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<!doctype html>
<html lang="en">
<head>
<meta charset="UTF-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>Math Prerequisites — GPU Learning</title>
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<link
href="https://fonts.googleapis.com/css2?family=IBM+Plex+Mono:wght@400;500;600&family=Source+Serif+4:ital,opsz,wght@0,8..60,300;0,8..60,400;0,8..60,600;1,8..60,400&display=swap"
rel="stylesheet"
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<link rel="stylesheet" href="base.css" fetchpriority="high" />
<style>
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</head>
<body>
<!-- Navigation -->
<nav class="lesson-nav">
<div class="lesson-nav__inner">
<a href="index.html" class="lesson-nav__title">← COURSE INDEX</a>
</div>
</nav>
<div class="lesson-container">
<!-- Hero -->
<header class="hero hero--lesson">
<div class="hero__label">Before You Begin</div>
<h1 class="hero__title">Math Prerequisites & Resources</h1>
<p class="hero__desc">
Not confident in your math background? This page helps you assess your
readiness and find the best free resources to fill any gaps.
</p>
</header>
<!-- Reassurance -->
<div class="reassurance">
<div class="reassurance__title">You can do this</div>
<p>
The math required for GPU programming is more accessible than it
looks. If you can follow recipes and understand that 3 rows of 4 items
equals 12 items, you already have the intuition. These resources will
help you formalize that intuition into the precise language GPUs
speak.
</p>
</div>
<!-- Diagnostic Quiz -->
<section class="section" id="diagnostic">
<div class="section__number">01 — SELF-ASSESSMENT</div>
<h2 class="section__title">Diagnostic Quiz</h2>
<p>
Take this 5-question quiz to assess your current readiness. Be honest
with yourself—the goal is to identify what you need to learn, not to
pass a test.
</p>
<!-- Question 1 -->
<div class="quiz" id="quiz-1">
<div class="quiz-q">
1. Matrix multiplication: If matrix A is 3x4 and matrix B is 4x2,
what are the dimensions of the result C = A x B?
</div>
<div class="quiz-opts">
<div class="quiz-opt" data-correct="false" tabindex="0">
<div class="quiz-mark"></div>
<span>3x4</span>
</div>
<div class="quiz-opt" data-correct="true" tabindex="0">
<div class="quiz-mark"></div>
<span>3x2</span>
</div>
<div class="quiz-opt" data-correct="false" tabindex="0">
<div class="quiz-mark"></div>
<span>4x4</span>
</div>
<div class="quiz-opt" data-correct="false" tabindex="0">
<div class="quiz-mark"></div>
<span>4x2</span>
</div>
</div>
<div class="quiz-fb"></div>
</div>
<!-- Question 2 -->
<div class="quiz" id="quiz-2">
<div class="quiz-q">
2. Index arithmetic: In row-major order, what linear index
corresponds to element [2][3] in a 5x6 matrix? (0-indexed)
</div>
<div class="quiz-opts">
<div class="quiz-opt" data-correct="false" tabindex="0">
<div class="quiz-mark"></div>
<span>11</span>
</div>
<div class="quiz-opt" data-correct="false" tabindex="0">
<div class="quiz-mark"></div>
<span>13</span>
</div>
<div class="quiz-opt" data-correct="true" tabindex="0">
<div class="quiz-mark"></div>
<span>15</span>
</div>
<div class="quiz-opt" data-correct="false" tabindex="0">
<div class="quiz-mark"></div>
<span>17</span>
</div>
</div>
<div class="quiz-fb"></div>
</div>
<!-- Question 3 -->
<div class="quiz" id="quiz-3">
<div class="quiz-q">
3. Floating point: Approximately how many decimal digits of
precision does float32 (single precision) provide?
