covered within the broader statistics/probability curriculum.

---

# What to study in Statistics & Probability

## 1. Exploring data

Learn:

- Categorical vs quantitative variables

- Distributions

- Frequency tables

- Two-way tables

- Conditional distributions

## 2. One-variable quantitative data

Learn:

- Histograms

- Distribution shape

- Center

- Spread

- Outliers

## 3. Summary statistics

HIGH PRIORITY.

Understand:

- Mean

- Median

- Variance

- Standard deviation

- Range

- Effects of outliers

Don't just memorize formulas. Understand what these quantities actually tell you about data.

## 4. Percentiles, z-scores and normal distributions

HIGH PRIORITY.

Learn:

- Percentiles

- Z-scores

- Standardization

- Normal distribution

- Density curves

You don't need a separate "Normal Probability and Statistics" course for this.

## 5. Two-variable data

HIGH PRIORITY.

Learn:

- Scatterplots

- Covariance

- Correlation

- Linear relationships

- Linear regression

- Interpretation of relationships

This is directly useful for understanding ML models and datasets.

## 6. Collecting data

Moderate priority.

Understand:

- Population vs sample

- Sampling

- Sampling bias

- Observational studies

- Experiments

- Randomization

The goal here is statistical thinking.

## 7. Probability

HIGH PRIORITY.

Study thoroughly:

- Probability rules

- Conditional probability

- Independence

- Bayes' theorem

- Addition rule

- Multiplication rule

- Dependent vs independent events

You don't need a separate College Probability course before this.

## 8. Random variables and probability distributions

HIGH PRIORITY.

Learn:

- Random variables

- Discrete vs continuous variables

- Expected value

- Variance

- Probability distributions

This is extremely important for understanding probabilistic ML.

## 9. Sampling distributions

Study:

- Sampling distributions

- Central Limit Theorem

- Sample means

- Standard error

## 10. Statistical inference

Study it, but it's lower priority than the material above.

Understand:

- Confidence intervals

- Hypothesis testing

- P-values

- Statistical significance

- Inference about means/proportions

- Regression inference

You don't need to spend months mastering every statistical test before starting ML.

## 11. Advanced statistics

Things such as:

- Chi-square tests

- ANOVA

- More advanced inference

are useful, but can be learned later depending on what area of ML you pursue.

---

# Courses you DON'T need to stack on top

You generally don't need:

- Arithmetic (unless you genuinely struggle with it)

- Pre-algebra (unless you have gaps)

- Integrated Math 1

- Integrated Math 2

- Integrated Math 3

- College Algebra

- College Probability as a separate prerequisite

- Normal Probability and Statistics as a separate prerequisite

- Both Calculus AB AND Calculus BC

- Differential Equations

- Multiple versions of Precalculus

- Test-prep courses

These are either alternative curricula, redundant material, or lower-priority mathematics for the specific goal of building an ML foundation.

---

# The final roadmap

GET READY FOR ALGEBRA 1

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ALGEBRA 1

│

▼

GEOMETRY (SELECTIVE)

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ALGEBRA 2

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TRIGONOMETRY

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PRECALCULUS

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├──────────────┐

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LINEAR ALGEBRA CALCULUS 1

│ │

└──────┬───────┘

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MULTIVARIABLE CALCULUS

(SELECTIVE TOPICS)

│

▼

AP/COLLEGE STATISTICS

│

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ML MATH READY