math geniuses come

i need to learn statistics, probability, calculus and linear algebra for my machine learning class. what prerequisites should i learn first before i get into those topics? i know like high school level algebra (solving linear equations, quadratic equations, etc). please suggest an order of topics to start from.

not a "genius" but im pretty decent so ill suggest

linear algebra (cus if ur algebra is weak then ur other aspects will suffer)
calculus
then probablity

this is how i was taught

edit for clarity:
we split up linear algebra

its linear (part) -> calc -> stats -> parts of trig + the remainder of linear
also the course is open sourced meaning ur supposed to self study parts of it

Perfect — since you already know high-school algebra, you’ve got a solid starting point.
Here’s a clear, step-by-step roadmap that builds the math foundation needed for machine learning in a logical order:

🧭 Stage 0 – Refresh Core Foundations

Before diving into advanced math, strengthen these essentials:

Algebraic Manipulation

Exponents, logarithms, inequalities

Functions and transformations (e.g.,
f(x)=ax2+bx+c
f(x)=ax
2
+bx+c, shifting/scaling)

Coordinate Geometry & Graphs

Lines, slopes, intersections

Understanding graphs of functions — this intuition helps a lot later

Basic Trigonometry

Sine, cosine, tangent, unit circle

Used in calculus and vector analysis

🧩 Stage 1 – Precalculus

This bridges algebra to calculus.

Functions and their properties (polynomial, exponential, logarithmic)

Inverse functions

Sequences and series (especially arithmetic/geometric)

Understanding limits (intuitive idea, not rigorous yet)

📘 Resources:

Khan Academy: Precalculus

“Precalculus” by Stewart, Redlin, & Watson (only first few chapters)

📈 Stage 2 – Calculus (Single Variable)

Crucial for optimization in ML.

Limits and Continuity

Derivatives – rate of change, gradient, tangent line

Applications of Derivatives – maxima, minima, optimization

Integrals – area under curve, cumulative functions

Partial Derivatives (Intro) – leads into multivariable calculus

📘 Resources:

Khan Academy Calculus I

Essence of Calculus (YouTube, 3Blue1Brown – fantastic for intuition)

🔢 Stage 3 – Linear Algebra

The language of ML. You’ll use it everywhere.

Vectors and Matrices

Matrix Operations (addition, multiplication, inverse)

Linear Transformations and Systems of Equations

Determinants and Rank

Eigenvalues and Eigenvectors (key for PCA, deep learning)

Vector Spaces and Basis (helps conceptual understanding)

📘 Resources:

Linear Algebra Done Right (Axler) – conceptual

Essence of Linear Algebra (3Blue1Brown series) – visual

Khan Academy Linear Algebra – structured progression

🎲 Stage 4 – Probability and Statistics

Core for ML understanding (models, inference, evaluation).

Set Theory & Counting (Combinatorics)

Basic Probability Rules (independence, conditional probability, Bayes’ theorem)

Random Variables & Distributions (Discrete + Continuous)

Expectation, Variance, Covariance

Sampling & Central Limit Theorem

Descriptive + Inferential Statistics (confidence intervals, hypothesis testing, regression)

📘 Resources:

Khan Academy: Probability & Statistics

Think Stats (Allen Downey) – free and intuitive

StatQuest (YouTube) – simple ML-focused stats explanations

🧮 Stage 5 – Multivariable Calculus + Optimization (optional but valuable)

If you want to go beyond basics for ML models like neural networks:

Gradient, Divergence, and Jacobians

Gradient Descent and Optimization Methods

Vector Calculus Concepts (dot product, cross product)

✅ Suggested Order Summary:

Algebra & Graphs →

Precalculus →

Calculus (single variable) →

Linear Algebra →

Probability & Statistics →

Multivariable Calculus (optional but recommended)

stats and probability you just need a graphing calculator 🤣also learn how to draw venn diagrams and know the stuff for the different variable types and probability types

You all learn that in university??? Wtf I learn all that in high school bro

you can start with basic differential and integral calculus as it is sometimes required in probability and stats but not to that extent so actually u can start in any order, but it is better if u do calculus first as it finds its way into everything

LA use gilbert strang's mit playlist or his book, cal1 and 2 use pauls notes (google them), stats idk, probability idk

