Topics on Nam Le

Mathematics Books

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

Mathematics Lecture Notes

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

Mathematics MOOCS

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

Study Mathematics at HCMUS

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

1. Applied Mathematics #

MNC - Research Methodologies
MTT001 - Advanced Functional Analysis
MTT006 - Advanced Linear Algebra
MTT011 - Numerical Analysis
MTT012 - Stochastic Process
MTT081 - Optimization Algorithms
MTT106 - Non-linear Programming
MTT107 - Set-valued Analysis
MTT083 - Convex Analysis
MTT130 - Numerical Programming for Applied Problems
MTT131 - Seminar in Applied Mathematics
MTT139 - Mathematical Models in Economics
MTT147 - Statistical Modelling
MTT099 - Differential Equations
MTT097 - Partial Differential Equations
MTH10403 - Functional Analysis
MTT090 - Complex Analysis
MTT149 - Convex Analysis and Optimization

2. Mathematical Analysis #

MTT001 - Advanced Functional Analysis
MTT006 - Advanced Linear Algebra
MTT099 - Differential Equations
MTT097 - Partial Differential Equations
MTT090 - Complex Analysis
MTT149 - Convex Analysis and Optimization

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

7. Probability and Statistics #

Probability Theory
Statistics
Statistical Learning
Stochastic processes

8. Numerical Analysis #

Numerical methods for PDEs
Numerical methods for ODEs
Computational Linear Algebra

9. Signal Processing #

10. Mathematics for Computer Science #

11. Mathematical Physics #

Cambridge Notes (Vietnamese)

Wed, 11 Jan 2023 00:00:00 +0000

Ghi chú bài giảng Cambridge #

Tất cả các ghi chú đều được dịch từ Cambridge Notes do Dexter Chua biên tập. Các bản dịch sang tiếng Việt được sử dụng cho mục đích học tập. Vui lòng không sử dụng cho mục đích thương mại.

Part IA #

Michaelmas Term

Phương trình vi phân - Differential Equations: HTML, PDF, PDF (Trim), PDF (defs), PDF (thm), PDF (thm+proof), Official Notes, PDF (Vi)
Lý thuyết nhóm - Groups
Số học và Tập hợp - Numbers and Sets
Vector và Ma trận - Vectors and Matrices

Lent Term

Giải tích I - Analysis I
Động học và Thuyết tương đối - Dynamics and Relativity
Xác suất - Probability
Giải tích vector - Vector Calculus

Part IB #

Michaelmas Term

Giải tích II - Analysis II
Đại số tuyến tính - Linear Algebra
Xích Markov - Markov Chains
Kỹ thuật toán học - Methods
Cơ học lượng tử - Quantum Mechanics

Lent Term

Giải tích phức - Complex Analysis
Kỹ thuật phức - Complex Methods
Điện tử - Electromagnetism
Cơ học chất lỏng - Fluid Dynamics
Hình học - Geometry
Nhóm, Vành và Modules - Groups, Rings and Modules
Giải tích số - Numerical Analysis
Thống kê - Statistics

Easter Term

Không gian Metric và Topo - Metric and Topological Spaces
Optimisation
Nguyên lý biến phân - Variational Principles

Part II #

Michaelmas Term

Topo Đại số - Algebraic Topology
Lý thuyết Galois - Galois Theory
Hệ khả tích - Integrable Systems
Giải tích tuyến tính - Linear Analysis
Độ đo và Xác suất - Probability and Measure

Lent Term

Logic và Lý thuyết tập hợp - Logic and Set Theory
Trường số học - Number Fields
Lý thuyết biểu diễn - Representation Theory
Vật lý thống kê - Statistical Physics

Part III #

Michaelmas Term

Xác suất nâng cao - Advanced Probability
Topo Đại số - Algebraic Topology
Giải tích về Phương trình Đạo hàm riêng - Analysis of Partial Differential Equations
Tổ hợp - Combinatorics
Hình học vi phân - Differential Geometry
Extremal Graph Theory
Hydrodynamic Stability
Trường địa phương - Local Fields
Các kỹ thuật thống kê hiện đại - Modern Statistical Methods
Percolation and Random Walks on Graphs
Tính toán lượng tử - Quantum Computation
Lý thuyết trường lượng tử - Quantum Field Theory
Symmetries, Fields and Particles

Lent Term

Lý thuyết trường lượng tử - Advanced Quantum Field Theory
Đại số - Algebras
Logic
Modular Forms and L-functions
Tính dương trong Đại số Hình học - Positivity in Algebraic Geometry
Lý thuyết Ramsey - Ramsey Theory
Hình học Riemannian - Riemannian Geometry
Tiến hóa Schramm–Loewner - Schramm–Loewner Evolutions
Giải tích ngẫu nghiên và Ứng dụng - Stochastic Calculus and Applications
Symplectic Geometry
Mô hình chuẩn - The Standard Model
Theoretical Physics of Soft Condensed Matter

