Mathematics · Columbia University
Basics of calculus and how to apply them to real-life examples. Starting from basic review of trig and algebra. then moves into understanding and applying limits, and then finally to derivatives and integrals.
Course material is difficult, and measure-theoretic Probability Theory is required. 1 Columbia University: Arts & Sciences Spring 2025 Course: MATHGU4156_001_2025_1-ADVANCEDPROBABILITYTHEORY : MATHGU4156_001_2025_1 - ADVANCED PROBABILITY THEORY Instructor: Ioannis Karatzas
In this class, Analysis and Optimization, I revisited linear algebra and calculus while learning various optimization methods to find extrema in different scenarios.
Learned Derivatives, Integration of derivatives, integrals.
Prof Karatzas is a very good instructor and very very knowledgeable in this field. Definitely take this course if you get the chance, but be warned that it can be fairly theoretical. 1 Columbia University: Arts & Sciences Fall 2023 Course: MATHGU4156_001_2023_3-ADVANCEDPROBABILITYTHEORY : MATHGU4156_001_2023_3 - ADVANCED PROBABILITY THEORY Instructor: Ioannis Karatzas
I reviewed a lot of concepts from before - calculus and linear algebra. I also learned a lot about analysis and optimization methods.
I really did not learn alot This course was so confusing to me.
How to find the maxima and minima of diverse types of functions, and ways to analyze your result. (This section is very theoretical with a few applied concepts in economics and physics)
Understanding Limits, Differentiation, Derivatives, and Integrals
For the first time I understood Taylor series.