---
title: "Math and Architectures of Deep Learning"
id: "15205"
type: "page"
slug: "mathandarchitecturesofdeeplearning"
published_at: "2026-07-19T22:17:18+00:00"
modified_at: "2026-07-19T22:34:20+00:00"
url: "https://preppers-paradise.com/library/mathandarchitecturesofdeeplearning/"
markdown_url: "https://preppers-paradise.com/library/mathandarchitecturesofdeeplearning.md"
excerpt: "This book offers a comprehensive exploration of the mathematical and architectural foundations essential for understanding deep learning. It covers fundamental concepts from linear algebra, vector calculus, and probability theory, demonstrating their direct application to building and training machi"
taxonomy_category:
  - "AI & Machine Learning"
  - "Books"
  - "Free Teaser"
taxonomy_post_tag:
  - "computer vision"
  - "deep learning"
  - "generative models"
  - "linear algebra"
  - "machine learning"
  - "neural networks"
  - "optimization"
  - "probability theory"
  - "pytorch"
  - "vector calculus"
---

# Math and Architectures of Deep Learning

This book offers a comprehensive exploration of the mathematical and architectural foundations essential for understanding deep learning. It covers fundamental concepts from linear algebra, vector calculus, and probability theory, demonstrating their direct application to building and training machine learning models, particularly neural networks. Readers will gain insights into topics such as vectors, matrices, tensors, gradient descent, various neural network architectures, forward and backpropagation, loss functions, optimization, and advanced topics like image classification, object detection, and generative modeling, often accompanied by practical implementations.

This page is free — overview and chapter list only.
Full book: $2.99 USDC · Per chapter: $0.25 USDC
[Buy / open complete book](/library/complete/mathandarchitecturesofdeeplearning/) · [Complete book Markdown](/library/complete/mathandarchitecturesofdeeplearning.md)

## Chapters

1. [Math And Architectures Of Deep Learning](/library/mathandarchitecturesofdeeplearning/01-math-and-architectures-of-deep-learning/) (Free teaser)
1. [About The Cover Illustration](/library/mathandarchitecturesofdeeplearning/02-about-the-cover-illustration/) ($0.25)
1. [Summary](/library/mathandarchitecturesofdeeplearning/03-summary/) ($0.25)
1. [26 Orthogonality Of Vectors And Its Physical Significance](/library/mathandarchitecturesofdeeplearning/04-26-orthogonality-of-vectors-and-its-physical-significance/) ($0.25)
1. [2111 Array View Multidimensional Arrays Of Numbers](/library/mathandarchitecturesofdeeplearning/05-2111-array-view-multidimensional-arrays-of-numbers/) ($0.25)
1. [Listing 217 Axis Of Rotation](/library/mathandarchitecturesofdeeplearning/06-listing-217-axis-of-rotation/) ($0.25)
1. [2154 Matrix Powers Using Diagonalization](/library/mathandarchitecturesofdeeplearning/07-2154-matrix-powers-using-diagonalization/) ($0.25)
1. [2171 Pytorch Code For Hyperellipses](/library/mathandarchitecturesofdeeplearning/08-2171-pytorch-code-for-hyperellipses/) ($0.25)
1. [34 Local Approximation For The Loss Function](/library/mathandarchitecturesofdeeplearning/09-34-local-approximation-for-the-loss-function/) ($0.25)
1. [Case 2 Fewer Rows Than Columns In Boldsymbol](/library/mathandarchitecturesofdeeplearning/10-case-2-fewer-rows-than-columns-in-boldsymbol/) ($0.25)
