Substitution (logic)

Rule Induction

Statics

Gödel's T and PCF

Recursive Types

Dynamic Languages as Typed Languages

Assignable References

Evaluation Dynamics

Control Stacks

Futures and Speculations

Judgments as Types

Dynamics

Function (computer programming)

Products and Sums

Dynamic Languages

Scoped Assignables

Representation Independence

Nested Data Parallelism

Monads

Proofs as Programs

Binding

Abstract Syntax

Substitution Lemma

Objects and Dynamic Dispatch

Church's λ-Calculus

System F

Cost Dynamics

Brent's Theorem

Communication in the π-calculus

Dependently Typed Programming

De Bruijn Indices

Definability and undefinability

Proof Techniques

Modernized Algol

Polymorphism (computer science)

Parallelism

Free Assignables

Concurrent Algol

15-312 Foundations of Programming Languages Carnegie Mellon University Spring 2014 A comprehensive course at Carnegie Mellon University that introduces fundamental principles of programming language design and implementation from a mathematical perspective. It delves deep into the structural and dynamic aspects of programming languages, studying concepts like recursion, objects, polymorphism, and parallelism. This course introduces the fundamental principles of programming language design, semantics, and implementation. Our goal is to examine the fundamental structure of programming languages from a mathematical perspective.   

15-312 Foundations of Programming Languages

Programming Languages

Histories of AI

Societal impacts of AI

Vector (mathematics and physics)

Dot product

Geometric interpretations

Taking gradients

Discrete random variables

Probability distributions

Mean

Variance

Marginal distributions

Conditional distribution

Big-O notation

Computational complexity

Recurrence relation

Dynamic programming

Continuous optimization

Objective functions

Gradient descent

Machine learning

Loss minimization

Hinge loss

Equitable performance

Design and organization of features

Computation graphs

Deep learning models composition

Cross-validation (statistics)

Search problem

Breadth-first search (BFS)

Uniform cost search (UCS)

UCS heuristics

Markov Decision Process (MDP)

Transportation problem

Discounting factor

Reinforcement learning (RL)

Model-free Monte Carlo

Q-learning

Function approximation

Game theory

Minimax algorithm

Temporal difference (TD) learning

Variable-based models

Backtracking search

Gibbs sampling

Bayesian network

Laplace smoothing

Logic

Entailment

Satisfiability

Soundness

Modus ponens

First-order logic

Unification (computer science)

Python

Linear regression

Linear classification

Stochastic gradient descent (SGD)

Non-linear functions

Neural network

Backpropagation

Generalization

K-means clustering

Exhaustive search

Depth-first search (DFS)

UCS correctness

Relaxed search problems

Dice game

Policy evaluation

Value iteration

Model-based Monte Carlo

State–action–reward–state–action (SARSA)

Epsilon-greedy exploration

Deep Reinforcement Learning

Halving game

Alpha-beta pruning

Nash equilibrium

Factor graphs

AC-3 algorithm

Markov random field

Hidden Markov Model (HMM)

Maximum Likelihood Estimation (MLE)

Propositional calculus (Propositional logic)

Contradiction

Model checking

Completeness

Horn clauses

Skolem functions

CS 221 Artificial Intelligence: Principles and Techniques Stanford University Autumn 2022-2023 Stanford's CS 221 course teaches foundational principles and practical implementation of AI systems. It covers machine learning, game playing, constraint satisfaction, graphical models, and logic. A rigorous course requiring solid foundational skills in programming, math, and probability. The goal of artificial intelligence (AI) is to tackle complex real-world problems with rigorous mathematical tools. In this course, you will learn the foundational principles and practice implementing various AI systems. Specific topics include machine learning, search, Markov decision processes, game playing, constraint satisfaction, graphical models, and logic.  This course is fast-paced and covers a lot of ground, so it is important that you have a solid foundation in a number of areas. Here are the basic skills that you need and the classes that teach those skills:

- Programming (ideally Python): [CS 106A](http://www.stanford.edu/class/cs106a/), [CS 106B](http://www.stanford.edu/class/cs106b/), [CS 107](http://www.stanford.edu/class/cs107/)
- Discrete math, mathematical rigor: [CS 103](http://www.stanford.edu/class/cs103/)
- Probability: [CS 109](http://www.stanford.edu/class/cs109/)
- Linear algebra: [Math 51](https://web.stanford.edu/class/math51/textbook.html)

It is less important that you know particular things (e.g., we don't use eigenvectors in this course even though that's a pillar of any linear algebra course), and more important that you've done enough related things that you feel at ease with it. While it is possible to fill in the gaps, this course does move quickly, and ideally you want to be focusing your energy on learning AI rather than catching up on prerequisites. We have made a few [prerequisite modules](https://stanford-cs221.github.io/autumn2022/modules) that you can review to refresh your memory, and the first homework (foundations) will allow you to also get some practice on these basics. ### Further Reading

There are no required textbooks for this class, and you should be able to learn everything from the lecture notes and homeworks. However, if you would like to pursue more advanced topics or get another perspective on the same material, here are some great resources:

- [Russell and Norvig. Artificial Intelligence: A Modern Approach](http://aima.cs.berkeley.edu/). A comprehensive reference for all the AI topics that we will cover.
- [Koller and Friedman. Probabilistic Graphical Models](http://mitpress.mit.edu/books/probabilistic-graphical-models). Covers factor graphs and Bayesian networks (this is the textbook for CS228).
- [Sutton and Barto. Reinforcement Learning: An Introduction](https://mitpress.mit.edu/books/reinforcement-learning). Covers Markov decision processes and reinforcement learning (free online).
- [Hastie, Tibshirani, and Friedman. The Elements of Statistical Learning](https://web.stanford.edu/~hastie/ElemStatLearn/). Covers machine learning from a rigorous statistical perspective (free online).
- [Tsang. Foundations of Constraint Satisfaction](http://www.bracil.net/edward/fcs.html). Covers constraint satisfaction problems (free online).

Note that some of these books use different notation and terminology from this course, so it may take some effort to make the appropriate connections.

CS 221 Artificial Intelligence: Principles and Techniques

Artificial Intelligence

Substitution (logic)

2 courses cover this concept

15-312 Foundations of Programming Languages

CS 221 Artificial Intelligence: Principles and Techniques