Theoretical computer scientists make an extensive use of elements from abstract algebra. From the design and analysis of algorithms and cryptographic protocols to the construction of desired combinatorial objects, the use of algebraic structures has repeatedly provided powerful and elegant solutions. Mastering the required mathematical background, however, requires isolating relevant parts from several courses in Mathematics or, alternatively, is done ad hoc.

This course provides a thorough introduction to abstract algebra, focusing on the useful elements required for the aforementioned use within computer science. In the first half of the course, we will study basic, frequently used, notions such as groups, rings, and finite fields. In the second part, we will consider more advanced notions from Commutative Algebra and Galois Theory. The math will be developed alongside applications in Theoretical Computer Science, Coding Theory, and Cryptography. We will take a bird's-eye view, focusing on the key notions and ideas while omitting some of the proofs. Some of the applications that will be discussed are:

​- Randomness mergers and the Kakeya Set problem

- Private Information Retrieval schemes

- Parvaresh–Vardy codes and the Guruswami-Umans-Vadhan expander graph​

For more information, see the course webpage at https://www.gilcohen.org/abstract-algebra-for-tcs