1. [454 Applying Svd Solving Arbitrary Linear Systems](/library/mathandarchitecturesofdeeplearning/11-454-applying-svd-solving-arbitrary-linear-systems/) ($0.25)
1. [Listing 46 Solving An Overdetermined Linear System By Pseudo](/library/mathandarchitecturesofdeeplearning/12-listing-46-solving-an-overdetermined-linear-system-by-pseudo/) ($0.25)
1. [Listing 47 Computing Pca Directly And Using Svd](/library/mathandarchitecturesofdeeplearning/13-listing-47-computing-pca-directly-and-using-svd/) ($0.25)
1. [Inverse Document Frequency](/library/mathandarchitecturesofdeeplearning/14-inverse-document-frequency/) ($0.25)
1. [462 Latent Semantic Analysis](/library/mathandarchitecturesofdeeplearning/15-462-latent-semantic-analysis/) ($0.25)
1. [Listing 48 Computing Lsa](/library/mathandarchitecturesofdeeplearning/16-listing-48-computing-lsa/) ($0.25)
1. [Listing 49 Lsa Using Svd](/library/mathandarchitecturesofdeeplearning/17-listing-49-lsa-using-svd/) ($0.25)
1. [Expected Value Of An Arbitrary Function Of A Random Variable](/library/mathandarchitecturesofdeeplearning/18-expected-value-of-an-arbitrary-function-of-a-random-variable/) ($0.25)
1. [572 Variance Covariance And Standard Deviation](/library/mathandarchitecturesofdeeplearning/19-572-variance-covariance-and-standard-deviation/) ($0.25)
1. [Listing 51 Log Probability Of A Univariate Uniform Random Di](/library/mathandarchitecturesofdeeplearning/20-listing-51-log-probability-of-a-univariate-uniform-random-di/) ($0.25)
1. [Listing 52 Mean And Variance Of A Uniform Random Distributio](/library/mathandarchitecturesofdeeplearning/21-listing-52-mean-and-variance-of-a-uniform-random-distributio/) ($0.25)
1. [Listing 54 Log Probability Of A Multivariate Normal Distribu](/library/mathandarchitecturesofdeeplearning/22-listing-54-log-probability-of-a-multivariate-normal-distribu/) ($0.25)
1. [Geometry Of Sampled Point Clouds Covariance And Direction Of](/library/mathandarchitecturesofdeeplearning/23-geometry-of-sampled-point-clouds-covariance-and-direction-of/) ($0.25)
1. [Listing 57 Log Probability Of A Binomial Distribution](/library/mathandarchitecturesofdeeplearning/24-listing-57-log-probability-of-a-binomial-distribution/) ($0.25)
1. [594 Multinomial Distribution](/library/mathandarchitecturesofdeeplearning/25-594-multinomial-distribution/) ($0.25)
1. [Listing 59 Log Probability Of A Multinomial Distribution](/library/mathandarchitecturesofdeeplearning/26-listing-59-log-probability-of-a-multinomial-distribution/) ($0.25)
1. [Variance Of A Multinomial Distribution](/library/mathandarchitecturesofdeeplearning/27-variance-of-a-multinomial-distribution/) ($0.25)
1. [Expected Value Of A Bernoulli Distribution](/library/mathandarchitecturesofdeeplearning/28-expected-value-of-a-bernoulli-distribution/) ($0.25)
1. [596 Categorical Distribution And One Hot Vectors](/library/mathandarchitecturesofdeeplearning/29-596-categorical-distribution-and-one-hot-vectors/) ($0.25)
1. [Summary 2](/library/mathandarchitecturesofdeeplearning/30-summary-2/) ($0.25)
1. [This Chapter Covers](/library/mathandarchitecturesofdeeplearning/31-this-chapter-covers/) ($0.25)
1. [611 Joint And Marginal Probability Revisited](/library/mathandarchitecturesofdeeplearning/32-611-joint-and-marginal-probability-revisited/) ($0.25)
