If you are interested in taking Math 232, you should send me an email. You are welcome to attend lectures as a guest before the add/drop deadline, and you should also talk to me before/after class to be added to the course Canvas page.
You can find the course syllabus here.
What tools do we have to calculate an integral like $\int_0^1 xe^{-x^2} \ dx$ or $\int_0^1 e^{-x^2} \ dx$?
When your calculator tells you that the value of $\int_0^1 e^{-x^2} \ dx \approx 0.746824$, how do you know it’s correct? How accurate is your calculator? Is it possible for an infinite region to have finite area? Can we calculate the area of a fractal?
You’ve previously seen in Math 101 that calculus is an important and powerful tool that allows us to describe the physical world around us. In Math 102, we will push the notion of integration to its utmost limits. In this class, we will build our toolbox for integration; we will study the behavior of the infinite, and we will learn how to quantify how accurate our approximations are.
In this course, you will develop the critical thinking and questioning skills needed to answer these complex questions. Moreover, you will become fluent in precisely communicating your ideas through the mathematical language of calculus.
]]>This post is a guide to the packages, commands, and other tweaks that I have compiled from across various sources to make my existing TeX files compile correctly as tagged pdfs. This post should be thought of as a supplement to the Tagging Project’s Guidelines for using LaTeX to generate accessible PDF.
Sample tex files and materials are included below, and I have checked that they are parsed correctly by VoiceOver (Apple’s built-in screen reader), and also pass the tests on my LMS (Canvas, Ally Course Accessibility Report).
DISCLAIMER: I am not an expert on accessibility nor an expert in the inner workings of TeX, and this post is not legal advice, nor it is a guarantee that your documents will automatically satisfy any or all accessibility standards or legal regulations.
If you are interested in learning more about digital accessibility in regards to mathematics, a good reference to get acquainted is Accessibility for the Working Mathematician by Julius Ross.
The tl;dr is that making documents accessible takes work, beyond the challenge of writing appropriate alt text (see sections 3.2-3.4). It may also require philosophical changes in how you structure your documents (see section 3.5). You may also need to remove or replace certain classes or packages (for example, beamer cannot create tagged pdfs, and will need to be replaced by ltx-talk).
My understanding is that if you were to start from scratch, many experts are recommending how to compose documents using a system that can create both HTML and pdf (and other) outputs such as Ximera or PreTeXt.
I will probably learn PreTeXt over the summer, and I definitely see the value in writing HTML output. However, I think there is value in having accessible pdfs because they are documents that can be downloaded and used by people without a stable or reliable internet connection (or when Canvas goes down).
Below are the modifications you will need to create digitally accessible pdfs from your TeX files. You can see sample TeX files below.
LuaLaTeX is recommended by the tagging project; but the packages and commands detailed below should work with pdfLaTeX. After switching to using LuaLaTeX, I saw no difference in compile times for the documents I am working on.
You should also make sure that you have the latest version of TeX installed (currently LaTeX 2025-11-01 as of this post). This is important for new classes and packages being developed, such as ltx-talk.
If you use Overleaf, here are instructions on how to change compiler and TeX version.
Note: the distribution of TeX used by overleaf (TexLive 2025) is not as up to date as the latest distribution of TeX (e.g. it does not yet have support for ltx-talk, but you can opt into the Overleaf Labs program for access to newer versions of TeX).
To create tagged pdfs from your TeX files, you should include this code in the preamble (e.g. before \begin{document}):
\DocumentMetadata{
tagging=on,
tagging-setup={math/setup=mathml-SE,math/alt/use}
}
The tagging-setup={math/setup=mathml-SE,math/alt/use} option turns on the necessary code for screenreaders to read mathematics (see below).
This command has other options - you can set the language (which is US English by default), the PDF standard, etc.
See the documentation for \DocumentMetadata here.
