# Mort’s small traces

Mort Yao“Tiger got to hunt, bird got to fly;

Man got to sit and wonder ‘why, why, why?’

Tiger got to sleep, bird got to land;

Man got to tell himself he understand.”

— Kurt Vonnegut

# 1 Mathematics

- Naive set theory
**Mathematical logic**- Classical logic
- Propositional logic
- First-order logic
- Second-order logic

- Axiomatic set theory (ZFC)
- Model theory
- Computability theory
- Peano axioms
- Gödel’s incompleteness theorems

- Structural proof theory
- Non-classical logic
- Intuitionistic logic
- Linear logic
- Probabilistic logic

- Algebraic logic

- Classical logic
- Linear algebra and matrix theory
- Abstract algebra
- Group theory
- Representation theory
- Category theory and homological algebra

- Topology and geometry
- General topology (point-set topology)
- Geometric topology
- Algebraic topology and geometry
- Differential topology and geometry
- Lie group

- Calculus
- Limit and continuity
- Differentiation
- Integration
- Series
- Special functions
- Vector calculus and tensor calculus
- Calculus of variations

- Analysis
- Measure theory
- Complex analysis
- Real analysis
- Functional analysis
- Harmonic analysis

- Differential equations and dynamical systems theory
- Ergodic theory
- Control theory
- Chaos and fractals

- Number theory
- Algebraic number theory
- Analytic number theory

- Combinatorics
- Arithmetic combinatorics
- Graph theory and knot theory
- Algebraic graph theory

# 2 Applied Mathematics

- Probability theory and statistics
- Stochastic process and martingale
- Advanced probability theory

- Information theory
- Coding theory
- Algorithmic information theory
- Quantum information theory

**Theory of Computation**- Formal language and automaton
- Computability
- Complexity

**Algorithms**- Data structures
- Sorting
- Searching
- Randomization
- Approximation
- Numerical analysis
- Computational number theory
- Computational geometry
- Computer graphics and visualization

**Cryptography**- Information-theoretic security
- Private-key cryptography
- Public-key cryptography
- Quantum cryptography

- Game theory and operations research
- Linear programming and mathematical optimization
- Evolutionary computation
- Algorithmic game theory
- Finance and financial markets

**Machine learning**- Neural networks and deep learning

**Computer vision and image processing**- Natural language processing
**Programming language theory**- Formal semantics
- Type theory and Curry-Howard correspondence
- Program analysis and transformation

# 3 Physics and Life Sciences

- Statistical mechanics
- Classical mechanics, electromagnetism and field theory
- Quantum mechanics and quantum field theory
- Electronics and signal processing
- Formal verification and temporal logic

- Genetics, genomics and bioinformatics
- Structural biology (biochemistry, biophysics and molecular biology)
- Computational systems biology

# 4 Software Technology

- Computer systems and architectures
- Operating systems
- Unix from user space
- System programming
- Linux kernel

- TCP/IP
- Internet protocol suite
- Socket programming

- Web and databases
- Relational database and normalization
- NoSQL
- Knowledge representation and Semantic Web

- Programming paradigms
- Functional programming
- Logic programming
- Dataflow programming and concurrency

- Compilers
**Information security**- Proof-carrying code
- Cryptocurrencies