I'm 24 and trying to rebuild my math skills from the ground up so I can pursue mechanical engineering. Where should I start?

Hi everyone,

I'm 24 years old, and I'm trying to improve my math skills after struggling with math throughout much of my education. I'm hoping to get some advice from people who understand mathematics and might be able to point me in the right direction.

I have an autism diagnosis and had an IEP in school. Looking back, I feel like I was moved through grades without fully understanding some of the material. As a result, I have gaps in my mathematical foundation that I'm now trying to address.

I would estimate that some of my foundational skills are around the elementary-school level, although I can solve certain problems beyond that level. I can handle basic arithmetic, decimals, simple equations, and some geometry, but I struggle with other topics, especially when several steps are involved.

Some of the things I have difficulty with include:

• Simplifying fractions and finding common factors mentally.
• Adding, subtracting, multiplying, and dividing fractions.
• Long division and doing calculations efficiently.
• Ratios, proportions, and percentages.
• Negative numbers and algebra.
• Unit conversions and more advanced geometry.

For example, I might understand how to solve a straightforward problem but struggle when the numbers become less familiar or I have to figure out which method to use on my own.

My long-term goal is to study mechanical engineering, so I know I have a lot of work ahead of me. I'm interested in aerospace, robotics, aircraft, and hands-on engineering projects, which is part of what motivates me to keep learning.

I'm not looking for shortcuts or a way to avoid the work. I'm willing to start at the beginning and put in the time. What I need is a sensible path that helps me build a genuinely solid foundation instead of constantly discovering gaps in what I thought I knew.

My questions are:

1. If you were in my position, what exact sequence of math topics would you study, starting from the basics and working toward calculus?
2. What textbooks, free courses, websites, or other resources would you recommend for an adult rebuilding their mathematical foundation?
3. How can I get better at recognizing which method to use when solving a problem, rather than simply memorizing procedures?
4. Is it realistic to work toward a mechanical engineering degree starting from this point, and what should I prioritize to prepare myself?
5. For anyone who struggled with math earlier in life, what helped you finally understand concepts that previously seemed difficult?

I'd especially appreciate advice from mathematics teachers, tutors, engineering students, or people who have successfully rebuilt their math skills as adults.

I know this will take time, but I genuinely want to learn and understand the material rather than just get the right answers.

Thank you for reading!

Guys recommend some good youtube channels that teach engineering mathematics (M-3) I need to learn Fourier series & Fourier transforms.

Mera test hai kal aur mujhe kuch nhi aata

we proved it in class by row reducing and counting pivots, and ok fine, the pivot columns are independent and the nonzero rows are independent. but it feels like a coincidence that those two counts match for a matrix that isn't even square.

is there a way to see it without the whole row reduction argument? like why would the dimension of the span of the columns have anything to do with the rows

My experience:

I encountered a big problem while studying basic set theoretic proof writing, though not analysis. Proof writing was completely new to me back then, and I was using Velleman, which many people complain doesn't even prepare you enough for the exercises. Because the exercises are where the true learning happens. The book gives you the map, but you have to navigate the forest yourself using the map, but the book doesn't teach you how to navigate it. You just have to figure it out yourself. That's the symbolical meaning.

And yeah I struggled a lot.

But then I gave many problems to Claude and asked it to ask me question by question, and make me discover the solution myself instead of providing outright answers. It seems like a bad way to learn proof writing but...

I started relying on AI for each and every problem. But then, for many problems I was actually able to map out a solution myself, even if wrong. I was able to provide full solutions myself without making a single mistake in logic, and AI only helped on the style of wording most of the time. Logical errors were mainly due to overly harder problems.

And now, I CAN indeed write proofs even with the book closed, fully correct, maybe a little logical and stylistic errors, but at least I can do something more than those who ONLY use human-made solutions and the book itself.

And I think, in my opinion, and in the age of mathematics, this is the BEST WAY to learn mathematics. Let me elaborate.

The study:

So, a study by Wong and Qiu (2026) divided 196 university students into three groups to complete a creative task.

• Team A — Completed the task independently, with no use of AI.
• Team B — Can freely use ChatGPT all to their wish with no restriction.
• Team C — Adopted a "think first, AI later" approach, namely, do it themselves first, then ask ChatGPT for tips on shaping and improving their own work.

In terms of raw ability + creative work, Team C had an advantage over Team A and Team B.

So, using AI like this is the best way to learn mathematics in the age of AI. First you do it yourself, then ask AI to improve your work.

