awesome-theoretical-computer-science

A modern, brief, and accessible text which introduces theoretical computer science for undergrads. It includes topics not usually included in standard undergrad text-books

undergrad introduction to theory of computation

A series of lectures on selected notable topics in theoretical computer science

A series of lectures on selected notable topics in theoretical computer science

A sweeping survey of complexity theory, emphasizing the field’s insights and challenges. It explains the ideas and motivations leading to key models, notions, and results

It spans complexity of mazes and games; optimization in theory and practice; randomized algorithms, interactive proofs, and pseudorandomness; Markov chains and phase transitions; and of quantum computing. It provides accessible explanations

A complete comprehensive encyclopediac handbook which surveys all related areas to theoretical computer science

A complete comprehensive encyclopediac handbook which surveys all related areas to theoretical computer science

A complete comprehensive encyclopediac handbook which surveys all related areas to theoretical computer science

A complete comprehensive encyclopediac handbook which surveys all related areas to theoretical computer science

undergrad introduction to theory of computation

It teaches basic concepts in theoretical computer science, such as NP-completeness, and what they imply for solving tough algorithmic problems

It focuses on the big fundamental questions of computing, and how understanding the power and limitations of algorithms helps us develop the tools to make real-world computers smarter, faster and safer

A standard text for introducing theory of computation for undergrads

Introductory undergrad textbook for automata, languages and theory of computation topics

A problem-set text for automata, languages, and complexity

( ) - Undergraduate course on computational complexity theory; It follows the same spirit of Sipser's part III

It covers most of what is believed to be known to get started in complexity theory research

Three weeks of lectures from the IAS/Park City Mathematics Institute Summer School on computational complexity. Topics include reductions, lower-bounds, average-case complexity, randomness, interactive proof systems, probabilistically checkable proofs, quantum computing, and proof complexity

A golden standard textbook, Surveying computational complexity theory for graduate students and researchers

A grad introduction to computation complexity theory, emphasizing the idea behind concepts of complexity theory

A very gentle introduction to some fundamental ideas of computational complexity like NP-completeness and P vs NP

An accessible, algorithmically oriented, research-centered, up-to-date guide to some of the most interesting techniques of complexity theory

Body of knowledge for studying the performance and limitations of computer algorithms. Among topics covered are: reductions and NP-completeness, cryptography and protocols, randomized algorithms, and approximability of optimization problems, circuit complexity, the structural aspects of the P=NP question, parallel computation, and the polynomial hierarchy

A graduate course which introduces the fundamental results and techniques in the area and some research frontier questions. Themes include: Communication models and the communication complexity zoo, Information vs. communication, Query-to-communication lifting, and Applications

An excellent and very readable introductory textbook to the field of communication complexity

A modern textbook surveying circuit complexity

An introduction to circuit complexity, boolean functions, and computation models

CS Masters level lectures on topics including Boson sampling, quantum interactive proofs, and quantum merlin arthur

Focuses on cutting edge topics in quantum information that relate to Complexity of Entanglement. - see this also

An introduction to modern proof complexity, emphasizing its connections with computational complexity and algorithms in optimization

Intuitively, It explains the idea of a computable function: a function whose values can be calculated in an effective or automatic way

A concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results

In this classic text, Dr. Davis provides a clear introduction to computability, at an advanced undergraduate level, that serves the needs of specialists and non-specialists alike

It gives a complete account of the theory of r.e degrees. The definitions, results and proofs are always clearly motivated and explained before the formal presentation; the proofs are described with remarkable clarity and conciseness

An impressive presentation of classical recursion theory. It is highly recommended to everyone interested in recursion theory

Computer scientists, mathematicians, and philosophers discuss the conceptual foundations of the notion of computability as well as recent theoretical developments

Presents a wide range of results in logic and computational complexity

Structure and Interpretation of Computer Programs - , , , , , - Fundamental principles of computer programming in Scheme, including recursion, abstraction, modularity, and programming language design and implementation

A broad introduction series to the mathematical underpinnings of reliable software. It's composed of proof scripts for the Coq proof assistant. It's is intended for a broad range of readers, With no specific background assumed

