This is sweet news. I'm over 40. I enrolled at my local university in January and I'm studying (literally right now) for my linear algebra midterm [0] which is in 45 minutes! I'm on HN to calm my nerves.
I graduated high school in the early 2000s and graduated college with major in computer science and a minor in math. My goal is 5-8 more classes for a second degree in math (major).
I went to the University of Texas but I took summer courses in Houston Community College (calculus II, physics II, and more -- those classes were SO bad at UT).
It was insane how much better the courses were in the community college. Tiny class of 15. $300 or something. Amazing professor that you could ask questions to like you could in high school. Normal 20-30 question textbook homework where you just work basic problems and build confidence that you know the material.
Meanwhile UT was the opposite. I think I paid $1400/class/semester (and that's a bargain). Lecture halls where you couldn't possibly ask a question. Weird math/physics homework that was like 3-5 super hard questions that I often couldn't figure out, demoralizing. Often a TA that could barely speak English. It's actually quite insulting.
I sometimes think about enrolling in a local college for fun, the experience was that good.
> Weird math/physics homework that was like 3-5 super hard questions that I often couldn't figure out, demoralizing
Had this experience at an elite uni as well for math courses. At the time I felt like it pushed me to really grow, and it was absolutely necessary to do well in that specific course (tests often had questions that ~required you to know how to do all the uber-hard homework problems), but I wonder what the research actually says about this sort of homework vs your more standard variety.
> I wonder what the research actually says about this sort of homework vs your more standard variety.
I have a vivid memory of one of the question on a final being basically “sketch the outline of this important thing we studied”. I couldn’t do it. I took the class but didn’t see the forest for the trees.
Later I met people who talked about things with each other, including the big picture. That’s the community I was missing when I took the class solo.
In retrospect, I could have gotten something more out of those problems that I thought were so hard.
I think it also depends on what the professor's and the student's goals are; and if they're aligned.
Is the course about learning the material at hand, or laying the foundation for graduate level courses in the same subject? About teaching the most efficient way or getting a student used to deriving equations when there's not a plug and play formula.
I'm sure we can draw similar parallels between csci college courses, big tech interviews, and professional software development. Even though it's all the same pipeline, each stage/stakeholder has different goals, motivations, etc... If you're having a discussion about the pros and cons of an approach, you have to make sure the goals are aligned else you'll just be talking past each other.
I had classes with take-home tests of three impossible questions, and standard tests of disguised regurgitation. The impossible questions are the ones that will really test your understanding of the fundamentals. It's the different between "add two numbers together", and "what does adding mean"?
I found out I can't stretch my brain to truly understand the fundamentals, so I stopped after a bachelors and don't use my degree at all. I don't mind. It takes truly special people to push the limits, and a lot of not so special people to keep the world running for them.
I have wondered this too as a person who has attended a regular (non-honors) Calculus II course at a fairly top-rank private university and then again at a community college.
From what I remember, the university course also had some rote exercises for homework so it isn’t like everyone is only focusing on working the trickier exercises.
This also reminds me of the story Donald Knuth has around working every exercise in the book for a calculus class.
Large universities are focused on research, and they incur a lot of expenses due to administrators' egos (build build build), the number of administrators, and the range of microstate services offered, like their own health care system and mental health counseling (a major thing in universities now). Community colleges are focused on teaching.
I had a similar experience -- took physics at a community college when I was in high school. The 'up-side' of the overproduction of PhDs is that many people from elite backgrounds end up teaching at community colleges.
The only negative for me was that the students were pretty checked out.
> The only negative for me was that the students were pretty checked out.
I didn't put a lot of thought into where I went to school but if I could do it over again this is something I would have considered when I applied. The school I ended up at did not have many serious students. It was a night and day difference taking courses with even one or two students who were similarly engaged with the material, but most of those students ended up transferring to better schools after a year or two.
You also run into the issue later on that the people you went to school with wash out of industry (or never work in it to begin with) at much higher rates in comparison to those who went to more serious schools.
Exactly the same experience. My AP Physics teacher in high school was incredibly better than university.
UT is research focused. Depending on the department, they make the professors teach classes, which is often not aligned with their interests at all. Sometimes I think they are actively trying for bad reviews from students to incentivize the university from making them take on course load.
