Mathematics ²⁴

Collected Lectures on Complex Analysis

📝 Introduction to Complex Analysis - Michael Taylor 📝 An Introduction to Complex Analysis and Geometry - John P. D’Angelo (University of Illinois) 📝 A First Course in Complex Analysis - Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka 📝 A Guide to Complex Variables - Steven G. Krantz 📝 Complex Analysis - Charles Walkden 📝 Complex Analysis - Christian Berg 📝 Complex Variables - R. B. Ash, W.P. Novinger 📝 Complex Analysis - Christer Bennewitz 📝 Complex Analysis - Donald E. Marshall 📝 A Concise Course in Complex Analysis and Riemann Surfaces - Wilhelm Schlag 📝 Complex Analysis - G. Cain (Georgia Tech) 📝 Complex Analysis - Juan Carlos Ponce Campuzano

Collected Lectures on Functional Analysis

📝 An Introduction to Functional Analysis - Laurent W. Marcoux (University of Waterloo) 📝 Functional Analysis: Lecture Notes - Jeff Schenker (Michigan State University) 📝 Functional Analysis Lecture Notes - T.B. Ward (University of East Anglia) 📝 Functional Analysis - Alexander C. R. Belton 📝 Topics in Real and Functional Analysis - Gerald Teschl 📝 Functional Analysis - Christian Remling 📝 Theory of Functions of a Real Variable - Shlomo Sternberg 📝 Functional Analysis - Lawerence Baggett

Collected Lectures on Harmonic Analysis

📝 Harmonic Analysis Lecture Notes - Richard S. Laugesen (University of Illinois at Urbana–Champaign) 📝 Harmonic Analysis - W. Schlag 📝 Lecture Notes: Fourier Transform and its Applications - Brad Osgood 📝 Fourier Analysis - Lucas Illing 📝 Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications - Julius O. Smith III (Stanford University)

Collected Lectures on Measure Theory

📝 An Introduction to Measure Theory - Terence Tao (UCLA) 📝 Lecture Notes on Measure Theory and Functional Analysis - P. Cannarsa, T. D’Aprile 📝 Lecture Notes in Measure Theory - Christer Borell 📝 A Crash Course on the Lebesgue Integral and Measure Theory - Steve Cheng 📝 Measure Theory - John K. Hunter (University of California at Davis) 📝 Measure and Integration - Dietmar A. Salamon (ETH Zürich) 📝 Lecture notes: Measure Theory - Bruce K. Driver

Collected Lectures on Ordinary Differential Equations (ODE)

📝 Difference Equations To Differential Equations - Dan Sloughter 📝 Ordinary Differential Equation - Alexander Grigorian (University of Bielefeld) 📝 Ordinary Differential Equations: Lecture Notes - Eugen J. Ionascu 📝 Ordinary Differential Equations - Peter Philip 📝 Ordinary Differential Equations - Gabriel Nagy 📝 Ordinary Differential Equations and Dynamical Systems - Gerald Teschl 📝 Notes on Differential Equations - Bob Terrell 📝 Elementary Differential Equations - William F. Trench 📝 Elementary Differential Equations With Boundary Value Problems - William F. Trench 📝 Notes on Diffy Qs: Differential Equations for Engineers - Jiří Lebl 📝 Differential Equations - H. B. Phillips (1922)

Collected Lectures on Partial Differential Equations (PDE)

📝 Notes on Partial Differential Equations - John K. Hunter (University of California at Davis) 📝 Partial Differential Equations: Lecture Notes - Erich Miersemann (Leipzig University) 📝 Linear Methods of Applied Mathematics - E. Harrell, J. Herod (Georgia Tech)