Techniques for thinking crisply about programming languages, write some fascinating programs, and discuss various design tradeoffs

A book introducing both machine-checked proof with Coq Proof Assistant and approaches to formal reasoning about program correctness

Lean Proof Assistant

Notes by Giovanni Sambin of a series of type theory lectures given in Padua, June 1980

This book describes different type theories (theories of types, polymorphic and monomorphic sets, and subsets) from a computing science perspective

The present book is intended as a first systematic exposition of the basics of univalent foundations, and a collection of examples of this new style of reasoning — but without requiring the reader to know or learn any formal logic, or to use any computer proof assistant

An online course on functional programming with Haskell programming language, and a live interactive Telegram community

A modern course on data structures and functional programming using OCaml

A first course on basic algorithms and data structures. — added by Erik himself!

A second course on algorithms and data structures. — added by Erik himself!

It covers major results and current directions of research in data structure

Notably uses ideas such as randomness, approximation, high dimensional geometry. Faces uncertainty, approaches to handle big data, handling intractability, heuristic approaches, ..etc

A legendary series by Donald Knuth on design and analysis of algorithms

A class taking a practical approach to proving problems can't be solved efficient

A sequel to Garey and Johnson's Computers and Intractability: A Guide to NP-Completeness. New topics include Parameterized Complexity, Lower bounds on approximation, Other hardness assumptions (ETH, 3SUM-conjecture, APSP-conjecture, UGC, Others), Online Algorithms, Streaming Algorithms, Polynomial Parity Arguments, and Parallelism

It shows that games and puzzles can serve as powerful models of computation, Offering a new way of thinking about computation

Key tools of probabilistic analysis, and application of these tools to understand the behaviors of random processes and algorithms. Emphasis is on theoretical foundations, though applications will be discussed in machine learning and data analysis, networking, and systems. Topics include tail bounds, the probabilistic method, Markov chains, and martingales, with applications to analyzing random graphs, metric embeddings, and random walks

Introduction to probabilistic methods in computer science

Harvey. and Course in Randomized Algorithms. Columbia. - Respectively, undergrad and grad courses for probabilistic methods in algorithms

Topics include Discrete probability, High-dimensional geometry and statistics, Information and entropy, and Markov chains and convergence to equilibrium

Supplemental notes to the standard books by Mitzenmacher & Upfals, and Motwani & Raghavan

A broad introduction to results and techniques with an emphasis on fundamental problems and widely applicable tools. Also more advanced and specialized topics

It includes greedy, local search, dynamic programming, randomized rounding, tree embeddings, and semidefinite programming

It includes convex programming-based, randomness, and metric methods

It includes greedy, local search algorithms, dynamic programming, linear and semidefinite programming, and randomization

A technique-oriented approach provides a unified view. It includes detailed algorithms, proofs, analyses, examples, and applications from research papers

Some elements of Algorithmic tasks of encoding and decoding and its connections with error-correction; These codes are now tools in the design and analysis of algorithms, and also in many aspects of computational complexity. The focus is on constructions of algorithmic and asymptotic importance. Requires only basic mathematical maturity

Scott Aaronson. Quantum Information Science. & - Part I: Presuppose only linear algebra and a bit of classical algorithms. Topics include quantum circuits, density matrices, entanglement entropy, Wiesner’s quantum money, QKD, quantum teleportation, the Bell inequality, interpretations of QM, the Shor 9-qubit code, and the algorithms of Deutsch-Jozsa, Bernstein-Vazirani, Simon, Shor, and Grover. Part II: Perspectives on quantum computing that go beyond the bare quantum circuit model, like Hamiltonians, Stabilizer formalism, Bosons and Fermions, Cluster states, and Matrix product states

It aims to strengthen the ties between computation and communication communities. It explores (1) information theoretic techniques in complexity theory and combinatorics, (2) Coding theory and applications, and (3) information theory, machine learning, and big data

It bridges the gap of Theoretical Computer Science and Bioinformatics communities, On new data compression techniques, and computation over compressed data

Advanced tutorials appropriate for self-study by experienced researchers,

An introduction to the interwoven domains of cryptography, proofs and randomness

The aim of the current course is to make the students familiar with some of randomized methods

