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| Hardcover ISBN: | 978-1-4704-8108-7 |
| Product Code: | GSM/252 |
| List Price: | $135.00 |
| MAA Member Price: | $121.50 |
| AMS Member Price: | $108.00 |
| Softcover ISBN: | 978-1-4704-8399-9 |
| Product Code: | GSM/252.S |
| List Price: | $89.00 |
| MAA Member Price: | $80.10 |
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| eBook ISBN: | 978-1-4704-8398-2 |
| Product Code: | GSM/252.E |
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| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Softcover ISBN: | 978-1-4704-8399-9 |
| eBook ISBN: | 978-1-4704-8398-2 |
| Product Code: | GSM/252.S.B |
| List Price: | $174.00 $131.50 |
| MAA Member Price: | $156.60 $118.35 |
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Book DetailsGraduate Studies in MathematicsVolume: 252; 2025; 504 ppMSC: Primary 62; 65; 68
Deep learning uses multi-layer neural networks to model complex data patterns. Large models—with millions or even billions of parameters—are trained on massive datasets. This approach has produced revolutionary advances in image, text, and speech recognition and also has potential applications in a range of other fields such as engineering, finance, mathematics, and medicine.
This book provides an introduction to the mathematical theory underpinning the recent advances in deep learning. Detailed derivations as well as mathematical proofs are presented for many of the models and optimization methods which are commonly used in machine learning and deep learning. Applications, code, and practical approaches to training models are also included.
The book is designed for advanced undergraduates, graduate students, practitioners, and researchers. Divided into two parts, it begins with mathematical foundations before tackling advanced topics in approximation, optimization, and neural network training. Part 1 is written for a general audience, including students in mathematics, statistics, computer science, data science, or engineering, while select chapters in Part 2 present more advanced mathematical theory requiring familiarity with analysis, probability, and stochastic processes. Together, they form an ideal foundation for an introductory course on the mathematics of deep learning.
Thoughtfully designed exercises and a companion website with code examples enhance both theoretical understanding and practical skills, preparing readers to engage more deeply with this fast-evolving field.
Ancillaries:
ReadershipAdvanced undergraduate students, graduate students, researchers and practitioners interested in deep learning.
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Table of Contents
-
Introduction
-
Mathematical introduction to deep learning
-
Linear regression
-
Logistic regression
-
From the Perceptron Model to Kernels to Neural Networks
-
Feed forward neural networks
-
Backpropagation
-
Basics of stochastic gradient descent
-
Stochastic gradient descent for multi-layer networks
-
Regularization and dropout
-
Batch normalization
-
Training, validation, and testing
-
Feature importance
-
Recurrent neural networks for sequential data
-
Convolution neural networks
-
Variational inference and generative models
-
Advanced topics and convergence results in deep learning
-
Transitioning from Part 1 to Part 2
-
Universal approximation theorems
-
Convergence analysis of gradient descent
-
Convergence analysis of stochastic gradient descent
-
The neural tangent kernel regime
-
Optimization in the feature learning regime: mean field scaling
-
Reinforcement learning
-
Neural differential equations
-
Distributed training
-
Automatic differentiation
-
Appendixes
-
Background material in probability
-
Background material in analysis
-
Bibliography
-
Index
-
-
Additional Material
-
RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseInstructor's Solutions Manual – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a courseAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
Deep learning uses multi-layer neural networks to model complex data patterns. Large models—with millions or even billions of parameters—are trained on massive datasets. This approach has produced revolutionary advances in image, text, and speech recognition and also has potential applications in a range of other fields such as engineering, finance, mathematics, and medicine.
This book provides an introduction to the mathematical theory underpinning the recent advances in deep learning. Detailed derivations as well as mathematical proofs are presented for many of the models and optimization methods which are commonly used in machine learning and deep learning. Applications, code, and practical approaches to training models are also included.
The book is designed for advanced undergraduates, graduate students, practitioners, and researchers. Divided into two parts, it begins with mathematical foundations before tackling advanced topics in approximation, optimization, and neural network training. Part 1 is written for a general audience, including students in mathematics, statistics, computer science, data science, or engineering, while select chapters in Part 2 present more advanced mathematical theory requiring familiarity with analysis, probability, and stochastic processes. Together, they form an ideal foundation for an introductory course on the mathematics of deep learning.
Thoughtfully designed exercises and a companion website with code examples enhance both theoretical understanding and practical skills, preparing readers to engage more deeply with this fast-evolving field.
Ancillaries:
Advanced undergraduate students, graduate students, researchers and practitioners interested in deep learning.
-
Introduction
-
Mathematical introduction to deep learning
-
Linear regression
-
Logistic regression
-
From the Perceptron Model to Kernels to Neural Networks
-
Feed forward neural networks
-
Backpropagation
-
Basics of stochastic gradient descent
-
Stochastic gradient descent for multi-layer networks
-
Regularization and dropout
-
Batch normalization
-
Training, validation, and testing
-
Feature importance
-
Recurrent neural networks for sequential data
-
Convolution neural networks
-
Variational inference and generative models
-
Advanced topics and convergence results in deep learning
-
Transitioning from Part 1 to Part 2
-
Universal approximation theorems
-
Convergence analysis of gradient descent
-
Convergence analysis of stochastic gradient descent
-
The neural tangent kernel regime
-
Optimization in the feature learning regime: mean field scaling
-
Reinforcement learning
-
Neural differential equations
-
Distributed training
-
Automatic differentiation
-
Appendixes
-
Background material in probability
-
Background material in analysis
-
Bibliography
-
Index