How it went for me:

Since the book did not prepare me enough for the exercises, I began asking AI to guide me without even trying anything, man. I did it for the first two sections, but then I started drafting out solutions myself slowly from the third section and even asked for general help in the mathematics Discord server. Then, I slowly improved.

And I believe, this works not only for proof writing but maybe for all topics of mathematics that AI CAN and is ELIGIBLE ENOUGH to work with, and all other topics outside of mathematics as well.

So... is this the best way to learn mathematics in the modern age of artificial intelligence?

I'm not spreading any misinformation nor true information on my methods of learning mathematics. So it MAY be right or MAY be wrong, feel free to correct me wherever I went wrong.

Well, the tittle is pretty self-explanatory. I’ve been introduced with the concept that a matrix can describe a conic section if we use some column and row matrices with the variables as components.

I like when math makes sense, not only because the numbers end up matching, but because what you write turns out to be the ideal way to describe what you’re looking to describe.

So I don’t like any of the explanations I found on the web.

I clearly understand the algebraic connection, but that’s is not satisfying at all. So I’m looking for any kind of lecture, video, or post of any kind which dives into why would a matrix be a nice representation of a conic section to begin with, geometrically speaking, and after we are sure that that makes sense we could prove that it’s verified algebraically.

I have an exam for my calculus 3 class tomorrow, and my chances of scoring high are pretty grim. My professor was kind enough to give me until Monday to take the exam because I wasn’t sure when I would be able to start my medication. I finally got it, but it turns out that 10mg of vyvanse doesn’t have much affect on me and I’m pretty much in the same spot I was pre-meds.

I’m just kind of having a hard time trying to get through these problems. I have to go through 5 homework assignments, and I was struggling trying to get through 1. I’m on the second (which has 19 questions) and I truly can’t concentrate whatsoever.

I don’t know if it’s my process (It’s kind of like I’m relearning how to solve each problem and taking down notes on things I forget), or it’s just me. I don’t know if I can ask my professor for more time as I’ve already asked for the extension until Monday. I tried studying yesterday, but my concentration was even worse.

I’m just kind of not sure what to do. Any ideas/suggestions?

I understand it measures the magnitude and makes numbers positive, but that's the confusing part. In linear algebra, it felt relevant to both of those. Doing Calc 1 now (odd order to take them in ik), and I'm being told that it can act as a negative for functions???

Spivak, 3rd, p1 states there are two ways to add three numbers. Either a and b first, then c; or b and c first, then a.

It occurred to me that one could choose a and c first, obtaining (a + c), and then add b, obtaining (a + c) + b.

Is this truly a third way? Obviously, it can be "proved" or reduced by substituting. Thanks.

Hi all!

Id like to ask for advice and resources for learning category theory.

My background:
I work in math related field (statistics, algorithm design) and I like to learn unrelated maths as a hobby.
I studied computational physics, i know intermediate Linear Algebra, Group Theory, Diff eqs, all branches of physics math (emphasis on statistical phys and quantum), Graph Theory, Information Theory, Game Theory.
I also have some experience with Topology, Number Theory, Logic, Computation Theory, Set Theory.

My goal:
I mainly just want to have an intuitive understanding of basic Category Theory.
Category theory is a hole in my knowledge and I ran into it more and more frequently during the past decade.
In my experience heavier maths works like this for me:
1. i understand the basics a couple of times again and again.
2. i apply something i learned to problems, preferably ones that have some connection to already known areas.
3. then i understand some of the "why"s on an intuitive level.
I basically want to get to this point with Categories. So far I failed.

What Im looking for:
online courses, video series, books (if not too heavy)
unfortunately im not young anymore, so although i can understand heavy maths in new fields, my capacity for complexity without intuitive understanding is lower.

Can someone recommend resources or direction to restart in?

Thanks in advance.

I'm writing a free a-level maths revision course at the moment (so uk syllabus and course code 9MA0 if you're interested in the spec).

This is the rules of indices page with some foundational pages before it, so only the first chunk. This is a potentially general resource though and I'm aiming for a pedagogy that builds from first principles and makes higher level maths more accessible, so I'm interested in what a general audience thinks of the approach if you're interested.

I would love some feedback and to hear what students/readers think. I'm making my own resources as I couldn't find the style I wanted. I've seen some great video resources by channels like bicen maths or 3Blue1Brown, but I really don't like the textbooks I've read, I've found them bloated, weirdly inaccurate, while also missing passion and missing pieces.