I went to a somewhat highly regarded (not MIT or CalTech tier) tech school, and then to a state university.
The tech school considered it a boast that it had more graduate students than undergrad. It was clear where the professors' emphasis was. I recognize the lecture halls where you couldn't ask questions, and the barely-anglophone instructors. (Everyone in the EE department, in particular, seemed to come "fresh off the boat" from China bringing precious little English knowledge with them. The prof for my introductory EE course mumbled on top of it.)
Then I went to state school. Ho-lee shit. Complete difference. The bad profs were incompetent chucklefucks who couldn't cut it in real academia. The good profs actually cared about teaching undergrads.
I learned a lot about choosing a college -- a few years and a few tens of thousands of dollars too late.
community colleges are... like... there for the community. and you feel that community.
a lot of big universities have people there for research. there is money to be made, grants to be given, and degrees to be minted. and you can feel that too.
source: got out of the military and went to one, then the other.
I had a long winding road through academia. Went to a big selective R1 state school in a different state after high school. Had an existential crisis, moved back home with my parents and went to community college for a year, finished my undergrad at a large, less selective R2 and then did grad school at a large, very selective private R1. I would rank the quality of instruction:
1. Community College
2. Probably a tie between the R2 and grad school. However, that grad school focused a lot on grad students, so it's possible the undergraduate experience isn't quite as good.
...
3. After a very large drop off the R1 state school.
You obviously can't extrapolate too much from my personal experience, but it does seem to line up with man others.
I hope it went well! I am in my fifties and enrolled in a master degree program for pure mathematics about 2 years ago (I don't need the degree, so I"m just taking all the classes they offer, so not about to graduate). It definitely took some time to get my brain sharper, but I am better each semester.
I hope people don't take away the negative side of the article, brain slows down, but the positive side: brain gets better with usage. Its uncomfortable, I can churn out programs as complex as programs I've already written and go to review meetings and planning meetings without much effort. But being able to solve PDEs reasonably quickly and accurately, I cannot, or have not without a great deal of practise. It's unconfortable in some weird mental but physical sense. But I'm sharper in everything else I do.
One interesting thing about software as career followed by math classes is that there's no compiler - you can type any janky thought into LaTeX and if you don't detect that it's bogus, nothing will, until you show it to a professor.
Also, the information density of maths notation is way higher than (good) code. We want code to be readable by some that doesn't know it; a lot of math seems to be readable when you sort of 80% already are familiar with all the prereqs. So no just skimming and then hitting compile/test/run (whatever validation you do). It's typing letter by letter and taking the mental effort to actually see and decipher the letter (at least, for me in my current stage; I'm trying to do novel research, but my demonstrated understanding of the details of the previous research is embarrassing low).
Also, weirdly, I still have the same fear of professors that I did as a young person. I manage it better with my decades of maturity (really) but it is still a part of my social interactions.
> One interesting thing about software as career followed by math classes is that there's no compiler - you can type any janky thought into LaTeX and if you don't detect that it's bogus, nothing will, until you show it to a professor.
The formal proof community is very interested in exactly this problem! It's not my specialty, but I believe that Lean (https://en.wikipedia.org/wiki/Lean_(proof_assistant)) is one of the very active communities.
I've done some intro to lean things, but no one in the maths program is into lean, so I'm just focusing on the math side. Terry Tao is big into the idea of lean tho, and combining LLMs with Lean.
> I've done some intro to lean things, but no one in the maths program is into lean, so I'm just focusing on the math side. Terry Tao is big into the idea of lean tho, and combining LLMs with Lean.
One of the best things about entering an underpopulated space is that you can become one of the leading experts very quickly. If it's something that appeals to you and fits your skill set, it might be worth investing the time to learn!
(Again, I say this as someone who's always been interested in formal proof, but haven't investigated it much myself, much less explored the merits and demerits of particular systems—so this is not an endorsement of Lean specifically, though it does seem to be one of the most active communities, which is important when you're trying to get into a topic.)
The information density is incredible. A 2x2 matrix (Jordan constants) containing enough information to produce a slice of a hyperbolic paraboloid. Leaves me mesmerized...
It's funny, at the end of each lecture I just want to yell... "NO! Don't stop! I must see how this ends!"
Very similar to when I stop our children's movie and tell them to go take a bath.
