scheme (last compiled 05 Feb 2026) (Scheme Theory this is my note for scheme theory. this is mainly based on (1) Görtz - Wedhorn AG 1 ...)
module (last compiled 08 Nov 2025) (Some words on commutative algebra from the perspective of smooth manifold and vector bundle Nguyen Ngoc Khanh November 8, 2025 ...)
pca (last compiled 04 Oct 2025) (PCA A tutorial on Principle Component Analysis Khanh Nguyen August 2022, March 2023 Revisited 1 Problem Setup In this section, ...)
sheaf_iso (last compiled 01 Sep 2025) (sheaf isomorphism ismorphisms of sheaves on open cover implies isomorphism on the whole sheaves Khanh Nguyen November 2024 Lemma 1. ...)
spectral (last compiled 28 Aug 2025) (From Mass-Spring Systems to Spectral Graph Neural Networks Nguyen Ngoc Khanh August 28, 2025 1 Mass-Spring System 1.1 The two ...)
filter (last compiled 28 Aug 2025) (filter originally from my facebook post https: // www. facebook. com/ share/ p/ xWTeaskbL57ndGgn Khanh Nguyen June 2024 0.1 TLDR ...)
finite_union_compactness (last compiled 28 Aug 2025) (compactness Khanh Nguyen September 2023 this text presents the idea of local-to-global principle as a definition of compactness In mathematics, ...)
2_study_notes
ma5204_notes (last compiled 26 Jan 2026) (MA5204 Commutative and Homological Algbera this is my notes for MA5204 Commutative and Homological Algbera. this course is taught by ...)
adjunction (last compiled 21 Jan 2026) (adjunction this is notes for adjunction, this is basically a chapter in Topology: A Categorical Approach which was very well-written ...)
ma5210_notes (last compiled 12 Jan 2026) (differentiable manifolds this is my notes for ma5210 differential manifolds taught by National University of Singapore Professor Loke Hung Yean ...)
vakil_foag (last compiled 22 Dec 2025) (My notes for "Ravi Vakil - The Rising Sea: Foundations of Algebraic Geometry" Nguyen Ngoc Khanh December 22, 2025 Contents ...)
ma5209_notes_at (last compiled 08 Nov 2025) (ma5209 - algebraic topology Khanh Nguyen January 2024 Chapter 1 CATEGORY AND HOMOLOGICAL ALGEBRA 1.1 BASIC HOMOLOGICAL ALGEBRA Definition 1 ...)
dummit_foote_algebra (last compiled 08 Nov 2025) (Algebra this is my notes for Dummit Foote - Abstract Algebra. Despiting hating math and algebra in my secondary school, ...)
kunneth_theorem (last compiled 08 Nov 2025) (K¨unneth Theorem subtitle Khanh Nguyen April 2024 1 UNIVERSAL COEFFICIENT THEOREM Theorem 1 (universal coefficient theorem). Let R be a ...)
hartshorne_algebraic_geometry (last compiled 04 Oct 2025) (Algebraic Geometry My notes on Hartshorne Algebraic Geometry Dec 2024 2 Chapter 1 Varieties 1.1 Affine Varieties 1.2 Projective Varieties ...)
ma4271_tut_wk3 (last compiled 28 Aug 2025) (MA4271 Tutorial Week 3 Nguyen Ngoc Khanh - A0275047B August 2023 Problem 1 Let u, v, w ∈R3 be three ...)
ma4271_hw3 (last compiled 28 Aug 2025) (MA4271 Homework 3 Nguyen Ngoc Khanh - A0275047B October 2023 1 Problem Problem 1 Prove that the absolute value of ...)
ma5259_hw1 (last compiled 28 Aug 2025) (ma5259 hw1 Nguyen Ngoc Khanh - A0275047B September 2024 1 Lecture Exercises 1.1 Lecture 1 Exercise 1 If E, F ...)
ma4271_tut_wk4 (last compiled 28 Aug 2025) (MA4271 Tutorial Week 4 Nguyen Ngoc Khanh - A0275047B September 2023 Problem 1 Find the curvature of α(t) = (t ...)