</div>
<div class="quiz-opts">
<div class="quiz-opt" data-correct="false" tabindex="0">
<div class="quiz-mark"></div>
<span>3-4 digits</span>
</div>
<div class="quiz-opt" data-correct="true" tabindex="0">
<div class="quiz-mark"></div>
<span>6-7 digits</span>
</div>
<div class="quiz-opt" data-correct="false" tabindex="0">
<div class="quiz-mark"></div>
<span>10-11 digits</span>
</div>
<div class="quiz-opt" data-correct="false" tabindex="0">
<div class="quiz-mark"></div>
<span>15-16 digits</span>
</div>
</div>
<div class="quiz-fb"></div>
</div>
<!-- Question 4 -->
<div class="quiz" id="quiz-4">
<div class="quiz-q">
4. Exponentials: Which function grows faster as x increases toward
infinity?
</div>
<div class="quiz-opts">
<div class="quiz-opt" data-correct="false" tabindex="0">
<div class="quiz-mark"></div>
<span>x^10 (polynomial)</span>
</div>
<div class="quiz-opt" data-correct="true" tabindex="0">
<div class="quiz-mark"></div>
<span>e^x (exponential)</span>
</div>
<div class="quiz-opt" data-correct="false" tabindex="0">
<div class="quiz-mark"></div>
<span>They grow at the same rate</span>
</div>
<div class="quiz-opt" data-correct="false" tabindex="0">
<div class="quiz-mark"></div>
<span>Depends on the value of x</span>
</div>
</div>
<div class="quiz-fb"></div>
</div>
<!-- Question 5 -->
<div class="quiz" id="quiz-5">
<div class="quiz-q">
5. Normalization: If you divide each element of [2, 4, 6] by their
sum (12), what do the resulting values sum to?
</div>
<div class="quiz-opts">
<div class="quiz-opt" data-correct="true" tabindex="0">
<div class="quiz-mark"></div>
<span>1</span>
</div>
<div class="quiz-opt" data-correct="false" tabindex="0">
<div class="quiz-mark"></div>
<span>0</span>
</div>
<div class="quiz-opt" data-correct="false" tabindex="0">
<div class="quiz-mark"></div>
<span>12</span>
</div>
<div class="quiz-opt" data-correct="false" tabindex="0">
<div class="quiz-mark"></div>
<span>3</span>
</div>
</div>
<div class="quiz-fb"></div>
</div>
<!-- Score Display -->
<div class="quiz-score" id="quiz-score">
<div class="quiz-score__value" id="score-value">0/5</div>
<div class="quiz-score__message" id="score-message"></div>
<p class="quiz-score__recommendation" id="score-recommendation"></p>
<button class="btn" id="reset-quiz">Retake Quiz</button>
</div>
</section>
<!-- Jump to Topics -->
<section class="section" id="topics">
<div class="section__number">02 — TOPICS</div>
<h2 class="section__title">Jump to a Topic</h2>
<div class="topic-nav">
<a href="#linear-algebra" class="topic-nav__link">Linear Algebra</a>
<a href="#matrix-ops" class="topic-nav__link">Matrix Operations</a>
<a href="#floating-point" class="topic-nav__link">Floating Point</a>
<a href="#exponentials" class="topic-nav__link"
>Exponentials & Logs</a
>
<a href="#index-arithmetic" class="topic-nav__link"
>Index Arithmetic</a
>
</div>
</section>
<!-- Linear Algebra Basics -->
<section class="section" id="linear-algebra">
<div class="section__number">03 — LINEAR ALGEBRA</div>
<h2 class="section__title">Linear Algebra Basics</h2>
<p>
Understanding vectors and matrices is fundamental. You don't need
proof-heavy linear algebra—focus on building visual and computational
intuition.
</p>
<div class="resource-card">
<div class="resource-card__header">
<h4 class="resource-card__title">
<a
href="https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab"
target="_blank"
rel="noopener"
>3Blue1Brown: Essence of Linear Algebra</a
>
</h4>
<div class="resource-card__meta">
<span class="resource-card__tag resource-card__tag--time"
>~3 hours</span
>
<span class="resource-card__tag resource-card__tag--beginner"
>Beginner</span
>
</div>
</div>
<p class="resource-card__desc">
The gold standard for visual intuition. Covers vectors, linear
transformations, matrix multiplication, and eigenvalues with
stunning animations. Watch chapters 1-7 for GPU programming
prerequisites.