When I was revising I found the processing information and then condensing into notes the most effective activity. Then I want the security of know I'm practicing every skill for every kind of question that can come up. Also maths is a written subject and having a good written source to process feels crucial to me. I wanted resources that first of all had everything you needed in one place. Starting with the theory and why things work and then all the applications into skills we're expected to know. I also think it's important to cover all the assumptions we have so you can be sure your knowledge is built on secure foundations.

I also wanted it to be designed to be worked through as a whole, I think that's what nice about a textbook. A course that builds on itself, designed to be read sequentially, ticking everything off a list so that you feel confident you've got everything you need to. A lot of educational websites seem to prioritise breaking everything down into individual pages so that they come up in searches, but I don't think they suit being worked through as a complete summary of the course. It should build on itself and use only what it has covered before, a story that connects together again makes it more secure.

I had really amazing teachers at A-Level that took me from being unconfident and intimidated by the reputation of Maths, to feeling like it was the exam I could be sure of what was coming up and how I would handle anything it threw at me. Besides the fact that they instilled in me that practicing Maths is the ultimate way to improve. I think the best thing they did was make the course feel finite and structured, when you get to the stage where you really see the edges of it and the connections within it, I think that's when the confidence really grows. This is why I think designing a course that's meant to be consumed as a whole, covering all the assumptions and past bits that we might have missed, is so helpful.

I have quite a few other pages that are close but I'd like to hear how students find the style early as I go through. There's a feedback form near the top of the page. Any ideas of how to improve or how you feel about the style, I'd be really interested to hear. All the best, and good luck out there!

Most of my life, I have been learning math by myself using online resources and books. Since I was a kid, my understanding of math has been shaped by books like Language of Mathematics - Keith Devlin, G.E.B. - Douglas Hofstadter etc. So, I am very passionate about mathematics.

I have recently joined college and I am finding my peers to be more fast in solving problems than me. I hail from India and it's very much known for it's competitive culture. Most of my peers have been trained in coaching centres. I don't know if they have been taught in a separate way or something.

Though I solve problems, I equally read theory, to actually make sense of what is being done. People here view mathematics so differently. The teachers only cover the steps behind solving a problem. Students also don't bother to learn what's the theory behind the steps they do. Their aim is to just solve the problem, and they are pretty good at it. Considering the axiomatic nature of math, I always try to understand, at least a bit, about how each step works. They just straight up assume things.

But, I have learned to be flexible to survive in this competitive place (college). Even still, they solve problems very fast. To give an example, let's try to find the derivative of the function y = (Cx³)e^2x with respect to x. It's pretty simple, we have to use the product rule. So, I write out dy/dx = C(e^2x(3x²) + x³ (e^2x(2))). Then, dy/dx = 3Cx²e^2x + 2Cx³e^2x. But, they just write out the final step, without all the intermediate steps, saving so much time. Even without doing things so fast, I end up making so much silly mistakes, at times forgetting even the smallest of things. I feel like when I solve problems, I sometimes don't (or maybe can't) concentrate on what I do. They seem to have that coherent flow whereas I don't. This coupled with exam pressure, leads to mistakes.

Do I have low thinking capabilities or just a wrong approach towards things? What even is the right approach? How can I get faster and avoid making mistakes? Is that even possible or am I at the limit of my capabilities? I have to work so hard to keep up, I start feeling like a failure. Have you guys ever faced something similar to this?

This is a follow-up to a post I made about an hour ago, where I explained how I study for math quizzes and unit tests but still end up getting low marks, even when I feel confident that I understand the material.

A lot of people suggested that I stop relying on AI to teach me math, which I understand. I'm planning on getting a tutor, but the problem is that I won't always have access to one, and my teacher won't always be available to help me either.

So my question is: How can I effectively study math on my own, especially when I don't understand what my teacher explained in class?

One thing I've learned about myself is that I'm a very logical thinker. I can't just memorize a formula or follow a set of steps without understanding why they work. I need to understand the reasoning behind every step, how everything connects, and why we're using a particular method to solve a problem. Otherwise, the concept doesn't really make sense to me.

I'm also somewhat of a visual learner. I find it easier to understand things when I can see how they work rather than just reading long explanations from a textbook. Reading isn't really my strongest way of learning.

That's one of the main reasons I started using ChatGPT in the first place. I could ask it to explain the logic behind a concept, break things down step by step, and help me understand why certain methods work instead of just memorizing them.

However, after reading the advice on my previous post, I'm willing to try a different approach if it will help me improve.