The basic theory underlying machine learning and the process of generalizing from data

Focuses on simplified proofs over what appears in the literature, and classical perspective of achieving a low test error for binary classification with IID data via standard (typically ReLU) feedforward networks

A broad overview of the theoretical foundations underlying common machine learning algorithms

Formally define and study various models that have been proposed for learning. The course will present and contrast the statistical, computational and online models for learning. We will present and rigorously analyze some of the most successful algorithms in machine learning that are extensively used today

It explores theoretical foundations for deep learning, emphasizing the following themes: (1) Approximation: What sorts of functions can be represented by deep networks, and does depth provably increase the expressive power? (2) Optimization: Essentially all optimization problems we want to solve in practice are non-convex. What frameworks can be used to analyze such problems? (3) Beyond-Worst Case Analysis: Deep networks can memorize worst-case data, so why do they generalize well on real-world data?

A seminar course that will focus on the following phenomenon: many problems in machine learning are formally intractable (e.g., NP-hard). Nevertheless they are solved in practice by heuristics. Can we design algorithms with provable guarantees (running time, solution quality)?

Emphasizing issues of computational efficiency, It introduces a number of central topics in computational learning theory

It provides an extensive theoretical account of the fundamental ideas underlying machine learning and the mathematical derivations that transform these principles into practical algorithms

Aligning and focusing theoretical and applied researchers on the common purpose of building empirically relevant theoretical foundations of deep learning. Specifically, the intention was to identify and make progress on challenges that, on one hand, are key to guiding the real-world use of deep learning and, on the other hand, can be approached using theoretical methodology

Identifying a set of core techniques and principles that form a foundation for the subject

Aims to grow the reach and impact of computer science theory within machine learning

Formal methods and machine learning can inform each other from deductive and inductive reasoning perspectives. This talk aims to facilitate the dialogue between the two communities by establishing some fundamental concepts in learning theory

A mini-course notes of two-fold goals: mini-course is twofold: (i) Explain how complexity theory has helped illuminate several barriers in economics and game theory; and (ii) Illustrate how game-theoretic questions have led to new and interesting complexity theory, including recent several breakthroughs

It combines algorithmic thinking with game-theoretic, or, more generally, economic concepts. The course will study a range of topics at this interface. The only prerequisite to the course is mathematical thinking

A broad graduate-level introduction to: auctions, existence and computation of equilibria in games and markets, algorithmic mechanism design, price of anarchy and price of stability, games relevant to networks and e-commerce. The emphasis will be on conceptual ideas and algorithmic aspects. No familiarity with game theory or economics will be assumed

The course discusses algorithmic aspects of game theory, such as a general introduction to game theory, auctions, mechanisms, the costs of a central control optimum versus those of an equilibrium under selfish agents, and algorithms and complexity of computing equilibria

TAs based these notes in large part on the lecture notes and accompanying videos of Tim Roughgarden's CS 364A and CS 364B courses at Stanford, and Jason Hartline's Mechanism Design and Approximation textbook

A graduate-level course covering the topics at the intersection of machine learning and game theory

A graduate level course covering topics at the interface between machine learning and game theory

The science and technology of blockchain protocols and the applications built on top of them, with an emphasis on fundamental principles rather than specific protocols. - See also

Games provide mathematical models for interaction, and numerous tasks in computer science can be formulated in game-theoretic terms

Basic chapters on algorithmic methods for equilibria, mechanism design and combinatorial auctions are followed by chapters on important game theory applications such as incentives and pricing, cost sharing, information markets and cryptography and security

The intersection is motivated by applications such as large-scale digital auctions and markets, and fundamental questions such as the computational complexity of Nash equilibria and complexity and approximation in mechanism design. Also, To productively model and study the Internet and its novel computational phenomena, Models and insights can be gained from from game theory and economic theory. The computational point of view, on the other hand, is essential to understand a world in which markets are networked and the default platforms of economic transactions are algorithmic

The intersection is manifested by (1) Data input to machine learning algorithms are generated by self-interested parties, (2) Machine learning is used to optimize economic systems or acts, (3) Machine learning models used in critical systems are becoming prone to adversarial attacks, and (4) Several machine learning approaches can be framed as finding the equilibrium of a game