1. [612 Conditional Probability](/library/mathandarchitecturesofdeeplearning/33-612-conditional-probability/) ($0.25)
1. [613 Bayes Theorem](/library/mathandarchitecturesofdeeplearning/34-613-bayes-theorem/) ($0.25)
1. [62 Entropy](/library/mathandarchitecturesofdeeplearning/35-62-entropy/) ($0.25)
1. [621 Geometrical Intuition For Entropy](/library/mathandarchitecturesofdeeplearning/36-621-geometrical-intuition-for-entropy/) ($0.25)
1. [622 Entropy Of Gaussians](/library/mathandarchitecturesofdeeplearning/37-622-entropy-of-gaussians/) ($0.25)
1. [63 Cross Entropy](/library/mathandarchitecturesofdeeplearning/38-63-cross-entropy/) ($0.25)
1. [Listing 62 Computing Cross Entropy](/library/mathandarchitecturesofdeeplearning/39-listing-62-computing-cross-entropy/) ($0.25)
1. [64 Kl Divergence](/library/mathandarchitecturesofdeeplearning/40-64-kl-divergence/) ($0.25)
1. [Listing 63 Computing The Kld](/library/mathandarchitecturesofdeeplearning/41-listing-63-computing-the-kld/) ($0.25)
1. [65 Conditional Entropy](/library/mathandarchitecturesofdeeplearning/42-65-conditional-entropy/) ($0.25)
1. [661 Likelihood Evidence And Posterior And Prior Probabilitie](/library/mathandarchitecturesofdeeplearning/43-661-likelihood-evidence-and-posterior-and-prior-probabilitie/) ($0.25)
1. [Listing 71 Perceptron](/library/mathandarchitecturesofdeeplearning/44-listing-71-perceptron/) ($0.25)
1. [A Perceptron For Logical And](/library/mathandarchitecturesofdeeplearning/45-a-perceptron-for-logical-and/) ($0.25)
1. [Listing 72 Modeling Logical Gates Using Perceptrons](/library/mathandarchitecturesofdeeplearning/46-listing-72-modeling-logical-gates-using-perceptrons/) ($0.25)
1. [753 Cybenkos Universal Approximation Theorem](/library/mathandarchitecturesofdeeplearning/47-753-cybenkos-universal-approximation-theorem/) ($0.25)
1. [754 Mlps For Polygonal Decision Boundaries](/library/mathandarchitecturesofdeeplearning/48-754-mlps-for-polygonal-decision-boundaries/) ($0.25)
1. [This Chapter Covers 2](/library/mathandarchitecturesofdeeplearning/49-this-chapter-covers-2/) ($0.25)
1. [811 Sigmoid Function](/library/mathandarchitecturesofdeeplearning/50-811-sigmoid-function/) ($0.25)
1. [Some Properties Of The Sigmoid Function](/library/mathandarchitecturesofdeeplearning/51-some-properties-of-the-sigmoid-function/) ($0.25)
1. [812 Tanh Function](/library/mathandarchitecturesofdeeplearning/52-812-tanh-function/) ($0.25)
1. [83 Linear Layers](/library/mathandarchitecturesofdeeplearning/53-83-linear-layers/) ($0.25)
1. [Algorithm 81 Training A Neural Network](/library/mathandarchitecturesofdeeplearning/54-algorithm-81-training-a-neural-network/) ($0.25)
1. [Listing 84 Training A Neural Network](/library/mathandarchitecturesofdeeplearning/55-listing-84-training-a-neural-network/) ($0.25)
1. [911 Quantification And Geometrical View Of Loss](/library/mathandarchitecturesofdeeplearning/56-911-quantification-and-geometrical-view-of-loss/) ($0.25)
1. [Listing 93 Pytorch Code For Binary Cross Entropy Loss](/library/mathandarchitecturesofdeeplearning/57-listing-93-pytorch-code-for-binary-cross-entropy-loss/) ($0.25)
1. [Listing 96 Pytorch Code For Focal Loss](/library/mathandarchitecturesofdeeplearning/58-listing-96-pytorch-code-for-focal-loss/) ($0.25)
