MATH 7113: Commutative Algebra

Zoom: https://westernuniversity.zoom.us/j/98894502867 passcode: commalg

Lectures:

(incomplete) lecturenotes : Proof-read and send in typos.

Lecture 01: introduction

Lecture 02: ideals

Lecture 03: decomposition

Lecture 04: existence

Lecture 05: radical

Lecture 06: associated primes (vid)

Lecture 07: Zariski topology (vid)

Lecture 08: Hilbert nullstellensatz (vid)

Lecture 09: graded rings (vid)

Lecture 10: review (vid)

Lecture 11: well-quasi-order (vid)

Lecture 12: Gröbner bases I (vid)

Lecture 13: Gröbner bases II (vid)

Lecture 14: Gröbner bases III (vid)

Lecture 15: Hilbert polynomial (vid)

Lecture 16: Simplicial Complex (vid)

Lecture 17: Homology (vid)

Lecture 18: Stanley-Reisner ring (vid)

Lecture 19: Free resolution (vid)

Lecture 20: Hilbert Syzygy Theorem (vid)

Lecture 21: Free Modules (intro to categorical language)

Lecture 22: Tensor Product

Lecture 23: Krull dimension

Projects:

Project list

Project Reports (with pictures of the speaker's during talk; audience is here: 1 2 3 4 , group photo: 1, 2, 3, 4)

Abel's theorem by Muhammad Haris 1 2 3

Application of HNF and SNF by Nasreen Irshad 1 2

Bezout theorem by Ijaz Jamil 1 2

Category of R-modules by Raheel Ahmad 1 2 3

Chip firing by Muhammad Ajmal 1

Ehrhart theory polynomial by Muhammad Usman 1 2

Elliptic curves by Ahsan Khan 1 2

Error corrections and coding theory by Muhammad Din 1

Galois theory by Tabina Azhar 1 2 3

Grobner fan by Atiqa Safdar 1 2

Local cohomology by Musab Umair 1

Macaulay's theorem by Warisha Ahmad 1 2 3

Mathematical cryptography by Zille Huma 1 2 3

Newton polytopes by Shakeela Riasat 1 2 3

Sheaves and Schemes by Arslan Anwar

Straight edge and compass constructions by Rabia Anwar 1 2 3

Symmetric functions by Hira Nasir 1 2

Toric ideals by Nimra Ismail 1 2 3

Tropical algebra by Serosh Jamil 1

Mathematical Humor:

Mathematics is too serious and, therefore, no opportunity should be missed to make it amusing.

Blaise Pascal

xkcd, a collection, a sample,