Mathematics - Mathematical analysis ¹¹

Main branches:

• Calculus
• Real analysis
• Complex analysis
• Functional analysis
• Harmonic analysis
• Differential equations
• Measure theory
• Numerical analysis
• Vector analysis
• Scalar analysis
• Tensor analysis

Other branches (small or related):

• Calculus of variations
• Geometric analysis
• Clifford analysis
• p-adic analysis
• Non-standard analysis
• Computable analysis
• Stochastic calculus
• Set-valued analysis
• Convex analysis
• Idempotent analysis
• Tropical analysis
• Constructive analysis
• Intuitionistic analysis
• Paraconsistent analysis

Mathematics - Calculus of Variations

Mathematics - Complex Analysis

Mathematics - Dynamical Systems

Mathematics - Functional Analysis

Mathematics - Harmonic Analysis

Mathematics - Measure Theory

Mathematics - Optimization

Branches of Optimization Research # Convex Optimization # Convex optimization focuses on problems where the objective function and constraints are convex, ensuring a single global optimum. This field is foundational in machine learning, signal processing, and control systems due to its guaranteed convergence and efficient algorithms. Convex Optimization by Boyd and Vandenberghe - PDF Convex Optimization Theory by Dimitri P. Bertsekas - PDF Discrete, Combinatorial, and Integer Optimization # This branch deals with optimization problems involving discrete variables, such as integers or combinatorial structures, often encountered in scheduling, network design, and logistics. Bayesian optimization, a subset, is particularly useful for optimizing expensive black-box functions.

Mathematics - Ordinary Differential Equations (ODE)

Mathematics - Partial Differential Equations (PDE)

Mathematics - Real Analysis

APA References for Convex Optimization and Analysis Books # Hendrix, E. M. T., & G.-Tóth, B. (2010). Introduction to nonlinear and global optimization. Springer. https://link.springer.com/book/10.1007/978-0-387-88670-1 Horst, R., & Pardalos, P. M. (1995). Handbook of global optimization. Springer. https://link.springer.com/book/10.1007/978-1-4615-2025-2 Mordukhovich, B. S. (2006a). Variational analysis and generalized differentiation I: Basic theory. Springer. https://link.springer.com/book/10.1007/3-540-31247-1 Mordukhovich, B. S. (2006b). Variational analysis and generalized differentiation II: Applications. Springer. https://link.springer.com/book/10.1007/3-540-31246-3 Mordukhovich, B. S. (2018). Variational analysis and applications. Springer. https://link.springer.com/book/10.1007/978-3-319-92775-6