We're going back to school from 20th January onwards. Many people are confused or overwhelmed, and many are quite fixed on what they want to take as electives.
Why do electives matter? They're the freedom to select courses beyond compulsory ones. This is the time when many people can take two or three electives, and some can take only one. I want to talk about how to make these electives helpful, whether it's one or three.
Build a Career Arc, Not Scattered Courses
I always say electives should form a career arc with other courses so they complement each other.
For example, you take an elective about basics of finance and structuring. But then there's no further electives that support that. Maybe there could be deep learning with finance, stochastic models in finance, or risk analysis in finance. You take those and build the next curve.
Rather than taking finance in one semester, then a scattered one like agentic AI where those two may not connect. One good thing at Columbia is there are finance-specific agentic AI courses too, which I saw in the fall. We might need to see whether those courses have connectivity or try for that.
Another thing: don't take electives just because your friends are taking them, or because of FOMO. This is the time that demands knowing your real interest. What are you going to focus on? It's not about seeing what others are doing and following.
Really spend some time. Take at least one day. You still have time to finalize courses. Have a good conversation with yourself. See all the courses and whether they can be good complements.
Electives can be completely new also. If you're really interested in learning something—say this year you're going to get started with robotic learning—and you feel you need a course that can accelerate that, obviously you can take a completely new course that supports your curiosity.
Specific Course Recommendations
High-Performance Machine Learning
For people really interested in software systems side of things. You get to learn about GPUs, CUDA programming, how to optimize GPU kernels.
Advanced Deep Learning
If you're not so into GPU or inference optimization, but more interested in different architectures—multimodal deep learning, state-space models—advanced deep learning is a good course for that.
NLP and Computer Vision
If you want to deep dive into NLP, there are NLP-related courses. Computer Vision 2 is there. For finance, there's deep learning for finance and operations research.
Causal Inference by Adam Kelleher
For people who are econometrics or data science-centric. His thoughts and content are really good. I've read his Substack, his work. He developed the causality package. Really interesting.
Causal inference along with statistical modeling and machine learning—these three things are like a very good bento box. That's something there.
The Analytics Engineer Combination
Many companies are hiring for Analytics Engineer roles. One of my ex-colleagues recently joined Adobe as Strategic and Analytics Engineer. There are a lot of these roles across startups and companies demanding good business understanding, statistics, foundations of data science, scalable data pipelines, AB testing fundamentals, causal inference, and statistical or machine learning models.
The typical combination would be: machine learning, statistical modeling, computer systems (so you learn scalable data pipelines and analytics workflows), and think of agentic workflows as part of that. Then causal inference.
This gives a unique combination for someone getting into data analytics, data science, product analytics. Roles at places like Perplexity or Anthropic—they hire for economic research, consumer research. Analytics engineers for economic research paying very good salaries.
Most students take courses to match dream jobs. Dream jobs are defined by future opportunities plus financial benefit.
The Systems Engineering for AI Combination
LLM-based generative AI and high-performance machine learning together give core systems engineering for AI models and agents. Both courses are covered by adjunct professors working in IBM research. They bring very good industrial insights.
Finance-Focused Paths
For people focusing on finance and markets, stochastic modeling is very much needed. Stochastic modeling plus statistical models reinforces understanding in probability and statistics.
If you can take another course focused on machine learning modeling for finance markets—alpha signal generation, regime detection, risk quantification—that's valuable. If such courses offer conformal prediction, that's very useful. Or one can learn conformal prediction if they're into markets, finance, investment—that's good leverage.
All these things deal with uncertainty. Whatever it takes to learn about uncertainty is what these courses provide.
Course vs. Self-Learning: They're Not the Same
One common notion I've seen: "Should I take this course or just self-learn and build projects?"
Both cannot be equated. A course gives you an attention demand of at least 100 hours. 15 weeks, every week the class is two hours—that's 30 hours. Plus equal amount for projects and assignments. Around 100 hours for a course.
As the course progresses, you get different perspectives and learn structurally. Self-learning has risk—a fresher versus an informed person self-learning have their own biased diversions. I've seen people get confined to "tutorial hell"—not learning things properly, just replicating what they see in videos.
A course demands research work. Write a paper, build an end-to-end project, present something, involve in a seminar that brings people from outside and enables interactions. That's worth doing.
On Auditing Courses
Auditing courses is good, but it shouldn't be just sitting idle or very irregular. If you're hard-hitting it, audit plus learn in public. Continuously build things along with that rather than just sitting in class. Auditing is just watching—there's no point otherwise.
Theory-Focused Courses Worth Considering
Continual Learning and Applied Causality
Seminar-based course by Professor Blei talking about extensions of causal modeling—causal representation learning, invariance, how causality can be combined with LLMs.
LLM Interpretability and Alignment
If you're interested in safety, alignment, preference-related stuff.
Mathematics for Machine Learning / Deep Learning
Offered by different departments—electrical engineering, mathematics, finance. Very useful if you're grounding your course towards research and applied research.
Having better theoretical understanding is a good path towards practical experience. I remember Vladimir Vapnik saying "a good theory itself is enough practice." Developing theoretical understanding—you struggle hard to develop it, parallelly the intuition gets built. With that intuition, you can think of what's right and wrong when you build projects or solve real problems.
On Research Projects for Credit
People might plan to take one research project for credit to maximize GPA. That's fine, but if the research work complements your other learnings, that's something good. Otherwise, if it's just doing some task that doesn't give you anything else, you might need to think about other options—what could make you learn more, bring better outcomes.
The Statistics Department Surprise
I was surprised that the statistics department has very nuanced electives at all stages. Not just theoretical statistics, but statistics in terms of finance, biostatistics, and information-theoretical aspects needed for LLMs and generative AI.
I'm happy about the freedom to get into these electives. I know many data science students have obsession about UW's data science program. Comparatively, they have fewer electives, and I find it more beginner-level than building your specialty.
Reinforcement Learning Options
Professor Shipra's RL—one of the best nuanced RL courses if you can take it, if you're really interested.
Parallelly, there are RL plus LLM related courses by Adam Block—more centered around LLMs. There's another RL course in the Electrical Engineering department.
We have enough space for RL, LLMs, NLP, generative AI. For causal inference, there's one in the data science department and another in the statistics department. The statistics one focuses more on potential outcome framework.
Lots of options. You just need your own strategy and a sorted way—a good assortment of courses so you don't distract yourself or disturb your intact structure.
Don't Break Continuity
Feel free to explore new ideas, but see whether it's really helping you. Sometimes people take completely scattered everything and miss continuity.
If you've taken courses in the past, keep reinforcing them. Don't just forget about fall courses. If you can see connectivity to relearn or reinforce—for example, statistical learning and modeling lets you look back at understanding in probability and statistics. Taking machine learning theory lets you look back at applied machine learning. Taking advanced deep learning lets you look into applied deep learning. Taking HPML, you try to develop a CUDA program of flash attention—you look back at understanding from applied deep learning sessions.
Do projects, not just for the final thing. Small experiments. Even failed experiments are fine.
The Interview Mindset Trap
Don't select courses for "what course can help me prepare for interviews." That's a bad mindset. Courses are intended for career building, understanding long-term aspects.
I'm still always happy I took applied soft computing and control systems in my undergrad—eight years back. Courses are not for short-term interview preparation. They can still help us in the very long-term.
Think about it so you build expertise. Sometimes people feel insecure about saying "I want to build my expertise in that." No—anyone can build expertise. Anyone can feel justified that they have expertise in a particular field. It's not others' game. It's everyone's game.
Make sure courses are helping you build expertise, not prepare you for interviews.
Choose deliberately. Build the arc.