Multivariable Math for Machine Learning

Syllabus

Texts

This semester we will be using a linear algebra text for the majority of the semester but will supplement with material from other texts.

Calendar

There is a proposed calendar on the syllabus, but here I will record what we actually get through in each class.

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  • 10/21/2026: Two out of three of you have told me that you are ill and not coming to class, so we will be cancelling class tonight due to illness. Please bring in the exam corrections next week. Take care.
  • 10/14/2026: This week you will get your exams back. On your paper will be a list of problems you can redo in order to earn back upto 40% of your lost points. Also this week, we will start having weekly quizzes at the beginning of class to help you stay on top of the skills that we have been covering in class. The quiz on 10/14/2026 will cover dot products, projections, normalizing vectors, and solving homogeneous systems of equations. There will be 5 questions and you will have 15 minutes to complete it.
    Tonight we covered the first couple of sections of the next slide deck. For nexts weeks quiz be sure you are familiar with the Gram-Schmidt Process, Orthogonal Decomposition, and Basic Least Squares (fit a line to three points).
  • 10/7/2026: Exam 1 on Linear Algebra Basics
  • 9/30/2026: The exam is next week, we will start class answering questions, but we can’t spend too much time on it because you need time to complete the exam. Review the material from the four sets of review slides which review the basic prerequisite linear algebra from a first course in linear algebra. In particular review your notes and the review slides and come in ready to demonstrate knowledge of the following review topics (Chapters/Sections refer to the 5th Edition of Lay’s Linear Algebra text that, as I have previously pointed out, is on reserve in the library and can probably be found online as a pdf):
    • Basic matrix, vector, and scalar arithmetic (Section 2.1),
    • Finding solutions to systems of equations by row reducing augmented matrices (Section 1.1-1.5),
    • Calculating dot products and using them to find the norm of a vector or the projection of one vector onto another (Section 6.1 and 6.2),
    • Finding the determinant of a matrix and explaining the significance of that determinant (Chapter 3),
    • Identifying if a set of vectors are linearly independent (Section 1.7, 4.3),
    • Identifying the span of a set of vectors (Section 1.3),
    • Identifying if a set of vectors is a basis for \(\mathbb{R}^n\) for \(n=2,3\) (Section 4.3 and 4.4),
    • Finding the change of basis matrix between two bases (Section 4.7),
    • Finding the eigenvalues and eigenvectors of a \(2\times 2\) or \(3\times 3\) matrix (Sections 5.1 and 5.2),
    • Diagonalizing a \(2\times 2\) or \(3\times 3\) matrix (Section 5.3).
  • 9/23/2026: We reviewed previous topics and covered most of the key material from the fourth set of review slides. We will do some review next week and have the exam on the Review of Linear Algebra on October 7th. Please carefully review the material from the four sets of review slides which review the basic prerequisite linear algebra from a first course in linear algebra. In particular review your notes and the review slides and come in ready to demonstrate knowledge of the following review topics:
    • Basic matrix, vector, and scalar arithmetic,
    • Finding solutions to systems of equations by row reducing augmented matrices,
    • Calculating dot products and using them to find the norm of a vector or the projection of one vector onto another,
    • Finding the determinant of a matrix and explaining the significance of that determinant,
    • Identifying if a set of vectors are linearly independent,
    • Identifying the span of a set of vectors,
    • Identifying if a set of vectors is a basis for \(\mathbb{R}^n\) for \(n=2,3\),
    • Finding the change of basis matrix between two bases,
    • Finding the eigenvalues and eigenvectors of a \(2\times 2\) or \(3\times 3\) matrix,
    • Diagonalizing a \(2\times 2\) or \(3\times 3\) matrix.
  • 9/16/2026: We went over the slides on GitHub and Code Spaces, looked through the Jupyter Notebook introduction linear algebra operations in Python, and then went through the third Review of Linear Algebra slide deck. We will finish the review next week and have the Unit 1 exam the week after. Please be sure to review the slide decks and your notes.
  • 9/9/2026: We started class by reviewing the material we covered the previous week. We will do the same thing next week, please review your notes so that it goes more smoothly. We thne worked through the second set of review slides. Next week, after review, we will look at how we will be using GitHub in this class, please create a personal fork of the repository for the class Link to Class Repository: https://github.com/cfroccajr/Mathematics-for-Machine-Learning.git. Here is a slide deck introducing some basics of what we will be looking at next week: GitHub and Code Spaces Slide Deck Link
  • 9/2/2026: We covered the syllabus and the material in the first set of slides. We will look at the second set of slides and Github/Jupyter notebooks next time.

Assignments:

Material for assignments will be pulled from the text books, from some projects that go along with Lay’s text (projects from Lay are at bit.ly/30IM8gT)

Miscellaneous:

  • Due 10/21/2026: Get setup on GitHub: Fork the class repository, Create a folder with your last name in the submissions folder, Create a Markdown readme file in the folder you just created (content isn’t important we’re just making sure you can complete the work), and create a pull request back to the original class repository as a way of submitting your work.

Projects:

Most of the the following projects are based on material in Lay’s Linear Algebra. As the semester progresses I will post Jupyter notebooks to GitHub to help get started on each project. Specifically they will give useful Python commands for carrying out the projects and some extensions of the projects.

  1. Due 11/4/2026: Complete the Fibonacci Jupyter Notebook on Github that is based on this project: Fibonacci Like Sequences.
  2. Dynamical Systems
  3. Power Method for Eigenvalues
  4. QR Method for Eigenvalues
  5. Integration by Parts
  6. Error Detecting and Correcting

Text Material

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Previous Semester Lecture Slides