Mathematics on Nam Le

Collected Lectures on Calculus of Variations

Mon, 07 Jul 2025 00:00:00 +0000

Gentle introductions #

Blog post “The Calculus of Variations” on Bounded Rationality, with intuitive explanations and worked brachistochrone-style examples.

Classic introductory textbooks (PDF) #

Gelfand & Fomin – Calculus of Variations (Dover). A standard first text, concise and focused on core theory and mechanics applications.
Bruce van Brunt – The Calculus of Variations (Springer Universitext); a bit more modern, with geometry and physics examples, suitable after multivariable calculus and basic analysis.
Hunter College notes “The Calculus of Variations” (covers lemmas, Euler–Lagrange, Weierstrass condition, etc.) for a structured, textbook-like PDF.

Lecture note sets #

Lukas Koch, Lecture notes for Calculus of Variations (Leipzig, 3rd-year course, includes classical theory and direct method, up to modern topics).
Riccardo Cristoferi, Calculus of Variations Lecture Notes (Carnegie Mellon, classical necessary and sufficient conditions, many examples).
Filip Rindler, Introduction to the Modern Calculus of Variations (goes beyond classical theory toward modern functional-analytic treatment).
Pisa “Lecture Notes Calculus of Variations A” (introduction, first variation, Euler–Lagrange, with PDE flavor).
Long Chen, Classic theory of calculus of variation (focused on Euler–Lagrange, Legendre, Jacobi, Weierstrass conditions, weak vs strong minima).

Collected Lectures on Complex Analysis

Mon, 07 Jul 2025 00:00:00 +0000

📝 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

Mon, 07 Jul 2025 00:00:00 +0000

📝 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

Mon, 07 Jul 2025 00:00:00 +0000

📝 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

Mon, 07 Jul 2025 00:00:00 +0000

📝 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)

Mon, 07 Jul 2025 00:00:00 +0000

📝 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)

Mon, 07 Jul 2025 00:00:00 +0000

📝 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

Mon, 07 Jul 2025 00:00:00 +0000

📝 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

Mon, 07 Jul 2025 00:00:00 +0000

Metric $k$-center

Mon, 07 Jul 2025 00:00:00 +0000

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:

The $k$-Center Clustering problem: Given a complete undirected graph $G = (V, E)$ with distances $d(v_i, v_j) \in \mathbb{N}$ satisfying the triangle inequality, find a subset $C \subseteq V$ with $|C| = k$ while minimizing:

$$ \max_{v \in V} \min_{c \in C} d(v, c) $$

Mathematics - Combinatorics

Thu, 27 Jun 2024 23:14:15 +0800

Related fields:

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

Mathematics for Computer Science

Thu, 27 Jun 2024 23:14:15 +0800

Reading list & mathematics resources.

Sat, 19 Aug 2023 00:00:00 +0000

Foundations of Mathematics #

Number Theory #

Algebra #

1/ Lay, D. C., Lay, S. R., & McDonald, J. (2016). Linear algebra and its applications. Pearson Education.

2/ Strang, G. (2019). Linear algebra and learning from data (Vol. 4). Cambridge: Wellesley-Cambridge Press.

Combinatorics - Graph Theory #

Graph theory books #

[1] Lewis, R. (2015). A guide to graph colouring (Vol. 7). Berlin: Springer.

[2] Tucker, A. (1994). Applied combinatorics. John Wiley & Sons, Inc..

[3] Li, Y., & Lin, Q. (2022). Elementary Methods of Graph Ramsey Theory (Vol. 211). Springer Nature.

[4] David Conlon - Extremal graph theory

[5] Trudeau, R. J. (1994). Introduction to graph theory. Dover Pubns.

[6] Reinhard, D. (2017). Graph Theory. GTM, vol. 173.

[7] Bondy, J. A., & Murty, U. S. R. (1976). Graph theory with applications (Vol. 290). London: Macmillan.

[8] Bollobás, B. (1998). Modern graph theory (Vol. 184). Springer Science & Business Media.

[9] Needham, M., & Hodler, A. E. (2019). Graph algorithms: practical examples in Apache Spark and Neo4j. O’Reilly Media.

[10] Guia, J., Soares, V. G., & Bernardino, J. (2017, April). Graph Databases: Neo4j Analysis. In ICEIS (1) (pp. 351-356).