For linear algebra, watch 3b1b essence of linear algebra. Idk for the other ones

in uni i took the ff in order (i wouldnt call myself a math genius though), ill mention some relevant topics for each subject cause ill also be taking a machine learning class next semester. being good at hs algebra and trig, conic sections really carried me through calculus

differential calculus: limits, derivatives (linear approx, extreme value theorem, mean value theorem, optimization, related rates, etc)

integral calculus: integrals (area between two curves, improper integrals, etc)

stats: common statistical distributions, hypothesis testing with one, two or multiple samples

linear algebra: linear transformations, vectors, idk im still taking the class rn

i think i took integral calculus before stats cause the proofs of some of the probability distributions required integration

statistics is a no brainer -> with high school math you should be fine, its mostly memorization and knowing how to use formulas properly

probability -> if you havent had experience with this you might need to learn from scratch, i recommend learning probability before stat bc you need to use some probability concepts (like binomial probability)

linear algebra -> linear algebra is a hard topic to grasp, but you can learn it directly from high school algebra

calculus -> similarly you just need a good understanding of algebra skills, learning trig is also helpful

each of these topics are going to take a long time, i dont know what your knowledge gaps are, but I would recommend starting with probability, then statistics because those two slightly overlap. I would say linear algebra next because the math skills you need aren't too heavy as in my opinion its more conceptual. Then calculus last.

I would go through each topic and just learn the stuff you are missing as you are going. There's plenty of good stat (I reccomend professor leonard for statistics) and probability (near infinite amounts of different ones) resources online.

Dr. Trefor Bazett on youtube has good linear algebra, and then once you are done with that I would definetly reccomend 3blue1brown's linear algebra serious. 3blue1brown in my opinion is more of an enrichment of what you already learned, not something to learn from scratch with. These resources aren't the very best, but its just what I prefer. Once again many good lin alg resources online.

lastly, what I call the holy grail of you tube math, Professor Leonard. I truly reccomend the calculus series by professor leonard which is very easy to understand. Also he also teaches some precalculus and algebra skills lectures so when in doubt you can go watch.

Ermmmm I study maths at uni idk if I'd I am a genius but I wouldn't really say you need to start with any particular subject and it sorta depends how much you need to know about since it's not like these subjects are isolated from one another. For example, you might need calculus for some stats problems and what not. You should probably create a schedule and try to study from each subject together instead of 1 by 1.

As for prerequistes, other understanding the basic of functions and recognising the elementary functions there aren't really anything you need to start studying these topics.

statistics : What u learned from high school schould be fine
probability : Learn permutations and combinations first makes life a lot easier then learn binomial theorem
Linear Algebra :I am assuming u have a good understand in set theory and functions and relations ,Quadratic Equation like graphs and shit , location of roots and thoery of equations along with vietta's and newton's formulas , complex number , mathematical induction, then linear transformations and vector 3d
Calculus : dont move unless u have done atleast the quadratic part , and the prerequisites of knowing before the quadratic part and linear transformation
start with differentiatial calculus then integral . Then continuity and differentiability
ya first complete these

idk for me stats and probability I always despised more so I would say focus on that more. Linear algebra and calculus are somewhat straightforward and doesn't require as much memorisation of formulas and just overall practice in general.

Calculus
Linear Algebra
Probability
Statistics

https://leibnizmathema.wordpress.com/wp-content/uploads/2020/08/cambridge-international-as-a-level-mathematics-probability-statistics-1-coursebook-cambridge-assessment-international-education-by-dean-chalmers-julian-gilbey-leibniz-math.org-1-1.pdf (equivalent to AP Stats and Maths would be stuff you would be doing in Uni now)
https://www.cs.ox.ac.uk/files/12921/book.pdf (linear algebra book)
https://ocw.mit.edu/courses/res-18-001-calculus-fall-2023/pages/textbook/ (calculus)

for calc, you'd need some trig knowledge, algebraic manipulation and the graphing from algebra itself.

honestly just learn the machine learning lol, you can learn as you go. knowing the integral of arcsin will not help you build cnns. even when you get to calc stuff (e.g. gradient descent) you can ask someone for an intuitive explanation, then forget it, use torch.autograd that does everything for you, and learn it later