CAPP 30271: Mathematics for Computer Science and Data Analysis (Winter 2024)
General information
- Instructor
- Timothy Ng (timng@uchicago.edu)
- Lecture meetings
- MWF 9:20–10:10, Ryerson 177
- MWF 10:30–11:20, Ryerson 177
- Tutorials
- Fridays 1:30–2:50 pm, CSIL 2, 3, 4
- Fridays 3:00–4:20 pm, CSIL 3
- Links
-
Overview
This course is an introduction to linear algebra with a slight emphasis on applications to data science. Traditionally, linear algebra is the study of linear systems. Such systems are described only by using scaling and addition. A key observation is that a table of data can also be represented as a linear system. One can then exploit the structural properties of linear systems to answer questions about data, such as classification and regression, by using linear algebra.
Topics
- Introduction to linear algebra
- Vectors, matrices, linear combination
- Matrices as linear systems
- Elimination, permutation, LU factorization
- Vector spaces
- Fundamental subspaces, linear independence, basis, dimensionality
- Orthogonality
- Orthogonality, projections, Gram-Schmidt, least squares
- Eigenvectors
- Determinants, eigenvalues, diagonalization
- The singular value decomposition
- Singular values, principal component analysis
Text and resources
The primary textbook for this course is Gilbert Strang. Linear Algebra for Everyone (2020). Lecture notes for each class will also be made available following each class.
A useful secondary textbook is Marc Peter Deisenroth, A. Aldo Faisla, and Cheng Soon Ong. Mathematics for Machine Learning. This book is a nice bridge between the mathematics that we'll be learning and the data analysis applications that it's used for.
Because of the connections to data analysis, linear algebra is a very popular subject nowadays and there are a wealth of resources available. Here are a few suggestions if you are seeking additional resources.
- The following are video resources:
- Other textbooks include:
Communication
There are a number of different tools we’ll be using to communicate about the class.
- Course materials
- Lecture notes will be made available via this course website. The course webpage will also contain course information and can be treated as the syllabus.
- Discussion and announcements
- We will use Ed Discussion, an online discussion forum, for course discussion and announcements. Restricted course materials will also be posted here. You should make it a habit to check Ed for updates and announcements regularly.
- Coursework
- All coursework, including homework and tests, will be distributed and submitted via PrairieLearn. It is important that you have access to a device with an internet connection and a web browser during tests in class. Instructions for accessing the PrairieLearn course will be given in class.
- Office hours
- Office hours are times when the course staff are available for you. The instructor and teaching assistants will have scheduled office hours in-person and/or online. While most students typically use this as an opportunity to ask about coursework, you're welcome to ask about or discuss things that are related directly or indirectly with the course.
Class meetings
- Lectures
- Lectures are often the first point at which students will be exposed to new ideas and material. They will cover material that is necessary for success in the course. However, lectures alone may not be sufficient for all students. It is not expected that students will master the material learned in lecture without significant review, inquiry, and practice outside of lecture.
- Tutorials
- Tutorial sessions are led by teaching assistants and are intended to give students an opportunity to practice and get feedback in a more active in-person setting than lecture. Quizzes are also administered during tutorial sessions.
Evaluation
Your computed grade in this course will be determined by the following coursework components.
- Weekly (8) homework, each worth $\frac 1 8$ of 25%.
- Tests worth 75% in total.
- Weekly (8) quiz, each worth at most $\frac 1 8$ of 50%.
- One (1) final examination, worth the remainder of the 75% allocated to tests. That is, the final examination will be worth at least 25%.
Homework
Homework is available and to be completed online on PrairieLearn. Homework is intended to give you practice for the tests. You should attempt to complete it on your own as much as possible.
Many homework exercises are required to be done multiple times in order to get full credit. Such questions have a value, a point total, and a point maximum.
- If you answer a question correctly, two things happen:
- The point total increases by the value, until you reach the point maximum.
- The value increases (2x, 3x, and so on).
- If you answer a question incorrectly, one thing happens:
- The value goes back to what it was originally (1x).
What does this mean? If you can answer a question correctly multiple times in a row, it shows that you've likely learned the underlying idea. If you answer a question incorrectly, there is no penalty, but you will need to answer the question correctly more times (i.e. practice). Note that your score will never decrease.
If you have already reached the maximum number of points, you can continue to answer questions to get more practice—very useful, since you can always generate new questions and have them graded immediately.
Tests
Tests are taken in-person, on PrairieLearn. You will require access to a device with an internet connection and a web browser during test sessions.
- Quizzes will be taken during tutorials on Fridays each week. Quizzes will be 30 minutes.
- The final examination will be scheduled during the week of March 4–8. The final examination will be 120 minutes (two hours). The time and location will be announced later.
Lectures
- January 3
- Introduction, vectors (1.1)
- January 5
- Linear combinations, geometry (1.2–1.3)
- January 8
- Matrices, linear independence (1.3–1.4)
- January 10
- Matrices as functions, linear equations (1.4–2.1)
- January 12
- Elimination (2.1–2.2)
- January 17
- Inverses, LU factorization (2.2–2.3)
- January 19
- LU factorization, vector spaces (2.3, 3.1)
- January 22
- Vector spaces and subspaces (3.1-3.2)
- January 24
- The null space, row-reduced echelon form (3.2-3.3)
- January 26
- The complete solution to $A \mathbf x = \mathbf b$ (3.3)
- January 29
- Basis and dimension (3.4)
- January 31
- Fundamental subspaces of a matrix (3.5)
- February 2
- Orthogonality of spaces (4.1)
- February 5
- Projection (4.2)
- February 7
- Projection, continued (4.2)
- February 9
- Least squares (4.3)
- February 12
- Orthonormal bases (4.4)
- February 14
- QR factorization, linear transformations (4.4, 5.3)
- February 16
- Eigenvectors (6.1, 5.1-5.2)
- February 19
- Diagonalization (6.2)
- February 21
- PageRank (The $25,000,000,000 Eigenvector)
- February 23
- Singular value decomposition, symmetric matrices (7.1, 6.3)
- February 26
- Class cancelled due to instructor illness
- February 28
- Singular value decomposition (7.1)
- Low rank approximation and PCA (7.3)
- March 1
- Wrapup/Q&A
Academic integrity
It is your responsibility to be familiar with the University’s policy on academic honesty. Instances of academic dishonesty will be referred to the Office of the Provost for adjudication. Following the guidelines above on collaboration and citation should be sufficient, but if you have any questions, please ask me (the instructor).
Accessibility
Students with disabilities who have been approved for the use of academic accommodations by Student Disability Services (SDS) and need reasonable accommodation to participate fully in this course should follow the procedures established by SDS for using accommodations. Timely notifications are required in order to ensure that your accommodations can be implemented. Please meet with me (the instructor) to discuss your access needs in this class after you have completed the SDS procedures for requesting accommodations.