To set the title and author of the PDF, you should include this code in the preamble:
\usepackage{hyperref}
and you should include this code in the body of the document (e.g. immediately after \begin{document})
\hypersetup{
pdftitle={Spring 2026 Math 102 Syllabus},
pdfauthor={Richard Wong},
pdfdisplaydoctitle%
}
The tagging project renders math formulas and equations using MathML, but some screenreaders (e.g. VoiceOver, Ally) treats them like images which require alt text.
The option tagging-setup={math/setup=mathml-SE,math/alt/use} in the \DocumentMetaData command described above will automatically generate the alt text via the latex commands used. For example, the formula $\displaystyle \int_0^1 xe^{-x^2} \ dx$ has alt text
Latex formula starts
\begin{math} \int_0^1 xe^{-x^2} \ dx \end{math}Latex formula ends
This setup also allows screen readers to “dig in” and navigate these formulas (e.g. one can move back and forth between the bounds of integration, or different parts of the integrand).
Note: Because the alt text currently repeats verbatim the latex commands used, you should be careful about the macros that you use.
See the documentation for math content here.
Adding alt text to images is easy - simply use the alt-text options in \includegraphics:
\includegraphics[alt={A picture of me and Ernie}]{ernie_mueller2020.jpg}
However, in my opinion, writing appropriate alt text is the most difficult part of making your documents accessible.
Especially in the context of teaching, writing alt text requires you to think carefully about the pedagogical intent of the image. (see Ross 3.2-3.4)
THe AMS, EMS, LMS, and SIAM also recently published Author Guidelines for Preparing Accessible Mathematics Content, which set standards for labeling complex math diagrams (with examples).
To indicate the headers of the table, you can include this code immediately before the relevant table:
\tagpdfsetup{table/header-rows={1}}
See the documentation for tables here.
This is another challenge of making accessible documents - you should make sure that your existing documents use headings (e.g. \section or \subsection, etc.) appropriately.
That is, you should make sure your document does not use purely visual commands (e.g. \textbf, \Large, etc.) to indicate headings or sections.
Otherwise, the command \DocumentMetadata described above will take care of the tagging.
If you are still encountering errors (which is likely), you should check package compatibility with the Tagging Project’s compatibility tracker.
A lot of packages are currently supported, but some packages are not supported yet (for example, packages like titlesec).
Other packages will never be supported due to the way the package works (e.g. beamer). In that case, you should look to alternatives (e.g. ltx-talk).
A worksheet for the second day of Calc II:
A syllabus for Calc II:
]]>This semester, I will be having weekly lunches at West Servery on Thursdays from 12-1pm. If you see me there, feel free to sit down and chat!
]]>I will also be coordinating Math 102; and I am helping organize the undergraduate math colloquium at Rice.
You can find the course syllabus here.
How can we describe the physical world mathematically? How can we use mathematics to describe phenomena in physics, biology, chemistry, or other STEM fields?
Calculus is the mathematical language that allows us to describe and model the behavior of the physical world around us, such as the speed and acceleration at which we travel, as well as our distance and displacement; or how a population grows and changes over time; or the rate at which chemicals react or move towards equilibrium.
In this course, you will develop the reasoning and questioning skills needed to explore these concepts mathematically. Moreover, you will become fluent in communicating your ideas through the mathematical language of calculus.
You can find the course syllabus here.
What tools do we have to calculate an integral like $\int_0^1 xe^{-x^2} \ dx$ or $\int_0^1 e^{-x^2} \ dx$?
When your calculator tells you that the value of $\int_0^1 e^{-x^2} \ dx \approx 0.746824$, how do you know it’s correct? How accurate is your calculator? Is it possible for an infinite region to have finite area? Can we calculate the area of a fractal?
You’ve previously seen in Math 101 that calculus is an important and powerful tool that allows us to describe the physical world around us. In Math 102, we will push the notion of integration to its utmost limits. In this class, we will build our toolbox for integration; we will study the behavior of the infinite, and we will learn how to quantify how accurate our approximations are.
