Mathematical Foundations for Signal Processing, Communications, and Networking

Introduction
Signal Processing Transforms, Serhan Yarkan and Khalid A. Qaraqe
Introduction
Basic Transformations
Fourier Series and Transform
Sampling
Cosine and Sine Transforms
Laplace Transform
Hartley Transform
Hilbert Transform
Discrete-Time Fourier Transform
The Z-Transform
Conclusion and Further Reading
Linear Algebra, Fatemeh Hamidi Sepehr and Erchin Serpedin
Vector Spaces
Linear Transformations
Operator Norms and Matrix Norms
Systems of Linear Equations
Determinant, Adjoint, and Inverse of a Matrix
Cramer’s Rule 
Unitary and Orthogonal Operators and Matrices
LU Decomposition
LDL and Cholesky Decomposition
QR Decomposition
Householder and Givens Transformations
Best Approximations and Orthogonal Projections
Least Squares Approximations
Angles between Subspaces
Eigenvalues and Eigenvectors
Schur Factorization and Spectral Theorem
Singular Value Decomposition (SVD)
Rayleigh Quotient
Application of SVD and Rayleigh Quotient: Principal Component Analysis
Special Matrices
Matrix Operations
Further Studies
Elements of Galois Fields, Tolga Duman
Groups, Rings, and Fields
Galois Fields
Polynomials with Coefficients in GF(2)
Construction of GF(2m)
Some Notes on Applications of Finite Fields
Numerical Analysis, Vivek Sarin 
Numerical Approximation
Sensitivity and Conditioning
Computer Arithmetic
Interpolation
Nonlinear Equations
Eigenvalues and Singular Values
Further Reading
Combinatorics, Walter D. Wallis
Two Principles of Enumeration
Permutations and Combinations
The Principle of Inclusion and Exclusion
Generating Functions
Recurrence Relations
Graphs
Paths and Cycles in Graphs
Trees
Encoding and Decoding
Latin Squares
Balanced Incomplete Block Designs
Conclusion
Probability, Random Variables, and Stochastic Processes, Dinesh Rajan
Introduction to Probability
Random Variables
Joint Random Variables
Random Processes
Markov Process
Summary and Further Reading
Random Matrix Theory, Romain Couillet and Merouane Debbah
Probability Notations
Spectral Distribution of Random Matrices
Spectral Analysis
Statistical Inference
Applications
Conclusion
Large Deviations, Hongbin Li 
Introduction
Concentration Inequalities
Rate Function
Cramer’s Theorem
Method of Types
Sanov’s Theorem
Hypothesis Testing
Further Readings
Fundamentals of Estimation Theory, Yik-Chung Wu
Introduction
Bound on Minimum Variance — Cramer-Rao Lower Bound
MVUE Using RBLS Theorem
Maximum Likelihood Estimation
Least Squares (LS) Estimation
Regularized LS Estimation
Bayesian Estimation
Further Reading 
Fundamentals of Detection Theory, Venugopal V. Veeravalli
Introduction
Bayesian Binary Detection
Binary Minimax Detection
Binary Neyman-Pearson Detection
Bayesian Composite Detection
Neyman-Pearson Composite Detection
Binary Detection with Vector Observations
Summary and Further Reading
Monte Carlo Methods for Statistical Signal Processing, Xiaodong Wang
Introduction 
Monte Carlo Methods
Markov Chain Monte Carlo (MCMC) Methods
Sequential Monte Carlo (SMC) Methods
Conclusions and Further Readings
Factor Graphs and Message Passing Algorithms, Ahmad Aitzaz, Erchin Serpedin, and Khalid A. Qaraqe
Introduction 
Factor Graphs
Modeling Systems Using Factor Graphs
Relationship with Other Probabilistic Graphical Models
Message Passing in Factor Graphs
Factor Graphs with Cycles
Some General Remarks on Factor Graphs
Some Important Message Passing Algorithms
Applications of Message Passing in Factor Graphs
Unconstrained and Constrained Optimization Problems, Shuguang Cui, Man-Cho Anthony So, and Rui Zhang
Basics of Convex Analysis
Unconstrained vs. Constrained Optimization
Application Examples
Linear Programming and Mixed Integer Programming, Bogdan Dumitrescu
Linear Programming
Modeling Problems via Linear Programming
Mixed Integer Programming
Majorization Theory and Applications, Jiaheng Wang and Daniel Palomar
Majorization Theory
Applications of Majorization Theory 
Conclusions and Further Readings
Queueing Theory, Thomas Chen
Introduction
Markov Chains
Queueing Models
M/M/1 Queue
M/M/1/N Queue
M/M/N/N Queue
M/M/1 Queues in Tandem
M/G/1 Queue
Conclusions
Network Optimization Techniques, Michal Pioro
Introduction 
Basic Multicommodity Flow Networks Optimization Models
Optimization Methods for Multicommodity Flow Networks
Optimization Models for Multistate Networks
Concluding Remarks
Game Theory, Erik G. Larsson and Eduard Jorswieck
Introduction 
Utility Theory
Games on the Normal Form
Noncooperative Games and the Nash Equilibrium
Cooperative Games
Games with Incomplete Information
Extensive Form Games
Repeated Games and Evolutionary Stability
Coalitional Form/Characteristic Function Form
Mechanism Design and Implementation Theory
Applications to Signal Processing and Communications
Acknowledgments
A Short Course on Frame Theory, Veniamin I. Morgenshtern and Helmut Bölcskei 
Examples of Signal Expansions
Signal Expansions in Finite Dimensional Hilbert Spaces
Frames for General Hilbert Spaces
The Sampling Theorem
Important Classes of Frames
Index
Exercises and References appear at the end of each chapter.