Personal Knowledge Base

Contents

• Mathematics
• Computer Science
• Competitions
• Software Engineering
• Links you might want to read

Mathematics

Pure Mathematics

Algebra & Algebraic Geometry

• Linear Algebra
• Multilineal Algebra
• Groups and Rings
• Galois Theory
• Commutative Algebra
• Representation Theory
• Category Theory
• Algebraic Topology
• Algebraic Geometry

Analysis & PDEs

• Precalculus
• Differential Calculus
• Integral Calculus
• Multivariate Calculus
• Applied Calculus
• Real Analysis
• Topology in ℝⁿ
• Analysis on Manifolds
• Complex Analysis
• Measure Theory
• Functional Analysis
• General Topology
• Applied Differential Equations
• Ordinary Differential Equations
• Partial Differential Equations

Geometry

• Differential Geometry
• Riemmanian Geometry

Mathematical Logic and Foundations

• Mathematical Logic
• Set Theory

Number Theory

• Elementary Number Theory
• Algebraic Number Theory
• Analytic Number Theory
• Elliptic Curves

Probability & Statistics

• Statistics
• Probability Theory
• Markov Chains

Applied Mathematics

Combinatorics

• Combinatorial Analysis
• Graph Theory
• Extremal Combinatorics
• Enumerative Combinatorics
• Discrete Geometry
• Matroid Theory
• Combinatorial Optimization
• Probabilistic Methods in Combinatorics
• Polynomial Method in Combinatorics

Computational Science & Numerical Analysis

• Numerical Analysis

Operations Research

• Linear Programming
• Convex Optimization

Seminars

• Advanced Topics in Random Structures

Computer Science

Artificial Intelligence

Machine Learning

• Introduction to Artificial Intelligence
• Introduction to Machine Learning
• Optimization for Machine Learning

Deep Learning

• Introduction Deep Learning
• Deep Reinforcement Learning
• Neural Computation

Natural Language Processing

• Introduction to NLP
• Advanced NLP

Computer Vision

• Introduction to Computer Vision

Seminars

• Probabilistic Graphical Model

Computer Systems

Operating / Distributed Systems

• Computer Systems Engineering
• Operating Systems and Systems Programming
• Advanced Operating Systems Structures and Implementation
• Distributed Systems

Architecture

• Parallel Computer Architecture

Computer Security

• Introduction to Computer Security

Computer Networks

• Introduction to Computer networks

Databases

• Introduction to Databases
• Advanced Database Systems
• Self-Driving Database Management System
• Multimedia Databases
• Data-Intensive Systems
• Mining Massive Datasets

Software Design and Engineering

Programming Languages

• Introduction to Programming
• Imperative Programming
• Object Oriented Programming
• Functional Programming
• Concurrent Programming
• Quantitative Program Analysis
• Programming Languages and Compilers
• Formal Verification

Software

• Software Construction
• Software Engineering
• Software Engineering for Startups
• Software Engineering for Scientific Computing
• Data Science
• Computer Graphics
• Human-Computer Interaction

Theory

Algorithms & Data Structures

• Introduction to Algorithms
• Intermediate Algorithms
• Advanced Algorithms
• Data Structures
• Computational Geometry
• Algorithmic Game Theory
• Combinatorial Algorithms
• Randomized Algorithms
• Parallel and Concurrent Algorithms

Automata, Computability and Complexity

• Computation Theory
• Complexity Theory
• Advanced Computational Complexity Theory

Cryptography

• Introduction to Cryptography

Seminars

• Algorithms and Computational Complexity
• The Sum-of-Squares Algorithm
• Hierarchies of Integer Programming Relaxations

Competitions

• IMO / IMC / Putnam
• IOI / ICPC

Software Engineering

Languages & Frameworks

• C++
• JavaScript
• Python
  • Django
  • FastAPI
  • pyenv
• R

Databases

• Oracle
• PostgreSQL
• Redis

DevOps

• AWS
• Docker

Engineering Productivity

• Git
• Bash
• Crontabs
• tmux
• Practices

Editors

• Vim
• Jupyter notebook

Links you might want to read

• Learn to Code - Evan Chen
• Why LaTeX? - Evan Chen
• Why Unix? - Evan Chen
• Doing Theoretical Computer Science research - Ryan O'Donnell
• Giving clear talks - Kayvon Fatahalian
• How I manage my BibTeX references, and why I prefer not initializing first names - Yufei Zhao
• If coding can be taught to someone without a college degree, what is the purpose of requiring a Bachelor’s degree for many coding jobs? - Tikhon Jelvis
• What are the biggest misconceptions about Computer Science? - Tikhon Jelvis
• What programming projects have given you the most insight on a programming concept/technique? - Tikhon Jelvis
• What do only people with 20-50 years of programming experience know? - Dave Voorhis
• High School and College - Evan Chen
• Math contests - Evan Chen
• What explains the Chinese domination at the IMO? - Zhaojun Zhang
• How do Russians learn competitive coding? - Egor Suvorov
• Does practice mean everything for competitive programming, or do I have to have an Einstein brain? - Bohdan Pryshchenko
• What made you quit competitive programming? - Sergey Kulik
• Why do I hate studying despite being highly intelligent? - Steve Denton
• Do most highly intelligent people get bored by routine learning in schools and hence cannot stand formal education? - Pieter Cortebeeck
• Do the top 1% students mostly rely on their talents or hard work to sustain their positions? - Chier Hu
• What piece of advice do you have for students to succeed academically and financially? - Balaji Viswanathan
• Why do some intelligent people lose all interest in academia? - Steven Thomason
• What's it like to be close friends with a genius? - Joe Wezorek
• Why do some people with a high IQ get depressed or have no friends? - Susanna Viljanen
• Are people with higher IQ more likely to be depressed? - Simon Chatzigiannis
• Do you find yourself to be a wasted talent? Do extremely intelligent people simply not care about what society deems as successful? - Susanna Viljanen
• Why is it that intelligent people tend to feel lonely most of the time? - Susanna Viljanen
• What is the brutal truth about people with low IQs? - Susanna Viljanen
• Are geniuses born or made? - Susanna Viljanen
• What's it like to be genuinely apolitical? - Tikhon Jelvis
• Biculturalism - Joel Spolsky
• A Career Cold Start Algorithm - Andrew Bosworth
• Say No - Andrew Bosworth