</p>
</div>
<div class="resource-card">
<div class="resource-card__header">
<h4 class="resource-card__title">
<a
href="https://www.khanacademy.org/math/linear-algebra"
target="_blank"
rel="noopener"
>Khan Academy: Linear Algebra</a
>
</h4>
<div class="resource-card__meta">
<span class="resource-card__tag resource-card__tag--time"
>~15 hours</span
>
<span class="resource-card__tag resource-card__tag--beginner"
>Beginner</span
>
</div>
</div>
<p class="resource-card__desc">
Structured course with practice problems. Great for reinforcing
concepts after watching 3Blue1Brown. Focus on "Vectors and spaces"
and "Matrix transformations" units.
</p>
</div>
<div class="resource-card">
<div class="resource-card__header">
<h4 class="resource-card__title">
<a
href="https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/"
target="_blank"
rel="noopener"
>MIT 18.06: Linear Algebra (Gilbert Strang)</a
>
</h4>
<div class="resource-card__meta">
<span class="resource-card__tag resource-card__tag--time"
>~35 hours</span
>
<span class="resource-card__tag resource-card__tag--intermediate"
>Intermediate</span
>
</div>
</div>
<p class="resource-card__desc">
Full university course. More rigorous and complete coverage. Watch
lectures 1-10 for core concepts. Professor Strang is legendary for
making linear algebra accessible.
</p>
</div>
</section>
<!-- Matrix Operations -->
<section class="section" id="matrix-ops">
<div class="section__number">04 — MATRIX OPERATIONS</div>
<h2 class="section__title">Matrix Operations</h2>
<p>
Matrix multiplication is the core operation in GPU computing. You need
to understand both the mechanics (how to compute it) and the geometry
(what it means).
</p>
<div class="resource-card">
<div class="resource-card__header">
<h4 class="resource-card__title">
<a
href="https://www.youtube.com/watch?v=XkY2DOUCWMU"
target="_blank"
rel="noopener"
>3Blue1Brown: Matrix multiplication as composition</a
>
</h4>
<div class="resource-card__meta">
<span class="resource-card__tag resource-card__tag--time"
>10 min</span
>
<span class="resource-card__tag resource-card__tag--beginner"
>Beginner</span
>
</div>
</div>
<p class="resource-card__desc">
Explains why matrix multiplication works the way it does.
Understanding this transforms matmul from "mysterious formula" to
"obvious composition of transformations."
</p>
</div>
<div class="resource-card">
<div class="resource-card__header">
<h4 class="resource-card__title">
<a
href="https://www.mathsisfun.com/algebra/matrix-multiplying.html"
target="_blank"
rel="noopener"
>Matrix Multiplication Guide</a
>
</h4>
<div class="resource-card__meta">
<span class="resource-card__tag resource-card__tag--time"
>Interactive</span
>
<span class="resource-card__tag resource-card__tag--beginner"
>Beginner</span
>
</div>
</div>
<p class="resource-card__desc">
Clear explanation of matrix multiplication with step-by-step examples.
Shows how each output element is computed from rows and columns. Essential
for understanding tiled matrix multiplication in CUDA.
</p>
</div>
<div class="resource-card">
<div class="resource-card__header">
<h4 class="resource-card__title">
<a
href="https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:multiplying-matrices-by-matrices/v/matrix-multiplication-intro"
target="_blank"
rel="noopener"
>Khan Academy: Matrix multiplication</a
>
</h4>
<div class="resource-card__meta">
<span class="resource-card__tag resource-card__tag--time"
>~2 hours</span
>
<span class="resource-card__tag resource-card__tag--beginner"
>Beginner</span
>
</div>
</div>
<p class="resource-card__desc">
Step-by-step walkthrough with practice exercises. Covers dimension
rules, the mechanics of computation, and common properties. Complete
the exercises until matmul feels automatic.
