A self-referential quiz is a logic game where the rules keep pointing back at themselves. Instead of asking you about history, science, or math, the game asks questions about… the game. One question might ask how many questions have the answer “A”, while another may say “the next 3 questions are all the same letter”. Every answer changes the rest, so it’s like trying to solve a puzzle that’s constantly staring back at itself.

• Some questions are designed to provide hints for other questions and may not be immediately helpful on their own.
• If a statement is not phrased as a True/False question, you may assume it is always true.
• There is exactly one solution to this puzzle. Every statement can be satisfied simultaneously in one and only one way.
• Most importantly, have fun!

If you enjoy this puzzle, I recommend checking out Brainzilla’s collection of self-referential quizzes for even more mind-bending challenges.

Note: If you know of a resource or learning tool that you feel was really helpful, please send me an email!

Finally, I’d like to thank Lasse Peters for inspiring this idea. If you’re interested in game-theoretic control and learning, I highly recommend checking out his collection of resources.

We model the world as it is and simulate the world as it could be.

What is Computational Engineering? Throughout my time in the department, I’ve noticed that several students who enter the major don’t fully realize what they are signing up for or just how significant the field has become. As a recent graduate of the department, I feel well positioned to share what Computational Engineering actually is. My goal in this post is to give incoming students (hopefully you) a clearer sense of the field and what makes it such a unique and exciting area to explore.

One of the challenges in explaining Computational Engineering is that it doesn’t sit neatly within a single well-defined category. Instead, it sits at the intersection of several established fields. It relies on mathematics like an applied mathematician, programming like a computer scientist, modeling like an engineer, and data analysis like a data scientist. This ambiguity is the main reason why I’ve seen recruiters, professors, and even current students struggle to understand exactly where Computational Engineering fits.

At its core, Computational Engineering is about building mathematical models of real-world systems and using computation to simulate how those systems behave. It is a way of turning physical intuition into something that can be tested, explored, and predicted on a computer before it is ever observed in reality.

While this definition does capture the core idea of the field, it can definitely feel like it leaves a lot of open questions about what Computational Engineering actually is and what it looks like in practice. By now you most likely have some questions floating in your mind (which I hopefully will be able to address):

• What really is Computational Engineering?
• What kinds of problems does Computational Engineering prepare you to solve, and what tools will you develop?
• How does Computational Engineering differ from Computer Science, Statistics and Data Science, Computer Engineering, and Software Engineering?
• What should you know before starting a degree in Computational Engineering?

These are all questions I either had myself or have heard repeatedly from prospective and incoming students. They are important questions. Choosing a major is ultimately about deciding what kinds of problems you want to answer and what tools you’ll have at your disposal to solve them. In my (definitely unbiased) opinion, Computational Engineering gives you a unique set of tools that allow you to ask and answer questions that would otherwise be difficult or sometimes impossible to explore.

What really is Computational Engineering?

To answer this properly, it helps to step back from the name itself and ask what computational engineers actually do.

Computational Engineers translate the laws of physics into mathematics and mathematics into simulations.

That quote has become my go-to description of Computational Engineering. At its core, it is about taking something from the real world (fluids moving past an airfoil, forces acting on a bridge, gases diffusing through pipes) and representing it in a form that can be analyzed mathematically and simulated on a computer.

In practice, this means starting from the physics that describes how a system evolves, translating that physics into a mathematical formulation, and then developing computational methods that allow a computer to approximate and solve the resulting model.

For example, consider airflow over an aircraft wing:

Physics Mathematics Computation

Airflow over a wing is a classic Computational Engineering problem: one physical system understood through physics, mathematics, and computation working together. Press Physics, Mathematics, or Computation above to see how each layer changes the picture.

This is one example of what Computational Engineering really is: turning real-world problems into mathematical models and using computation to study how those models behave. Everything in the field ultimately traces back to that same process of modeling reality and turning it into computable predictions.

