Table of Contents:

1. Introduction to Deep Learning Mathematics
   1.1. Linear Algebra
       1.1.1. Scalars, Vectors, and Matrices
       1.1.2. Matrix Operations
       1.1.3. Eigenvalues and Eigenvectors
       1.1.4. Singular Value Decomposition (SVD)
   1.2. Calculus
       1.2.1. Functions and Derivatives
       1.2.2. Partial Derivatives and Gradients
       1.2.3. Chain Rule
       1.2.4. Multivariable Calculus
       1.2.5. Integration
   1.3. Probability and Statistics
       1.3.1. Probability Distributions
       1.3.2. Expectation and Variance
       1.3.3. Bayesian Inference
       1.3.4. Maximum Likelihood Estimation (MLE)
       1.3.5. Information Theory

2. Neural Networks and Deep Learning
   2.1. Feedforward Neural Networks
       2.1.1. Activation Functions
       2.1.2. Loss Functions
       2.1.3. Backpropagation Algorithm
   2.2. Regularization Techniques
       2.2.1. L1 and L2 Regularization
       2.2.2. Dropout
       2.2.3. Batch Normalization
   2.3. Optimization Algorithms
       2.3.1. Gradient Descent
       2.3.2. Stochastic Gradient Descent (SGD)
       2.3.3. Momentum
       2.3.4. Adaptive Learning Rate Methods (AdaGrad, RMSProp, Adam)

3. Convolutional Neural Networks (CNNs)
   3.1. Convolution Operation
       3.1.1. Discrete Convolution
       3.1.2. Convolutional Layers
       3.1.3. Padding and Stride
   3.2. Pooling Layers
       3.2.1. Max Pooling
       3.2.2. Average Pooling
   3.3. Advanced CNN Architectures
       3.3.1. Inception Networks
       3.3.2. Residual Networks (ResNet)
       3.3.3. DenseNet

4. Recurrent Neural Networks (RNNs)
   4.1. RNN Architectures
       4.1.1. Vanilla RNNs
       4.1.2. Long Short-Term Memory (LSTM)
       4.1.3. Gated Recurrent Units (GRU)
   4.2. Backpropagation Through Time (BPTT)
   4.3. Sequence-to-Sequence Models
       4.3.1. Encoder-Decoder Architecture
       4.3.2. Attention Mechanism

5. Generative Models
   5.1. Variational Autoencoders (VAEs)
       5.1.1. Variational Inference
       5.1.2. Reparameterization Trick
   5.2. Generative Adversarial Networks (GANs)
       5.2.1. Minimax Game Theory
       5.2.2. Wasserstein GANs

6. Reinforcement Learning
   6.1. Markov Decision Processes (MDPs)
       6.1.1. Bellman Equations
       6.1.2. Value Iteration and Policy Iteration
   6.2. Q-Learning
       6.2.1. Temporal Difference Learning
       6.2.2. Deep Q-Networks (DQN)
   6.3. Policy Gradient Methods
       6.3.1. REINFORCE Algorithm
       6.3.2. Actor-Critic Methods

7. Advanced Topics
   7.1. Graph Neural Networks (GNNs)
       7.1.1. Graph Convolutional Networks (GCNs)
       7.1.2. Graph Attention Networks (GATs)
   7.2. Natural Language Processing (NLP)
       7.2.1. Word Embeddings
       7.2.2. Transformer Models
       7.2.3. BERT and GPT Architectures
   7.3. Unsupervised Learning
       7.3.1. Clustering Algorithms
       7.3.2. Dimensionality Reduction Techniques
   7.4. Transfer Learning
       7.4.1. Fine-tuning
       7.4.2. Domain Adaptation
   7.5. Meta-Learning
       7.5.1. Model-Agnostic Meta-Learning (MAML)
       7.5.2. Reptile Algorithm

This table of contents provides a comprehensive outline of the underlying mathematics of deep learning, from basic concepts to advanced graduate-level topics. Each section is linked to a specific deep learning usage, ensuring that the mathematical concepts are directly relevant to the field. What you discuss in q learning