</p>
</div>
</section>
<!-- Floating Point Numbers -->
<section class="section" id="floating-point">
<div class="section__number">05 — FLOATING POINT</div>
<h2 class="section__title">Floating Point Numbers</h2>
<p>
GPUs use various floating point formats (FP32, FP16, FP8, FP4).
Understanding the bit layout helps you reason about precision,
overflow, and quantization.
</p>
<div class="resource-card">
<div class="resource-card__header">
<h4 class="resource-card__title">
<a href="https://float.exposed/" target="_blank" rel="noopener"
>float.exposed</a
>
</h4>
<div class="resource-card__meta">
<span class="resource-card__tag resource-card__tag--time"
>Interactive</span
>
<span class="resource-card__tag resource-card__tag--beginner"
>Beginner</span
>
</div>
</div>
<p class="resource-card__desc">
Toggle individual bits and see how the value changes. Best way to
build intuition for sign, exponent, and mantissa. Try entering
values like 0.1 to see why it can't be exactly represented.
</p>
</div>
<div class="resource-card">
<div class="resource-card__header">
<h4 class="resource-card__title">
<a
href="https://www.youtube.com/watch?v=PZRI1IfStY0"
target="_blank"
rel="noopener"
>Computerphile: Floating Point Numbers</a
>
</h4>
<div class="resource-card__meta">
<span class="resource-card__tag resource-card__tag--time"
>9 min</span
>
<span class="resource-card__tag resource-card__tag--beginner"
>Beginner</span
>
</div>
</div>
<p class="resource-card__desc">
Clear explanation of IEEE 754 format with hand-drawn diagrams.
Covers why floats exist, how they work, and common pitfalls like
precision loss.
</p>
</div>
<div class="resource-card">
<div class="resource-card__header">
<h4 class="resource-card__title">
<a
href="https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html"
target="_blank"
rel="noopener"
>What Every Computer Scientist Should Know About Floating-Point
Arithmetic</a
>
</h4>
<div class="resource-card__meta">
<span class="resource-card__tag resource-card__tag--time"
>~2 hours</span
>
<span class="resource-card__tag resource-card__tag--intermediate"
>Intermediate</span
>
</div>
</div>
<p class="resource-card__desc">
The canonical reference by David Goldberg. Dense but comprehensive.
Read sections 1-2 for fundamentals. Return to later sections when
you encounter specific precision issues.
</p>
</div>
<div class="resource-card">
<div class="resource-card__header">
<h4 class="resource-card__title">
<a
href="https://www.youtube.com/watch?v=dQhj5RGtag0"
target="_blank"
rel="noopener"
>Computerphile: Floating Point Numbers (Part 2) - Problems</a
>
</h4>
<div class="resource-card__meta">
<span class="resource-card__tag resource-card__tag--time"
>12 min</span
>
<span class="resource-card__tag resource-card__tag--beginner"
>Beginner</span
>
</div>
</div>
<p class="resource-card__desc">
Real-world examples of floating point disasters: the Patriot missile
bug, Ariane 5 explosion. Understanding these failures helps you
write robust numerical code.
</p>
</div>
</section>
<!-- Exponentials and Logarithms -->
<section class="section" id="exponentials">
<div class="section__number">06 — EXPONENTIALS</div>
<h2 class="section__title">Exponentials and Logarithms</h2>
<p>
Softmax uses exp(), log-sum-exp tricks prevent overflow, and
understanding growth rates helps you reason about numerical stability.
</p>
<div class="resource-card">
<div class="resource-card__header">
<h4 class="resource-card__title">
<a
href="https://www.youtube.com/watch?v=m2MIpDrF7Es"
target="_blank"
rel="noopener"
>3Blue1Brown: What's so special about Euler's number e?</a
>
</h4>
<div class="resource-card__meta">
<span class="resource-card__tag resource-card__tag--time"
>15 min</span
>
<span class="resource-card__tag resource-card__tag--beginner"
>Beginner</span
>
</div>
</div>
<p class="resource-card__desc">
Beautiful explanation of why e appears everywhere. Understanding
e^x's unique property (its derivative equals itself) explains why
it's used in softmax and probability.