How to quantify the impact of strategic user behavior on overall performance in games including traffic routing as well as online auctions

An introduction to discrete mathematics oriented toward computer science and engineering. -

An expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply

A classic math-oriented introduction to computer science

A textbook for a one quarter introductory course in theoretical computer science

A series dedicated to math topics and their relevance to computer science

A concise offered as an accessible reference on mathematical logic for the professional computer scientist

It presents a careful selection of the material most needed by students in their first two years studying computer science

For lower undergraduates, It introduces the reader to logic, proofs, sets, and number theory, Focusing on foundations. It provides complete details and derivations of formal proofs

Suitable for undergraduate introductions to logic and early graduate courses on logic

Semantic tableaux are used because they are theoretically sound and easy to understand

Uses your familiarity with ideas from programming and software to teach mathematics

A range of mathematical topics to provide a solid foundation for an undergraduate course in computer science, starting with a review of number systems and their relevance to digital computers, and finishing with differential and integral calculus

Presents an algorithmic approach to mathematical analysis, with a focus on modelling and on the applications of analysis

calculus lecture notes taught for undergrad computer science students

It covers a large number of the math/CS topics that you need to know for reading and doing research in Computer Science Theory - alternatively:

Things prof. Madhur wish he knew in first year of grad school

It covers hashing, dimension reduction, linear and convex programming, gradient descent and regression, sampling and estimation, compressive sensing, linear-algebraic techniques (principal components analysis, singular value decomposition, spectral techniques), and an intro to differential privacy

It covers a large number of the math/CS topics that you need to know for reading and doing research in Computer Science Theory

It covers a large number of the math/CS topics that you need to know for reading and doing research in Computer Science Theory

It covers a large number of the math/CS topics that you need to know for reading and doing research in Computer Science Theory

Aimed primarily at first and second year graduate students who plan to do research in theoretical computer science. We will introduce probabilistic, algebraic, combinatorial, and algorithmic methods useful in proofs

It covers a collection of geometric techniques that apply broadly in modern algorithm design

Combinatorial techniques written largely with an eye to their applications in TCS, and mostly in complexity

Fall 2017 of the Yale course CPSC 202a, Mathematical Tools for Computer Science

Honors lecture notes on discrete math -

A complete survey of roughly all topics of discrete math and their relevance to computing and communication engineering

A canonical discrete math textbook, accessible for even high school students

It endows the reader with an operational conceptual and methodological understanding of discrete mathematics for computing

It attempts to change the way we teach logic to beginning students. Instead of teaching logic as a subject in isolation, we regard it as a basic tool and show how to use it

Learn the language of Computer Science. Learn the math that defines computer science, and practice applying it through mathematical proofs and Python code

and - Showing some combinatorial object exists and prove that a certain random construction works with positive probability. The course focuses on methodology as well as combinatorial applications

A standard reference for researchers in probabilistic methods in combinatorics. Shows also connections to theoretical computer science

An introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find also deep insights into a range of less common topics rarely considered within a single book

Takes us on a broad sweep of scientific knowledge and related technologies: propositional logic of the ancient Greeks (microprocessors); quantum mechanics (silicon chips); network and system phenomena (internet and search engines); computational intractability (secure encryption); and efficient algorithms (genomic sequencing)

Feynman’s Course on Computation - See also Preskill's update 40 years later

Important connections between thermodynamics and complexity are proposed and discussed. Pedagogically written, serves as a fundamental introduction to black holes and their complex physical interpretation

It examines the relevance of modern theoretical computer science to traditional questions in philosophy, and conversely, what philosophy can contribute to theoretical computer science

A general illustration of relations between faith and science

Turing’s place in the history and philosophy of science

It argues that computational complexity theory leads to new perspectives on the nature of mathematical knowledge and other philosophical questions

It describes how quantum mechanics can be tested in the limit of high complexity regime by extending the usual scientific paradigm to include

It highlights the significance of complexity theory relative to questions traditionally asked by philosophers of mathematics while also attempting to isolate some new ones

The foundations of complexity theory, and its potential significance on philosophy of computer science, philosophy of mathematics and epistemology