I guess nobody knows all of math and it is constantly a learning process, but things like "Jordan constants" which defines proper nouns to thousands upon thousands of math concepts, symbols, theorems and approaches just makes it a even harder to memorize the whole shebang. Fascinating but sometimes overly complex.
I like your point about feedback. That's how I describe my difficulties with proofs, too.
There is no way of knowing a proof is right without knowing it's right. (Or maybe I am just missing the point)
Good luck! You can do it! I started doing statistics classes three years ago when I was 45, continued doing a MSc degree, which I finished successfully a few months ago. I am now looking into doing a PhD. This is more fun than I ever imagined (fair enough: I was a teenager when imagining it).
Good luck! You should check out Math Academy, it's more effective/efficient/cheaper but also a good supplement since it's accredited.
I recently turned 40 myself and I'm working through their Foundations courses (made to help adults catch up) before tackling the Machine Learning and other uni courses.
I'll tell you my experience as someone who's been using Math Academy for past 6 months.
Math Academy does what every good application or service does. Make things convenient. That's it. No juggling heavy books or multiple tabs of PDFs. Each problem comes with detailed solution so getting them wrong doesn't mean looking around on the internet for a hint about your mistake (this is pre ChatGPT era of course, where not getting something correct meant putting down MathJax on stackexchange).
> better than just prompting ChatGPT/Claude/etc
The convenience means you are doing the most important part of learning maths with most ease: problem solving and practice. That is something an LLM will not be able to help you with. For me, solving problems is pretty much the only way to mostly wrap my head around the topic.
I say mostly because LLMs are amazing at complementing Math Academy. Any time I hit a conceptual snag, I run off to ChatGPT to get more clarity. And it works great.
So in my opinion, Math Academy alone is pretty good. Even great for school level maths I'd say. Coupled with ChatGPT the package becomes a pretty solid teaching medium.
Yes, much better. ChatGPT/Claude/etc. are useful the times I want extra explanation to help connect the dots, but Math Academy incorporates spaced repetition, interleaving, etc. the way a dedicated tutor would, but in a better structured environment/UI.
Their marketing website leaves a lot to be desired (a perk since they are all math nerds focused on the product), but here are two references on their site that explain their approach:
They also did a really good interview last week that goes in depth about their process with Dr. Alex Smith (Director of Curriculum) and Justin Skycak (Director of Analytics) from Math Academy: https://chalkandtalkpodcast.podbean.com/e/math-academy-optim...
I used an early e-learning platform not because I wanted to but because I was one of its developers. I didn't develop the course-content just the technical implementation.
What I didn't like about the content is I often had questions about it but there was no-one to ask the questions from. Whoever wrote that material was no longer around. It's a frustrating feeling when you can't really trust what you're studying is factually correct, or is misleading.
I assume AI will have a huge improvement in this respect.
The second link really impressed me, I'm tentatively sold on (and excited for) their approach. Does anyone know of any other accredited programs similar to Math Academy, but for other subjects?
Anything in the soft sciences, or biology/organic chemistry, or comp sci. I know there are a lot of courses for the latter especially, but I'm looking for accredited ones.
Not OP, but I have found MathAcademy to be infinitely better. I really liked the assessment portion which levels you and gives you an idea of where you are are at the present. As someone who graduated with an engineering degree a while ago, there were things I realized I didn’t know as well as I thought I did and I probably would not have prompted an LLM to review.
Math is something that should be taught in an opinionated way with an eye toward pedagogy. Self study with GPT is an excellent tool in math, but only for those who have enough perspective to know which directions to set out on. I don’t think anybody who doesn’t know linear algebra should be guiding their studies themselves.
Given my ChatGPT and friends experience has been one of overwhelming frustration due to incorrect information, I would say Math Academy is in an entirely different galaxy. ChatGPT is great if you want to learn that pi is equal to 4.
b-b-b-but the next supercalifragilistic ChatGPT version will be able to tell you that pi is between 3.1 and 3.2. that will be a Quantum improvement, asymptotically close to AGI.
at least, i think i heard alt samman say so.
you plebs and proles better shell out the $50 a month, increasing by $10 per day, to keep dis honest billionaires able to keep on buying deir multi-million dollar yachts and personal jets.
be grateful for the valuable crumbs we toss to you, serfs.