1. [Multiclass Support Vector Machine Loss Hinge Loss For Classi](/library/mathandarchitecturesofdeeplearning/59-multiclass-support-vector-machine-loss-hinge-loss-for-classi/) ($0.25)
1. [Listing 99 Pytorch Code For A Loss Function And Sgd Optimize](/library/mathandarchitecturesofdeeplearning/60-listing-99-pytorch-code-for-a-loss-function-and-sgd-optimize/) ($0.25)
1. [Listing 911 Pytorch Code To Run The Training Loop Numepochs](/library/mathandarchitecturesofdeeplearning/61-listing-911-pytorch-code-to-run-the-training-loop-numepochs/) ($0.25)
1. [928 Root Mean Squared Propagation](/library/mathandarchitecturesofdeeplearning/62-928-root-mean-squared-propagation/) ($0.25)
1. [Listing 912 Pytorch Code For Various Optimizers](/library/mathandarchitecturesofdeeplearning/63-listing-912-pytorch-code-for-various-optimizers/) ($0.25)
1. [931 Minimum Descriptor Length An Occams Razor View Of Optimi](/library/mathandarchitecturesofdeeplearning/64-931-minimum-descriptor-length-an-occams-razor-view-of-optimi/) ($0.25)
1. [932 L2 Regularization](/library/mathandarchitecturesofdeeplearning/65-932-l2-regularization/) ($0.25)
1. [Listing 914 Dropout](/library/mathandarchitecturesofdeeplearning/66-listing-914-dropout/) ($0.25)
1. [Listing 102 Pytorch Code For 1D Edge Detection](/library/mathandarchitecturesofdeeplearning/67-listing-102-pytorch-code-for-1d-edge-detection/) ($0.25)
1. [Listing 103 Pytorch Code Directly Invoking The Convolution F](/library/mathandarchitecturesofdeeplearning/68-listing-103-pytorch-code-directly-invoking-the-convolution-f/) ($0.25)
1. [1031 Image Smoothing Via 2D Convolution](/library/mathandarchitecturesofdeeplearning/69-1031-image-smoothing-via-2d-convolution/) ($0.25)
1. [Listing 105 Pytorch Code For 2D Edge Detection](/library/mathandarchitecturesofdeeplearning/70-listing-105-pytorch-code-for-2d-edge-detection/) ($0.25)
1. [Listing 106 Pytorch Code For 3D Convolution](/library/mathandarchitecturesofdeeplearning/71-listing-106-pytorch-code-for-3d-convolution/) ($0.25)
1. [105 Transposed Convolution Or Fractionally Strided Convoluti](/library/mathandarchitecturesofdeeplearning/72-105-transposed-convolution-or-fractionally-strided-convoluti/) ($0.25)
1. [1061 Pytorch Adding Convolution Layers To A Neural Network](/library/mathandarchitecturesofdeeplearning/73-1061-pytorch-adding-convolution-layers-to-a-neural-network/) ($0.25)
1. [This Chapter Covers 3](/library/mathandarchitecturesofdeeplearning/74-this-chapter-covers-3/) ($0.25)
1. [1121 Vgg Visual Geometry Group Net](/library/mathandarchitecturesofdeeplearning/75-1121-vgg-visual-geometry-group-net/) ($0.25)
1. [133 Fully Bayes Parameter Estimation Gaussian Unknown Mean K](/library/mathandarchitecturesofdeeplearning/76-133-fully-bayes-parameter-estimation-gaussian-unknown-mean-k/) ($0.25)
1. [A Linear Latent Space](/library/mathandarchitecturesofdeeplearning/77-a-linear-latent-space/) ($0.25)
1. [1477 Choice Of Prior Zero Mean Unit Covariance Gaussian](/library/mathandarchitecturesofdeeplearning/78-1477-choice-of-prior-zero-mean-unit-covariance-gaussian/) ($0.25)
1. [1478 Reparameterization Trick](/library/mathandarchitecturesofdeeplearning/79-1478-reparameterization-trick/) ($0.25)
1. [But The Gamma Distribution](/library/mathandarchitecturesofdeeplearning/80-but-the-gamma-distribution/) ($0.25)