Philosophical implication of mathematization and computerization of the world

A collection of historical, technical and philosophical papers

Classic papers by thinkers ranging from Aristotle and Leibniz to Norbert Wiener and Gordon Moore that chart the evolution of computer science

, , - Collected works in celebration of Laszlo Lovasz, Connecting discrete math with computer science

A historical overview of computational complexity

It explains the remarkable work of Shafi and Silvio and their works' implications on foundations of cryptography

TCS Conferences collected in one table

An aggregator for CS theory workshops and schools

DMANET spreads information on conferences, workshops, seminars etc. relating to discrete mathematics and algorithms

Selected Conferences

Programs, Events, and workshops, that aim toward maximizing impact and engagement across the theoretical computer science community

A series of online seminars in theoretical computer science. The goal is to make engaging talks accessible to the widest possible audience

Aims for a mathematical understanding of fundamental issues in Computer Science, and to use this understanding to produce better algorithms, protocols, and systems, as well as identify the inherent limitations of efficient computation

and - ACM Turing Award Laureates delivers a lecture before a forum of their choice on a subject of their choice

Collection of workshops

Surveys, tutorials, conferences reports, events, open problems and solutions, PhD Theses, and entertaining contributions

ACM's official theoretical computer science news feed

It provides monographs written by leaders that give tutorial coverage of subjects, research retrospectives as well as survey papers that offer state-of-the-art reviews fall within the scope of the journal

Features breakthroughs in the field, written in an accessible style for non-experts

A blog Aggregator for all blogs related to TCS

A research methods course, concentrating on the how rather than the what. It focuses on research practices common for computer science theory research

In celebration of 25 years for “TOC: a Scientific Perspective (1996),” by Oded Goldreich and Avi Wigderson. It spots the light on a criticism directed to TCS, that it is not as deep as Math and not as useful as CS

Manuel Blum, A very popular figure in TCS, gives research advices for juniors

A note devoted to three rules that must be followed if you want to be successful in scientific research

Personal Essays by Oded Goldreich. They are very unique in their conceptual message of TCS and its community

Tips for anyone interested in theoretical computer science

Surveys for high-school, undergraduate, and even researchers

Posts oriented more for a less-technically matured audience

A list of theory blogs for computer science

Karp addresses: In 1968 computer science at Berkeley was problematic, with two departments working independently to develop programs, and his personal reflections

Why do so few scientists make significant contributions and so many are forgotten in the long run? The talk is about what Hamming has learned

Lessons for students and researchers given by Steven Weinberg

Five contributors draw on their experiences of mathematical life and research, and to offer advice that they might have liked to receive when they were just setting-out on their careers

A collection of various pieces of advice on academic career issues in mathematics, roughly arranged by the stage of career at which the advice is most pertinent

Why should you introduce a conceptual preliminary motivating the story of your paper

A list of master programs in TCS

TCS Jobs announcements

A crowdsourced spreadsheet created to collect information about theory hires in year 2022

Research-oriented Q&A of theoretical computer science

Theoretical computer science's subreddit

Lex Fridman - | | | | |

Interviews with eminent figures in Berkeley

Short accessible videos which populate theory of computation

Researchers, practitioners and innovators who are at the intersection of research and practice, sharing their experiences, lessons, visions for the future

ACM's students magazine special issue for theory of computation

A nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond

A story about people, pioneers with diverse backgrounds and characters who established a new field

It covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory,computability and complexity theory, quantum computing, cryptography, the information content of quantum states, and the interpretation of quantum mechanics

The Fabric of Reality presents a startlingly integrated, rational and optimistic world view – the result of taking seriously the deepest ideas of modern science and the philosophy of science

The world of computation according to Turing, an interactive tutoring program, as told to star-crossed lovers: a novel

Essays which spans the entire rich spectrum of Turing's life, research work and legacy

A Guided Tour through Alan Turing's Historic Paper on Computability and the Turing Machine

Interviews with era's greatest scientists about their inspirations, discoveries, and personal interests

A sheet of notes containing essential toolboxes needed by any theoretical computer scientist

Mathematics

Freely available lecture notes on mathematics

& - Logic, Math, Proof Assistants, and Type Theory

Math

and curricula by