Combinatorics

k-wise Independence

Error Correcting Codes

SL=L

Code concatenation

Expander Mixing Lemma

Existence of Seeded-Extractors

Next-Bit Unpredictability

Discrete Fourier Analysis

Cheeger's Inequality

Error reduction

Graph Theoretic View

Trevisan's Extractor

Pseudorandom generator (PRG)

Expander Graphs

Randomness Extractors

Small biased distributions

Random Walks on Expanders

Leftover Hash Lemma

Nisan-Wigderson Construction

Max-Cut

ε-Biased Distributions

Zig-Zag Product

Spectral Expansion

Samplers

Two-Source Extractor

CS 294-202 Pseudorandomness UC Berkeley Fall 2021 This course explores the role of randomness in computation and pseudorandomness, focusing on the applications in error-correcting codes, expander graphs, randomness extractors, and pseudo-random generators. The course will also address the question of derandomization of small-space computation. Prerequisites are unspecified, but the course content suggests a high level of expertise. Randomized algorithms give a broad and rich algorithmic toolkit (e.g., sampling, Monte Carlo methods). Randomness is an essential resource in distributed computing, cryptography, and interactive proofs. In this course, we would explore the role of randomness in computation: Can we derandomize algorithms without changing their time or space complexity? Can we "purify" randomness from a weak source of randomness? 

Pseudo-randomness is the property of "appearing random" while having little or no randomness. Pseudo-randomness plays a significant role in error-correcting codes, expander graphs, randomness extractors, and pseudo-random generators. In this course, we will see all these beautiful applications. In the second part of the course, we would focus on the question of derandomization of small-space computation, also known as the "**RL** versus **L**" question. It asks whether all problems that can be decided in randomized logarithmic space (RL) can also be decided in deterministic logarithmic space (L). We would cover recent approaches towards showing that RL = L.    Salil Vadhan -  [Pseudorandomness](https://www.google.com/url?q=https%3A%2F%2Fpeople.seas.harvard.edu%2F~salil%2Fpseudorandomness%2F&sa=D&sntz=1&usg=AOvVaw2jc9ipUift6CNRnbiOuSkb)

CS 294-202 Pseudorandomness

Theoretical Computer Science

Counting

Conditional probability

Bayes' theorem

Independence (probability theory)

Random variable

Expectation

Variance

Bernoulli distribution

Binomial distribution

Poisson distribution

Continuous Random Variables

Normal distribution

Joint probability distribution

Statistical inference

Beta distribution

Central Limit Theorem

P-Value

Algorithmic Analysis

Maximum Likelihood Estimation (MLE)

Maximum A Posteriori (MAP)

Naive Bayes

Logistic Regression

Bootstrapping

CS 109 Probability for Computer Scientists Stanford University Spring 2023 This course offers a thorough understanding of probability theory and its applications in data analysis and machine learning. Prerequisites include CS103, CS106B, and Math 51 or equivalent courses. CS109: Probability for Computer Scientists starts by providing a fundamental grounding in combinatorics, and then quickly moves into the basics of probability theory. We will then cover many essential concepts in probability theory, including common probability distributions, properties of probabilities, and mathematical tools for analyzing probabilities. The last third of the class will focus on data analysis and machine learning as direct applications of probability we've learned in the weeks prior. Read more here to learn what CS109 is all about. This is going to be a great quarter and we are looking forward to the chance to teach you!! After you're finished with CS109, we hope you'll have achieved the following learning goals:

- Reason about situations using probabilities, expectation, and variance.
- Feel comfortable learning about new probability concepts beyond the scope of this class (e.g., through one's own research, studies, or interests).
- Write programs to simulate random experiments and to test experiment hypotheses.
- Understand and implement simple machine learning algorithms like Naive Bayes and Logistic Regression.

## Course Topics

Here are the broad strokes of the course (in approximate order). More information is available on our Schedule page. We cover a very broad set of topics so that you are equipped with the probability and statistics you will see in your future CS studies!

- Counting and probability fundamentals
- Single-dimensional random variables
- Probabilistic models
- Uncertainty theory
- Parameter estimation
- Introduction to machine learning The prerequisites for this course are CS103, CS106B, and Math 51 (or equivalent courses). Probability involves a fair bit of mathematics (set theory, calculus, and familiarity with linear algebra), and we'll be considering several applications of probability in CS that require familiarity with algorithms and data structures covered in CS106B. Here is a quick rundown of some of the mathematical tools from CS103 and Math 51 that we'll be using in this class: multivariate calculus (integration and differentiation), linear algebra (basic operations on vectors and matrices), an understanding of the basics of set theory (subsets, complements, unions, intersections, cardinality, etc.), and familiarity with basic proof techniques. We'll also do combinatorics in the class, but we'll be covering a fair bit of that material ourselves in the first week. Past students have managed to take CS106B concurrently with CS109 and have done just fine. CS103 is the pre-requisite that we rely on the least. See our FAQ for more information. ## Optional Textbook

Sheldon Ross, *A First Course in Probability* (10th Ed.), Pearson Prentice Hall, 2018.

This is an optional textbook, meaning that the text is not required material, but students may find Ross offers a different and useful perspective on the important concepts of the class. Suggested, optional reading assignments from the textbook (10th Ed.) are in the schedule on the course website. The 8th, 9th, and 10th editions of the textbook are all fine for this class.

*Borrowing the textbook online*: HathiTrust, a library archive of which Stanford is a member, has granted the university online access to the 8th edition (2010) for the duration of the Fall quarter. The "check out" system works similarly to print reserves: A user can check out the book an hour at a time as long as they are actively using it. Access guidelines are on the [HathiTrust How To Use It webpage](https://www.hathitrust.org/ETAS-How-To). Once you're logged in, the book is at [this link](https://catalog.hathitrust.org/Record/006904347).

All students should retain receipts for books and other course-related expenses, as these may be qualified educational expenses for tax purposes. If you are an undergraduate receiving financial aid, you may be eligible for additional financial aid for required books and course materials if these expenses exceed the aid amount in your award letter. For more information, review your award letter or visit the [Student Budget website](https://financialaid.stanford.edu/undergrad/budget/index.html).

CS 109 Probability for Computer Scientists

Mathematical Foundations

Combinatorics

2 courses cover this concept

CS 294-202 Pseudorandomness

CS 109 Probability for Computer Scientists