ma4271_hw2 (last compiled 28 Aug 2025) (MA4271 Homework 2 Nguyen Ngoc Khanh - A0275047B September 2023 1 Problem Problem 1 Is the set A = {(x, ...)
set (last compiled 28 Aug 2025) (set Khanh Nguyen June 2023 some identities related to set 1 Zermelo–Fraenkel set theory 9 axioms in ZFC serve as ...)
real_analysis (last compiled 28 Aug 2025) (Some theorems we might missed in Real Analysis Khanh Nguyen August 2023 Definition 1 (left limit and right limit) Let ...)
calculus (last compiled 28 Aug 2025) (Calculus Khanh Nguyen May 2023 As a physics student in high school, CS undergraduate in NTU, I never have a ...)
ma5210_a1 (last compiled 28 Aug 2025) (ma5210 assignment 1 Nguyen Ngoc Khanh - A0275047B August 2024 Let (M, T ) be a topological space. We assume ...)
ma4261_hw3 (last compiled 28 Aug 2025) (ma4261 hw3 Nguyen Ngoc Khanh - A0275047B August 2024 1 Question 1 Let pY |X be a ternary channel with ...)
CZ4071 Network Science Assignment 2 (last compiled 28 Aug 2025) (CZ4071 Network Science Assignment 2 - Final Report Survey and Implementation of Paper: [7] Difan Zou, Ziniu Hu, Yewen Wang, ...)
ma4261_hw2 (last compiled 28 Aug 2025) (ma4261 hw1 Nguyen Ngoc Khanh - A0275047B August 2024 1 Problem 1 Consider random variables X and Y such that ...)
ma5259_notes (last compiled 28 Aug 2025) (Probability Theory a rigorous treatment to probability theory and its applications to stochastic processes Khanh Nguyen August 2024 Chapter 0 ...)
ma5205_notes (last compiled 28 Aug 2025) (ma5205 - measure and integral Nguyen Ngoc Khanh September 2023 Chapter 1 Measurable Space 1.1 Measurable Space In R, we ...)
ma5211_hw1 (last compiled 28 Aug 2025) (ma5211 hw1 Nguyen Ngoc Khanh - A0275047B January 2024 1 Problem Set I (1) Let Mn be the space of ...)
topbook_harder (last compiled 28 Aug 2025) (topbook harder Khanh Nguyen June 2023 some harder or interesting problems in topbook2023.pdf Common I will put here some common ...)
triangle-inequality (last compiled 28 Aug 2025) (triangle inequality khanh Sep 2021 Given an inner product space V over field F (R or C). The inner product ...)
topology_categorical_approach (last compiled 28 Aug 2025) (topology - a categorical approach Khanh Nguyen June 2024 Chapter 1 FOUR CONSTRUCTIONS OF TOPOLOGY Categorical definitions of some common ...)
differential_forms_and_stoke_theorem (last compiled 28 Aug 2025) (Differential Forms and Stoke’s Theorem Khanh Nguyen August 2023 this is my notes on Differential Forms and Stoke’s Theorem from ...)
ma5209_a2 (last compiled 28 Aug 2025) (ma5209 assignment 1 Nguyen Ngoc Khanh - A0275047B March 2024 1 Problem 1 Define a category Ho(Top) in the following ...)
ma5209_a3 (last compiled 28 Aug 2025) (ma5209 assignment 3 Nguyen Ngoc Khanh - A0275047B March 2024 1 Problem 1 (a) Let p be a prime number ...)
ma5259_hw3 (last compiled 28 Aug 2025) (ma5259 hw3 Nguyen Ngoc Khanh - A0275047B November 2024 1 Q1 We roll a fair die repeatedly until the sum ...)
ma4271_hw1 (last compiled 28 Aug 2025) (MA4271 Homework 1 Khanh Nguyen August 2023 Problem 1 Let α : I →R3 be a parameterized smooth curve with ...)
ma5259_hw2 (last compiled 28 Aug 2025) (ma5259 hw2 Khanh Nguyen October 2024 1 Q1 Let ξ1, ξ2, ... be a sequence of i.i.d coin tosses with ...)