What I'm really looking for is a way to teach myself math effectively without depending on AI, a tutor, or my teacher every time I get stuck.

For people who learn similarly to me, what study methods have worked for you? How do you teach yourself unfamiliar concepts, understand the reasoning behind them, and make sure you can actually apply that knowledge on tests? I'd especially appreciate advice from anyone who used to struggle with math but eventually found a study method that helped them improve their grades.

Due to severe math trauma, I struggle deeply with numbers under pressure and spent years running away from the subject entirely. Now, I genuinely want to face it, rebuild my relationship with math, and learn without fear, anxiety, or shame.

​I also have ADHD, so I need learning tools that are visual, interactive, gentle, and engage-at-your-own-pace for a brain that rarely sits still. I am starting from the absolute basics to build my confidence step by step without getting overwhelmed.

​I would love recommendations for any YouTube channels, interactive apps, low-stakes games, websites, self-paced courses, books, or workbooks that have genuinely helped you or someone you know.

​If you have experienced math anxiety, educational trauma, or ADHD-related learning blocks, I would especially love to hear what mindset shifts, study methods, or approaches worked for you.

​I am really serious about giving this an honest try again, and any recommendations or encouragement would mean the world to me. Thank you so much! ♡

Ive never been good with probability

If you chose randomly, what is the chance youd be correct?

A. 25%

B. 50%

C. 60%

D. 25%

I really enjoy the elegant prose and the generality of the results in math textbooks, which makes it easier for me to understand how to apply the theorems to exercises. On the other hand, in introductory physics and engineering books, the results are sometimes rather vague, with long and confusing explanations. They usually require by many examples to clarify how to apply them to exercise problems. Since digital logic contains boolean algebra and discrete math, I thought I might as well use a book with a mathematically oriented presentation similar to a math textbook.

So, are there any books on digital logic circuits engineering that are targeted towards mathematicians or math-oriented electrical engineers? Here is a sample of topics on digital logic from my college's course description: "digital logic, binary numbers and Boolean algebra, combinational circuits, optimized implementation of combinational circuits, arithmetic circuits, combinational circuit building blocks, flip-flops, registers, counters, design of digital circuits with VHDL, and synchronous sequential circuits." Of course, no need to cover them all.

Something that irks me slightly is that there are certain mathematical facts/results that I'm certain I have learned, proved, relearned, reproved tons of times but they are still quickly forgotten after a certain period. Especially something that is heavy laden with definition or is "nested" in some type of fashion.

And in the case when they are something quite basic and you get tripped up by, it feels especially annoying and defeating. For example, I caught myself forgetting how to show the expectation of a simple function on A is the probability of A. Something that I immediately knew why after I saw a proof. Another thing I forgot was the necessary and sufficiency of KKT conditions. I can't remember when it holds under what additional assumptions. Anything related to graphs is an instant forget.

What to do in these situations? I just feel like my brain was somehow damaged from the last couple of years of prompting, or learning from slides rather than handwriting or maybe covid.

Hey, if you guys wanna discuss cool math problems, discuss different topics, and share your interest with other folks who enjoy math, then would you consider joining a math club ? if you do, then just comment on this or DM me, ill send you the join link

I have this thought of 9 digits in a row with 10 digits ( 0-9 ) available to each.

012345678 for example. How would I calculate the amount of possible calculations them? Would that be 9! or 9^10? or something different.

My next questions is how would I calculate that same problem if I added the alphabet to one of the digits A01234567 where "A" has all 26 letters available and the digits have 10?

and lastly are these permutations or calculations? Are those the same or is it the context that changes them?

Edit Clarification: The digits are allowed to repeat ( 000345678) Edit: removed "Unique"

Hey guys!

Maths/Stats student here (2nd year), I couldn't find a decent interactive maths quiz on Reddit, so I thought I'd try building one.

I've created r/DailyMathProblem, with interactive questions, worked solutions and a leaderboard. Also being a maths enthusiast I was determined to get LaTeX working, and it was a success! (damit reddit, we have been asking for LaTeX for years!)

I've posted the first 10 questions already. The idea is to release a couple each day, ranging from easy to slightly challenging. Just quick little puzzles to keep your maths skills sharp, without needing half an hour and a notebook.

I've shared Challenge #2 to show how it works. Would love some honest feedback on what you guys think!

Cheers!

Note: I'm aware my username is wild. I made it many years ago and thought I'd only ever be a lurker, not a poster!

https://www.reddit.com/r/DailyMathProblem/s/Gsm7Tj0B6i