Amadou Bah

Everything linear algebra should cover from linear systems to determinants, to linear spaces, transformations, inner products, eigenvalues and eigenvectors, as well as proofs when it comes to showing just about all the ins and outs.

Rings, Fields, Polynomials, and some Galois Theory

We learned about continuity of functions, limits, derivatives, finding tangent lines, word problems, L'Hospital's rule, integrals, and more.

First part is more computational information and intro to matrices, second part is more theoretical and how bases are related to each other, third part is also more theoretical(ie more theorems).

I took this course together with topology, and I found a lot in common between these two courses, such as simple extension and one-point compactification, which seemed to have nothing to do with each other at first. What shocks me about this thing is that in my opinion, this is how to learn new things. You have to add points (root) one by one, and also add things related to the newly added points (topology or + - * /) , Only in this way can we continue to learn new knowledge, and the old knowledge is also a whole.

Everything mentioned on the standard linear algebra syllabus.

Galois theory and ring theory, polynomials. I also learned quite a few number-theoretic results.

limits, derivatives, integrals, a lil bit of trig

Learned much about the theoretical side of matrix algebra, as well as many ways to manipulate vectors in matrix form. A few geometric interpretations were provided, yet the course remained largely theoretical.

The class is required for the major, but I would recommend it regardless. Moreso than the Analysis seq., I really enjoyed the algebra seq. and think people considering a math major should definitely take them. Prof. Bah is a terrific instructor and I certainly recommend taking it with him if possible. 1 Columbia University: Arts & Sciences Fall 2023 Course: MATHGU4042_001_2023_3-INTROMODERNALGEBRAII : MATHGU4042_001_2023_3 - INTRO MODERN ALGEBRA II Instructor: Amadou Bah