Collected Lectures on Real Analysis

📝 MIT OpenCourseWare Lectures on Calculus - G. Strang 📝 Elementary Calculus: An Approach Using Infinitesimals - Professor H. Jerome Keisler 📝 An Introduction to Real Analysis - John K. Hunter (University of California at Davis) 📝 Introduction to Real Analysis - William F. Trench (Trinity University, Texas) 📝 Basic Analysis: Introduction to Real Analysis - Jiří Lebl 📝 Elementary Real Analysis - Thomson, Bruckner 📝 Lecture Notes in Real Analysis - Eric T. Sawyer (McMaster University) 📝 Real Analysis - C. McMullen 📝 Real Analysis for Graduate Students - Richard F. Bass 📝 Modern Real Analysis - William P. Ziemer (Indiana University) 📝 Mathematical Analysis Vol I - Elias Zakon 📝 Mathematical Analysis Vol II - Elias Zakon 📝 Advanced Calculus - Lynn Loomis, Schlomo Sternberg 📝 Analysis of Functions of a Single Variable - Lawerence Baggett 📝 The Calculus of Functions of Several Variables - Dan Sloughter 📝 A ProblemText in Advanced Calculus - John M. Erdman 📝 Calculus and Linear Algebra. Vol. 1 - Wilfred Kaplan, Donald J. Lewis 📝 Calculus and Linear Algebra. Vol. 2 - Wilfred Kaplan, Donald J. Lewis 📝 Introduction to Calculus I and II - J.H. Heinbockel 📝 Active Calculus - Matt Boelkins 📝 Supplements to the Exercises in Chapters 1-7 of Walter Rudin’s “Principles of Mathematical Analysis” - George M. Bergman 📝 Calculus Made Easy - Silvanus P. Thompson (1910) 📝 Elements of Differential and Integral Calculus - William Anthony Granville (1911) 📝 Precalculus - Carl Stitz, Jeff Zeager

Ebooks on Combinatorics

Metric $k$-center

General $k$-center problem statement: Let \((X, d)\) be a metric space where \(X\) is a set and \(d\) is a metric. A set \(V \subseteq X\) is provided together with a parameter \(k\). The goal is to find a subset \(C \subseteq V\) with \(|C| = k\) such that the maximum distance of a point in \(V\) to the closest point in \(C\) is minimized. The problem can be formally defined as follows: Input: a set $V \subseteq X$, and a parameter $k$. Output: a set $C \subseteq V$ of $k$ points. Goal: Minimize the cost $r^C(V) = \max_{v \in V} d(v, C)$ The k-Center Clustering problem can also be defined on a complete undirected graph $G = (V, E)$ as follows:

Mathematics - Algebra

Major branches: Elementary algebra Linear algebra Abstract algebra Group theory Ring theory Field theory

Mathematics - Calculus of Variations

Mathematics - Combinatorics

Related fields: Combinatorial optimization Coding theory Discrete and computational geometry Combinatorics and dynamical systems Combinatorics and physics

Mathematics - Complex Analysis

Mathematics - Dynamical Systems

Mathematics - Functional Analysis

Mathematics - Harmonic Analysis

Mathematics - Mathematical analysis

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 - Measure Theory

Mathematics - Ordinary Differential Equations (ODE)

Mathematics - Partial Differential Equations (PDE)

Mathematics - Real Analysis

Mathematics for Computer Science

Reading list & mathematics resources.

Math Reading List

Mathematics

Study Mathematics # Master of Science in Mathematics @ HCMUS Branches of Mathematics # 1. Foundation of Mathematics # Transition To Pure Rigour Math Set Theory Logic Category Theory Type Theory Homotopy Type Theory Surreal Numbers 2. Number Theory # Algebraic Number Theory Analytic Number Theory 3. Algebra # Abstract Algebra Group Theory Linear Algebra Ring Theory Galois Theory Lie Algebras 4. Combinatorics # Probabilistic methods in Combinatorics Algebraic Combinatorics Graph Theory 5. Geometry Topology # Differential Geometry Algebraic Geometry Algebraic Statistics Topology Algebraic Topology 6. Mathematical analysis # Real Analysis Harmonic Analysis Complex Analysis Functional Analysis Measure Theory ODE PDE Variational Analysis Calculus of Variations Calculus (Single/ Multi-variables) Optimization & Operation Research Dynamical Systems Set-valued Analysis 7. Probability and Statistics # Probability Theory Statistics Statistical Learning Stochastic processes 8. Numerical Analysis # 9. Signal Processing # 10. Mathematics for Computer Science # 11. Mathematical Physics #