In this course, you will develop the critical thinking and questioning skills needed to answer these complex questions. Moreover, you will become fluent in precisely communicating your ideas through the mathematical language of calculus.
]]>I will be giving a presentation on Midweek Math Training at Rice.
I (along with José Pastrana) will also be presenting a poster on Year 1 of the HHMI Driving Change efforts in redesigning Calc I and II.
]]>I will also be coordinating Math 102; and I am helping organize the undergraduate math colloquium at Rice.
You can find the course syllabus here.
What tools do we have to calculate an integral like $\int_0^1 xe^{-x^2} \ dx$ or $\int_0^1 e^{-x^2} \ dx$?
When your calculator tells you that the value of $\int_0^1 e^{-x^2} \ dx \approx 0.746824$, how do you know it’s correct? How accurate is your calculator? Is it possible for an infinite region to have finite area? Can we calculate the area of a fractal?
You’ve previously seen in Math 101 that calculus is an important and powerful tool that allows us to describe the physical world around us. In Math 102, we will push the notion of integration to its utmost limits. In this class, we will build our toolbox for integration; we will study the behavior of the infinite, and we will learn how to quantify how accurate our approximations are.
In this course, you will develop the critical thinking and questioning skills needed to answer these complex questions. Moreover, you will become fluent in precisely communicating your ideas through the mathematical language of calculus.
]]>I will also be coordinating Math 102; and I am helping organize the undergraduate math colloquium at Rice.
You can find the course syllabus here.
How can we describe the physical world mathematically? How can we use mathematics to describe phenomena in physics, biology, chemistry, or other STEM fields?
Calculus is the mathematical language that allows us to describe and model the behavior of the physical world around us, such as the speed and acceleration at which we travel, as well as our distance and displacement; or how a population grows and changes over time; or the rate at which chemicals react or move towards equilibrium.
In this course, you will develop the reasoning and questioning skills needed to explore these concepts mathematically. Moreover, you will become fluent in communicating your ideas through the mathematical language of calculus.
You can find the course syllabus here.
What tools do we have to calculate an integral like $\int_0^1 xe^{-x^2} \ dx$ or $\int_0^1 e^{-x^2} \ dx$?
When your calculator tells you that the value of $\int_0^1 e^{-x^2} \ dx \approx 0.746824$, how do you know it’s correct? How accurate is your calculator? Is it possible for an infinite region to have finite area? Can we calculate the area of a fractal?
You’ve previously seen in Math 101 that calculus is an important and powerful tool that allows us to describe the physical world around us. In Math 102, we will push the notion of integration to its utmost limits. In this class, we will build our toolbox for integration; we will study the behavior of the infinite, and we will learn how to quantify how accurate our approximations are.
In this course, you will develop the critical thinking and questioning skills needed to answer these complex questions. Moreover, you will become fluent in precisely communicating your ideas through the mathematical language of calculus.
]]>I am part of a cluster hire in the HHMI Driving Change initiative. In particular, we are currently focusing on how calculus is taught at Rice.
]]>You can find the course syllabus here.
What does it mean to prove a theorem? Why are the theorems you saw in Math 33A true? How do we generalize the properties of $\mathbb{R}^n$ as a vector space over $\mathbb{R}$?
115A is the second course in linear algebra. In math 33A, you learned the computational tools of linear algebra in $\mathbb{R}^n$. In math 115A, you will learn how to prove the theorems and tools you saw in 33A. Moreover, you will generalize these theorems to the setting of abstract vector spaces.
115A may also be your first exposure to mathematical proofs. In other words, this course will help you develop the mathematical reasoning and questioning skills needed to explore abstract mathematical concepts. Moreover, you will become fluent in communicating your mathematical ideas, and you will develop the ability to prove (or find counterexamples) to mathematical statements.
This course provides the foundation for exploring other topics in advanced mathematics.
]]>