Theory of Computation - Spring 2026 CSCI-UA 453

Announcements

/p>


Administrative Information

  • Time/Place: Mondays 12:30-3:00 PM in CIWW 317
  • Instructor: Marshall Ball, Office Hours: TBD

Course Description

In the late 1940s, Claude Shannon introduced a mathematical theory of information, quantifying information in terms of uncertainty. Since Shannon's pioneering work on the limits of data compression and reliable/secure communication, intuitions and techniques from information theory have impacted not just our modern communication infrastructure but also a diverse array of other scientific endeavors, including theoretical computer science. In this course, we will begin by covering the foundations of information theory (entropy, mutual information, KL-divergence, etc) before branching off to explore various applications, primarily in theoretical computer science. Potential application topics include: channel and source coding, error correcting codes, communication complexity, hardness amplification, data structures, Kolmogorov complexity, information-theoretic cryptography, pseudoentropy, the Lovasz Local Lemma, and applications in combinatorics. While there are no specific prerequisites, fluency in basic probability and mathematical maturity are required.

Topics will draw from the following:

  • Fundamentals: Entropy, Conditional Entropy, Mutual Information, KL Divergence, Source Coding, Channels
  • Elements of Coding Theory: Concatenated Codes, Polar Codes, Reed-Muller Codes
  • Communication Complexity: Lower bounds, Information Complexity, Compression
  • Application: Lower Bounds for Data Structures and Cryptography
  • Application: Hardness Amplification (Worst-case to average-case reductions, Parallel Repetition, Derandomization)
  • Algorithmic Information: Kolmogorov Complexity
  • Pseudorandomness and pseudoinformation variants: Cryptographic Applications
  • Randomness Extractors

Course Work

4 Problem Sets

Prerequisites

The primary prerequisite is mathematical maturity. You should be comfortable reading and writing proofs. Some familiarity with the basics of algorithms, the theory of computation, and probability is expected.

If you are unsure about whether this class is suitable for you, please contact the instructor via email.

Resources

While we will not be following a textbook, a number of excellent resouces are available.


Lectures

Class Date Topic Notes
1 Sep 14 Introduction: Entropy, Conditional Entropy, Mutual Information, KL Divergence
2 Sep 21
3 Sep 28
4 Oct 5
5 Oct 12
6 Oct 19
7 Oct 26
8 Nov 2
9 Nov 9
10 Nov 16
11 Nov 23
12 Nov 30
13 Dec 7
14 Dec 14

Course Policies

Homework

Homework should be submitted in PDF form in Gradescope. We prefer homework submissions typeset in LaTex. If you are not familiar with LaTex, it is a great skill to learn. Overleaf provides a simple web interface for writing and compiling LaTex (as well as extensive documentation). We will provide LaTex source for you to edit. You are encouraged to insert scanned figures or illustrations where appropriate. Scanned handwritten submissions will only be graded if perfectly legible. If you are unsure about your handwriting, I strongly suggest you type your solutions.

An important part of this class is about learning to communicate your mathematical ideas and proofs clearly and concisely. Accordingly, you will be graded not simply for correctness, but also clarity.

Collaboration

We strongly encourage you to discuss assignments with up to 3 peers, but you must (a) list the names of your discussion partners on your submission, and (b) you must write up your solution on your own. You may not look at the written solutions of any other student before submitting your own solution. If you do not not list the names of your collaborators, you will be penalized.

Late Policy

Late homework will not be accepted, but the lowest scored homework will be dropped.

External Resources

You must explicitly acknowledge any external resources consulted in your homework.

However, you are not allowed to consult any resource for the purpose of finding homework solutions. For example, you may not consult homework solutions for a previous version of this class or ask an LLMViolations to this policy is plagiarism and will not be tolerated.

Religious Observance

As a nonsectarian, inclusive institution, NYU policy permits members of any religious group to absent themselves from classes without penalty when required for compliance with their religious obligations. The policy and principles to be followed by students and faculty may be found in the University Calendar Policy on Religious Holidays.

Disability Disclosure

Academic accommodations are available to any student with a chronic, psychological, visual, mobility, learning disability, or who is deaf or hard of hearing. Students should please register with the Moses Center for Students with Disabilities.