complex (last compiled 28 Aug 2025) (complex Khanh Nguyen May 2023 this is the note for my learning on complex analysis 1 Definition of complex numbers ...)
ma4261_hw1 (last compiled 28 Aug 2025) (ma4261 hw1 Nguyen Ngoc Khanh - A0275047B August 2024 1 Problem 1 Let [m] = {1, 2, ..., m}. A ...)
ma5210_a2 (last compiled 28 Aug 2025) (ma5210 assignment 2 Nguyen Ngoc Khanh - A0275047B August 2024 1 Questions 1-4 1.1 Question 1 Let A be an ...)
ma5205_chapter2_hw (last compiled 28 Aug 2025) (Chapter 2 HW Khanh Nguyen August 2023 3 If [a′, b′] is a subinterval of [a, b], show that P[a′, ...)
ma5209_a1 (last compiled 28 Aug 2025) (ma5209 assignment 1 Nguyen Ngoc Khanh - A0275047B February 2024 Problem 1. Let Ωbe an open subset of R2. Write ...)
ma5209_notes_ha (last compiled 28 Aug 2025) (homological algebra Khanh Nguyen April 2024 1 CATEGORICAL CONSTRUCTION OF HOMOLOGICAL ALGEBRA Definition 1 (initial object, terminal object, pointed category, ...)
zorn_lemma (last compiled 28 Aug 2025) (Zorn’s Lemma Nguyen Ngoc Khanh October 2023 Definition 1 (Partially Order Set) A partial order on a set X is ...)
conflict-based-search (last compiled 28 Aug 2025) (conflict-based-search nguyenngockhanh.pbc March 2021 Given a set of resources R and a set of k agents A. Each agent associates ...)
fyp (last compiled 28 Aug 2025) (Project No: SCSE19-0810 Cluster Analysis on Dynamic Graphs Submitted by: Nguyen Ngoc Khanh Matriculation Number: U1720451D Supervisor: Asst Prof Ke ...)
set_function (last compiled 28 Aug 2025) (On the set function in Rn the ideas of these proofs below are from MA5205 Graduate Analysis I instructed by ...)
3_less_interesting
single_solution (last compiled 28 Aug 2025) (Given the problem: Minimize: f(x) subject to: c0(x) = n X i=1 xi = 1 and ci(x) = −xi ≤0 ...)
cycle (last compiled 28 Aug 2025) (cycle nguyenngockhanh.pbc April 2021 Is there an natural number function that always has a cycle and the cycle length is ...)
approximation-pattern (last compiled 28 Aug 2025) (approximation-pattern nguyenngockhanh.pbc March 2021 Consider the problem of minimizing a function f : D →R In many scenarios, it is ...)
two_sum (last compiled 28 Aug 2025) (Two-Sum Khanh Nguyen August 28, 2025 1 Preliminaries Let first define some data structures Denote [a, b] = {a, a ...)
test (last compiled 28 Aug 2025) (Find all functions f : [0, +∞) →[0, +∞) such that f(f(x)) + 3f(x) −270x = 133 For each real ...)
mapf-gp (last compiled 28 Aug 2025) (mapf-gp nguyenngockhanh.pbc January 2021 Contents 1 Chapter 1 Introduction Our central problem is defined as follow: Problem 1 (Problem 1). ...)
mapf-gp-summary (last compiled 28 Aug 2025) (mapf-gp-summary nguyenngockhanh.pbc March 2021 Contents 1 Chapter 1 Problem Decomposition 1.1 Problem Statement In the map of a specific location ...)
diffusion-convection (last compiled 28 Aug 2025) (Your Paper You August 28, 2025 Abstract Your abstract. 1 Introduction Your introduction goes here! Simply start writing your document ...)
My old documents
Aug 2024: My notes on differential manifolds: here
Aug 2024: My notes on probability theory and information theory: here
Jul 2024: My notes on adjunction in the book Tai-Danae Bradley, Tyler Bryson, John Terilla - Topology A categorical approach: here
Jun 2024: Some intuitions on filter in order and set: here
Jun 2024: Some notes on Topology - A categorical approach: here
Apr 2024: On homological algebra and algebraic topology: here