CAPP 30271: Mathematics for Computer Science and Data Analysis (Winter 2026)

General information

Instructor

Timothy Ng (timng@uchicago.edu)

Lecture meetings

Section	Day	Time	Location
1	MWF	11:30–12:20	Ryerson 276
2	MWF	14:30–15:50	Ryerson 358

Lab meetings

Section	Day	Time	Location
1L01	Thurs	14:00–15:20	Ryerson 255
1L02	Thurs	15:30–16:50	Ryerson 255
2L01	Thurs	14:00–15:20	1155 140C
2L02	Thurs	15:30–16:50	Ryerson 277

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 the structure of linear systems. Such systems are described only by using scaling and addition. A key insight in data analysis is that tabular 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.

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, the Gram-Schmidt algorithm, least squares
Eigenvectors: Determinants, eigenvalues, diagonalization
Singular value decomposition: Singular values, principal component analysis

Text and resources

Lecture notes will be made available following each class.

Lecture notes were largely drawn from Linear Algebra for Everyone (2020) by Gilbert Strang. Section numbers listed with each lecture refer to this text.
Here are some useful alternative/secondary texts:
- Mathematics for Machine Learning by Marc Peter Deisenroth, A. Aldo Faisla, and Cheng Soon Ong. This freely available book is a nice bridge between the mathematics that we'll be learning and the data analysis applications that it's used for.
- Understanding Linear Algebra by David Austin. This is a freely available text that includes interactive exercises.
- Linear algebra for data science by Soran Mitran. This is a more compact freely available text that details the relationship between linear algebra and data science.
- Introduction to Linear Algebra, 5th ed. by Gilbert Strang. This is an older but slightly more comprehensive version of the newer Strang text.
The following are video resources:
- Gilbert Strang’s recorded lectures from MIT’s 18.06 on MIT OpenCourseWare.
- Grant Sanderson’s series on 3Blue1Brown.

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 lab sessions. 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. 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.
Lab: Lab 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 administered during lab sessions.

Evaluation

Your computed grade in this course will be determined by the following coursework components.

Homework, worth $\frac 1 4$ in total.
Tests, worth $\frac 3 4$ in total.
- Weekly (8) quiz, each worth at most $\frac 1 {16}$ for a total of up to $\frac 1 2$.
- One (1) final examination, worth the remainder of the $\frac 3 4$ allocated to tests. That is, the final examination will be worth at least $\frac 1 4$.

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 lab on Thursdays each week. Quizzes will be 20 minutes.
The final examination will be scheduled during the week of March 10–13. The final examination will be 120 minutes (two hours). The time and location will be announced later.

Lectures

January 5: Introduction, vectors (1.1)
January 7: NumPy, geometry (1.2)
January 9: Matrices, linear independence (1.3)
January 12: Matrix products, linear systems (1.4–2.1)
January 14: Gaussian elimination (2.1–2.2)
January 16: Permutation, inverses (2.2–2.3)
January 21: LU factorization, vector spaces (2.3, 3.1)
January 23: Vector spaces (3.1–3.2)
January 26: The null space (3.2–3.3)
January 28: The row-reduced echelon form (3.3)
January 30: The complete solution to $A \mathbf x = \mathbf b$ (3.3)
February 2: Basis and dimension (3.4–3.5)
February 4: Fundamental subspaces (3.5, 4.1)
February 6: Orthogonality (4.1)
February 9: Projection onto a line (4.2)
February 11: Projection onto a space (4.2)
February 13: Least squares approximation (4.3)
February 16: Orthogonal matrices (4.4)
February 18: QR factorization, linear transformations (4.4, 5.3)
February 20: Eigenvalues and eigenvectors (6.1, 5.2)
February 23: Diagonalization (6.2)
February 25: Symmetric matrices (6.3)
February 27: Singular value decomposition (7.1)
March 2: Low rank approximation (7.3)
March 4: Principal component analysis (7.2–7.3)
March 6: 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.