Computational Engineering in the Real World

To me, the best way to understand Computational Engineering is through the problems it tackles. Below I’ve gathered a few examples of the questions Computational Engineering students at UT Austin have worked towards solving:

Q1. How can engineers test an aircraft before it is ever built? +

Q2. How can we predict the weather before it happens? +

Q3. How can we design a drug before it's ever tested on a patient? +

Q4. How can we land a spacecraft on another planet millions of miles away? +

Q5. How can a self-driving car make decisions in a fraction of a second? +

Q6. How can engineers determine whether a bridge will remain safe under years of traffic, wind, and weather? +

The Toolbox of a Computational Engineer

Just as someone might reach for a hammer, screwdriver, or measuring tape to construct a structure, Computational Engineers have their own toolbox filled with the skills they use to build models, run simulations, and analyze complex systems that would otherwise be difficult to study directly.

Throughout the degree, you’ll spend your time learning how to:

Throughout the degree, you’ll develop a collection of mathematical and computational techniques to help tackle a wide range of challenges. Below are some key terms that encapsulate the tools a Computational Engineer can call upon in order to solve a problem.

Click a book on the shelf to learn more about it

Select a book

Each volume covers a core concept in the Computational Engineering toolbelt.

As you move through the Computational Engineering curriculum, you’ll encounter courses that build different parts of this toolbox. While each class has its own focus, most of them contribute to one of three complementary foundations that together define the degree:

These are the tools that Computational Engineers use to tackle complex problems. While the specific application that you pursue may differ, these ideas appear again and again across the models, simulations, and analyses that define the field.

The Fields of a Computational Engineer

Because the need to model, simulate, and predict appears across so many industries, the skills developed in Computational Engineering are valuable in a remarkably wide range of fields. Below are some of the areas where Computational Engineers commonly apply their knowledge.

While each discipline has its own theories and specialized knowledge, many of them increasingly rely on the same computational approach: build a model, simulate its behavior, and use the results to better understand the problem at hand. Hence, even though the details of the problem may change across disiplines, the need to build models and utilize simulations to gain insight stays consistent.

What is the Difference between Computational Engineering and Other Fields?

Unfortunately, because of how unique the field is, I’ve noticed that several groups, especially recruiters, aren’t quite sure what we do and tend to place us into one of three categories: Computer Science, Statistics and Data Science, or Computer Engineering. Hopefully, this section serves as a useful reference when answering the question: “So how are you different from [insert field here]?”

At its core, Computational Engineering is about taking real physical systems, building mathematical models of them, and using computation to simulate how they behave. We spend just as much time learning how to construct those models as we do learning how to actually simulate them on a computer.

What should you know before starting a degree in Computational Engineering?

If you’re someone who enjoys mathematics, physics, engineering, programming, or simply wants to understand how those subjects are used to solve real-world problems, then Computational Engineering is absolutely the field for you. One of the big reasons I was originally drawn to the field was that it allowed me to combine each discipline and learn the skills to apply them to problems that I found interesting.

Looking back, one of the biggest takeaways for me was realizing that the degree is much less about learning individual topics in isolation and much more about understanding how those topics work together in the world of simulations. As a freshman, it can sometimes feel like you’re collecting a random assortment of puzzle pieces: calculus, differential equations, programming, physics, linear algebra, and more. It is not always obvious how those pieces connect.

Over the multitude of courses, however, that picture becomes much clearer. Mathematics gives you a language for describing a problem. Physics and engineering provide the principles that govern how a system behaves. Computation allows you to study models that would otherwise be impossible to solve by hand. Eventually, those seemingly separate courses stop feeling like separate subjects and start feeling like different parts of the same puzzle.

That, more than anything else, is how I see Computational Engineering today. It is a field centered around modeling and simulation, built on the idea that mathematics, physics, and computation are the most powerful when used together. More personally, Computational Engineering ended up being one of the most rewarding decisions I made during college. It introduced me to incredible friends, fascinating problems, and a set of tools that changed the way I think about the world.

Contact and Connect

If you have any questions about Computational Engineering, UT Austin, research opportunities, coursework, or anything else related to the program, feel free to reach out at yjtexas2005@gmail.com. Also if you notice any typos or have any suggestions for this blog, please reach out.  

Finally, don’t be afraid to talk to current students. One of the best ways to learn about Computational Engineering is by hearing from people who are in the program. Every student has a slightly different perspective, and those conversations can often provide insights that you won’t find on a degree plan or university website.

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