</p>
</div>
<div class="resource-card">
<div class="resource-card__header">
<h4 class="resource-card__title">
<a
href="https://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/"
target="_blank"
rel="noopener"
>Better Explained: An Intuitive Guide To Exponential Functions &
e</a
>
</h4>
<div class="resource-card__meta">
<span class="resource-card__tag resource-card__tag--time"
>20 min</span
>
<span class="resource-card__tag resource-card__tag--beginner"
>Beginner</span
>
</div>
</div>
<p class="resource-card__desc">
Text-based explanation with interactive examples. Great complement
to the 3Blue1Brown video. Focuses on building intuition rather than
formal proofs.
</p>
</div>
<div class="resource-card">
<div class="resource-card__header">
<h4 class="resource-card__title">
<a
href="https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs"
target="_blank"
rel="noopener"
>Khan Academy: Logarithms</a
>
</h4>
<div class="resource-card__meta">
<span class="resource-card__tag resource-card__tag--time"
>~4 hours</span
>
<span class="resource-card__tag resource-card__tag--beginner"
>Beginner</span
>
</div>
</div>
<p class="resource-card__desc">
Complete coverage of logarithms with practice problems. Focus on
"Introduction to logarithms" and "Properties of logarithms." The
log-sum-exp trick uses these properties directly.
</p>
</div>
</section>
<!-- Programming Math -->
<section class="section" id="index-arithmetic">
<div class="section__number">07 — INDEX ARITHMETIC</div>
<h2 class="section__title">Programming Math (Index Arithmetic)</h2>
<p>
GPU kernels constantly convert between multi-dimensional indices and
linear memory addresses. This is mechanical but crucial to get right.
</p>
<div class="resource-card">
<div class="resource-card__header">
<h4 class="resource-card__title">
<a
href="https://numpy.org/doc/stable/reference/arrays.ndarray.html#internal-memory-layout-of-an-ndarray"
target="_blank"
rel="noopener"
>NumPy: Internal memory layout of an ndarray</a
>
</h4>
<div class="resource-card__meta">
<span class="resource-card__tag resource-card__tag--time"
>15 min</span
>
<span class="resource-card__tag resource-card__tag--intermediate"
>Intermediate</span
>
</div>
</div>
<p class="resource-card__desc">
Official NumPy documentation explaining strides and memory layout.
Understanding this directly translates to CUDA memory access
patterns.
</p>
</div>
<div class="resource-card">
<div class="resource-card__header">
<h4 class="resource-card__title">
<a
href="https://eli.thegreenplace.net/2015/memory-layout-of-multi-dimensional-arrays"
target="_blank"
rel="noopener"
>Memory layout of multi-dimensional arrays</a
>
</h4>
<div class="resource-card__meta">
<span class="resource-card__tag resource-card__tag--time"
>20 min</span
>
<span class="resource-card__tag resource-card__tag--beginner"
>Beginner</span
>
</div>
</div>
<p class="resource-card__desc">
Clear explanation with diagrams comparing row-major (C) vs
column-major (Fortran) ordering. Essential for understanding why
memory access patterns matter for performance.
</p>
</div>
<div class="resource-card">
<div class="resource-card__header">
<h4 class="resource-card__title">
<a
href="https://en.wikipedia.org/wiki/Row-_and_column-major_order"
target="_blank"
rel="noopener"
>Wikipedia: Row- and column-major order</a
>
</h4>
<div class="resource-card__meta">
<span class="resource-card__tag resource-card__tag--time"
>10 min</span
>
<span class="resource-card__tag resource-card__tag--beginner"
>Beginner</span
>
</div>
</div>
<p class="resource-card__desc">