[11] Harary, Frank - Graph Theory-Perseus Books (1999)

[12] Miklós Bóna - A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory, World Scientific (2016)

[13] Robin J. Wilson - Introduction to Graph Theory, Fourth Edition-Addison Wesley (1996)

[14] (Textbooks in Mathematics) Jonathan L. Gross, Jay Yellen, Mark Anderson - Graph Theory and Its Applications, third edition (2018)

[15] Introduction to Graph Theory, Douglas B. West

Geometry & Topology #

Analysis #

Probability & Statistics #

1/ Gould, R., & Ryan, C. N. (2015). Introductory statistics: Exploring the world through data. Pearson.

2/ Johnson, R. A., & Wichern, D. W. (2002). Applied multivariate statistical analysis.

3/ Härdle, W. K., & Simar, L. (2019). Applied multivariate statistical analysis. Springer Nature.

Numerical Analysis #

Signal processing #

Applied mathematics #

Machine learning #

1/ Deisenroth, M. P., Faisal, A. A., & Ong, C. S. (2020). Mathematics for machine learning. Cambridge University Press.

2/ Bishop, C. M., & Nasrabadi, N. M. (2006). Pattern recognition and machine learning (Vol. 4, No. 4, p. 738). New York: springer.

3/ Koller, D., & Friedman, N. (2009). Probabilistic graphical models: principles and techniques. MIT press.

4/ Barber, D. (2012). Bayesian reasoning and machine learning. Cambridge University Press.

5/ Hastie, T., Tibshirani, R., Friedman, J. H., & Friedman, J. H. (2009). The elements of statistical learning: data mining, inference, and prediction (Vol. 2, pp. 1-758). New York: springer.

6/ Mohri, M., Rostamizadeh, A., & Talwalkar, A. (2018). Foundations of machine learning. MIT press.

7/ Williams, C. K., & Rasmussen, C. E. (2006). Gaussian processes for machine learning (Vol. 2, No. 3, p. 4). Cambridge, MA: MIT press.

8/ Vapnik, V. (1999). The nature of statistical learning theory. Springer science & business media.

9/ Shalev-Shwartz, S., & Ben-David, S. (2014). Understanding machine learning: From theory to algorithms. Cambridge university press.

10/ Wainwright, M. J., & Jordan, M. I. (2008). Graphical models, exponential families, and variational inference. Foundations and Trends® in Machine Learning, 1(1–2), 1-305.

Optimization #

1/ Kochenderfer, M. J., & Wheeler, T. A. (2019). Algorithms for optimization. Mit Press.

2/ Kochenderfer, M. J., Wheeler, T. A., & Wray, K. H. (2022). Algorithms for decision making. MIT press.

3/ Boyd, S. P., & Vandenberghe, L. (2004). Convex optimization. Cambridge university press.

4/ Bertsekas, D. (2009). Convex optimization theory (Vol. 1). Athena Scientific.

5/ Papadimitriou, C. H., & Steiglitz, K. (1998). Combinatorial optimization: algorithms and complexity. Courier Corporation.

6/ Cook, W. J., Cunningham, W. H., Pulleyblank, W. R., & Schrijver, A. (2009). Combinatorial optimization. Oberwolfach Reports, 5(4), 2875-2942.

Mathematics

Sat, 08 Apr 2023 00:00:00 +0000

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 #

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

Mathematics on Nam Le

Collected Lectures on Calculus of Variations

Gentle introductions #

Classic introductory textbooks (PDF) #

Lecture note sets #

Collected Lectures on Complex Analysis

Collected Lectures on Functional Analysis

Collected Lectures on Harmonic Analysis

Collected Lectures on Measure Theory

Collected Lectures on Ordinary Differential Equations (ODE)

Collected Lectures on Partial Differential Equations (PDE)

Collected Lectures on Real Analysis

Ebooks on Combinatorics

Metric $k$-center

Mathematics - Combinatorics

Mathematics for Computer Science

Reading list & mathematics resources.

Foundations of Mathematics #

Number Theory #

Algebra #

Combinatorics - Graph Theory #

Graph theory books #

Geometry & Topology #

Analysis #

Probability & Statistics #

Numerical Analysis #

Signal processing #

Applied mathematics #

Machine learning #

Optimization #

Mathematics

Study Mathematics #

Branches of Mathematics #

1. Foundation of Mathematics #

2. Number Theory #

3. Algebra #

4. Combinatorics #

5. Geometry Topology #

6. Mathematical analysis #

7. Probability and Statistics #

8. Numerical Analysis #

9. Signal Processing #

10. Mathematics for Computer Science #

11. Mathematical Physics #