Easter Term

Classical and Quantum Solitons

Part IV #

Michaelmas Term

Topics in Geometric Group Theory

Lent Term

Topics in Number Theory

Easter Term

Bounded Cohomology

Daniel Raban's Note Repository Notes (Vietnamese)

Wed, 11 Jan 2023 00:00:00 +0000

Daniel Raban’s Note Repository #

[UCLA] Math 206A: Combinatorial Discrete Geometry (Igor Pak, F18): PDF, PDF (Vi)

[UCLA] Math 206B: Algebraic Combinatorics (Igor Pak, W19): [PDF], PDF (Vi)

[UCLA] Math 210A: Algebra (Romyar Sharifi, F18): PDF, PDF (Vi)

[UCLA] Math 210B: Algebra (Romyar Sharifi, W19): PDF, PDF (Vi)

[UCLA] Math 210C: Algebra (Romyar Sharifi, Sp19): [PDF], PDF (Vi)

[UCLA] Math 245B: Real Analysis (Tim Austin, W19): PDF, PDF (Vi)

[UCLA] Math 245C: Real Analysis (Wilfrid Gangbo, Sp19): PDF, PDF (Vi)

[UCLA] Math 246A: Complex Analysis (John Garnett, F18): [PDF], PDF (Vi)

[UCLA] Math 246B: Complex Analysis (Michael Hitrik, W19): PDF, PDF (Vi)

[UCLA] Math 246C: Complex Analysis (Michael Hitrik, Sp19): PDF, PDF (Vi)

[UCLA] Math 247A: Classical Fourier Analysis (Monica Visan, W20): PDF, PDF (Vi)

[UCLA] Math 254A: Topics in Entropy and Statistical Mechanics (Tim Austin, Sp21): PDF, PDF (Vi)

[UCLA] Math 254B: Ergodic Theory and Fractals (Tim Austin, Sp19): [PDF], PDF (Vi)

[UCLA] Math 255A: Functional Analysis (Michael Hitrik, F18): PDF, PDF (Vi)

[UCLA] Math 255A’: Functional Analysis (Tim Austin, F19): PDF, PDF (Vi)

[UCLA] Math 255B: Functional Analysis (Michael Hitrik, W20): PDF, PDF (Vi)

[UCLA] Math 259A: Operator Algebras in Hilbert Space (Sorin Popa, F19): PDF, PDF (Vi)

[UCLA] Math 275D: Stochastic Calculus (Jun Yin, F19): PDF, PDF (Vi)

[UC Berkeley] CS 294: Analysis of Boolean Functions (Avishay Tal, Sp23): [PDF], PDF (Vi)

[UC Berkeley] EE 229A: Information Theory and Coding (Venkat Anantharam, F21): PDF, PDF (Vi)

[UC Berkeley] Math 142: Algebraic Topology (Jamie Conway, Sp18): PDF, PDF (Vi)

[UC Berkeley] Math 222A: Partial Differential Equations (Daniel Tataru, F21): PDF, PDF (Vi)

[UC Berkeley] Math 222B: Partial Differential Equations (Sung-Jin Oh, Sp22): PDF, PDF (Vi)

[UC Berkeley] Math 249: Algebraic Combinatorics (Mark Haiman, F17): [PDF], PDF (Vi)

[UC Berkeley] Math 250A: Groups, Rings, and Fields (Richard Borcherds, F17): PDF, PDF (Vi)

[UC Berkeley] Math 272: Theory of Combinatorial Limits (Dan Král, S25): [PDF], PDF (Vi)

[UC Berkeley] Math 279: Topics in Stochastic Partial Differential Equations (Fraydoun Rezakhanlou, F21): PDF, PDF (Vi)

[UC Berkeley] Stat 155: Game Theory (Oscar Hernan Madrid Padilla, Sp18): PDF, PDF (Vi)

[UC Berkeley] Stat 206B: Stochastic Processes (Jim Pitman, Sp 18): [PDF], PDF (Vi)

[UC Berkeley] Stat C206B: Statics and Dynamics of Random Surfaces (Shirshendu Ganguly, Sp 22): [PDF], PDF (Vi)

[UC Berkeley] Stat 210A: Theoretical Statistics (Will Fithian, F21): PDF, PDF (Vi)

[UC Berkeley] Stat 210B: High-Dimensional Statistics (Song Mei, Sp22): PDF, PDF (Vi)