Keep making those pushes! I was a non-traditional graduate student because around 10 years I got very serious about going for my doctorate. I literally scheduled times with my friends to watch Khan Academy videos on upper level maths and spent time practicing those skills. Then grad school is just one intensive learning session.
Years of martial arts ingrained that sense of being a life-long learner. I was taught the mantra of "Progress comes to those who train" and "Practice makes permanent" and even though those phrases were focused on learning to beat someone up, I've carried them on into other parts of my life.
Congrats! It is never too late to be doing this type of study and work.
I'm doing something similar: I just turned 50 and have been taking graduate ML classes where I work (at Carnegie Mellon). When I finish the graduate certificate program in generative AI and LLMs that I am enrolled in, I will be only two semesters away from earning a full masters degree.
It’s been twenty years so my opinion is skewed and my memory is quite faded, however, I’ve got opinions on the guide and class in general.
The main thing is there are no surprises or tricks. The exams are straightforward and EXHAUSTIVE. I do all the assigned homework twice. Once when we cover the material and again before the exam. Let’s hope that strategy pays off again.
This college requires something like taking 30 credits from the institution to award a degree. That's somewhere between 7-10 classes (mix of 3/4 credits each).
Yes, through admissions. Getting a degree in math, maybe... depends on how much stress this adds to my life. If I were retired I'd just take a full load, but raising a family and running my business I can only take it one class at a time.
I didn't ace it, but knew immediately what I had done wrong as I rode my bicycle home. I kept checking my linear transformation matrix and the Eigen values didn't compute... Looked again at the TI-89 when I got home and realized I swapped the orientation on the Jordan constants. I wrote all the equations out, so maybe my professor will have mercy on me. Oh well, another case of elevator wit - https://en.wikipedia.org/wiki/L%27esprit_de_l%27escalier
I've used an LLM for tutoring, but it doesn't replace the experience of biking across campus, ordering a coffee, unpacking my TI-89/iPad, cracking jokes with the professor and other students, paying attention, taking notes, and having to remember the material until exam day. This process is culture, and it's honing my mental blade. Then, as a solo-entrepreneur, I go home and use Cline+Sonnet to hack on a few side projects. These two processes compliment each other, greatly. Like I've mentioned in other replies, this is for "#2 fun" and to see if the "old guy (me) has still got it."
I have padlocks that I use to lock up my tools, or my bike, etc. The problem is, I often go several months without using some of them and forget the combinations. So, I decided to write down their combinations, but then I always lose the sheet. Being the math geek that I am, I decided on the following solution. I choose a 3 × 3 matrix and multiply this matrix by the combination and write the result on the back of the lock. For example, on the back of one lock is written “2688 − 3055 − 2750 : Birthdays,” indicating that the 3 × 3 matrix that I chose for that particular lock is the matrix whose rows consist of the birthdays of my brothers and me (from youngest to oldest). My brother Rod was born on 7/3/69, I was born on 7/28/66, and my older brother was born on 7/29/57. What is the combination of the lock?
Now, technically the LLM didn't quite know how to parse "2688 − 3055 − 2750" and ran the calculation with "[2688;-3055;2750]" and produced a response of, "These values are clearly not typical lock combinations, which suggests a potential issue with the encoding process."
Smart, kind-of. I reran with a more explicit prompt and it calculated the correct combination.
Overall though, I'm impressed with using ChatGPT as a linear algebra tutor. I wouldn't hesitate to use it in the future.
I just tried your prompt: o1, gpt4.5, gemini 2 pro solved it correctly (21-19-36), sonnet3.7 and grok3 failed because of the parsing error you described.
> graduated college with major in computer science and a minor in math.
Me too. High five!
> My goal is 5-8 more classes for a second degree in math (major).
But why? Wouldn't it make more sense to go for a master in computer science? Are you going to use it for work. Otherwise, aren't you going to "lose it" anyways? Also, is your job paying for the degree or are you paying out of pocket?
I graduated high school in the early 2000s and graduated college with major in computer science and a minor in math. My goal is 5-8 more classes for a second degree in math (major).
Wish me luck!
[0] Study guide: https://course1.winona.edu/bperatt/M311S25/Tests/Test%202/te... Course: https://course1.winona.edu/bperatt/M311S25/Administrative/M3...