Code repository for MTH3199: Special Topics in Mathematics: Theory and Application of Algebraic Structures. This course is taught by Professor Sarah Spence Adams (Olin College of Engineering).
MTH3199 is a self-directed math course in which students choose topics in Linear and Abstract Algebra to explore further and build projects to demonstrate their understanding of technical material. Given my interest in data science and machine learning, I chose several "capstone"-like topics (Least Squares Approximation, Singular Value Decomposition, Matrix Calculus) from these fields and prepared technical presentations along with Jupyter Notebooks to share my understanding with the class and the public.
My first deliverable: Least Squares Approximation from Scratch
My second deliverable: Latent Semantic Analysis: Low Rank Approximation of the TF-IDF Matrix
My third deliverable: Introduction to Matrix Calculus
Note: If you are interested in my second deliverable please also visit calculate.ipynb for the most accurate explanation and code to build the TF-IDF matrix from scratch. Use this explanation to replace the TF-IDF section in the original notebook.
I used the following resources for my learning this semester:
- Gil Strang's Linear Algebra course (18.06 at MIT)
- Gil Strang's Introduction to Linear Algebra: 4th edition textbook
- Gil Strang's Matrix Methods (upper-level undergrad/graduate) course (18.065 at MIT)
- MIT's Matrix Calculus IAP Course
- Matrix Calculus Notes
- Mathematics for Machine Learning Textbook
- Databricks Academy -- LSA
- 3B1B Essence of Linear Algebra (Videos 3 and 4)
- 3B1B on Khan Academy - Jacobian Matrices and its Determinant
Lastly, I would like to thank Professor Sarah Spence Adams for her support throughout the semester and many helpful OH sessions!
Contact: zaynpatelwhs@gmail.com
Please reach out if you would like to learn more about what I learned this semester or have your own ideas for projects in the data science/machine learning field! I would love to help if I can.