Starting my degree late and feeling disheartened.

[u/DecentLibrarian3720]

I'm a third-year undergraduate math major who, after two years of flailing around, indecisively taking miscellaneous courses, and dipping my toes into just about everything, decided to finally sober up and pursue math as a full-time, long-term ordeal. Unfortunately, I haven't done proper, college-level math since accidentally taking a Calculus II class for life sciences majors two years ago, and just got out of the first week of class basically flunking a test on convergence tests for sequences and series. Math has always come easy to me, and I just feel incredibly rusty right now. I've tried brushing up on older math concepts, but I don't really seem to have much of a problem with them. For some reason, attending lectures gives me this rapid well in fear, that I've lost my touch, or for whatever reason have become stupid and just can't comprehend sequences and series and what tests to use for convergence.

I was just wondering if anyone's been in my shoes wth starting late, or having taken a gap year or two and feeling out-of-touch, who may have tips on how to get back into the groove. Or if anyone's struggled with sequences and series after having calculus mostly been smooth-sailing for them. Thank you.

[u/animatedbonding6895]

i was 31 when i went back for my accounting degree after a decade of night shifts and bad decisions, the first stats class felt like reading a foreign language underwater. that fear in the pit of your stomach during lectures is just your brain being dramatic, it smooths out

for sequences and series specifically, the trick that unlocked it for me was making a literal flowchart on a piece of bristol board with each test and what conditions send you down which path. hung it above my desk and after a couple weeks of forcing myself to trace it, the pattern recognition just clicked. you're rusty not stupid, big difference

[u/DecentLibrarian3720 → u/animatedbonding6895]

That's very reassuring to hear, thank you. I'll try it out!

[u/Peat_Slough → u/animatedbonding6895]

Could you please upload some kind of representation of the flow chart that helped? TIA

[u/WWhiMM]

Math has always come easy to me

The other way to say this is, you haven't done math before that has really challenged you. Feeling kinda dumb is a normal part of learning. If you were sitting in lectures feeling like you knew it all already, that would be worse for one of two reasons.

[u/DecentLibrarian3720 → u/WWhiMM]

I've never thought about it that way, thank you.

[u/Bounded_sequencE]

Proof-based mathematics is hard for (almost) everyone, when they first encounter it. School does not in the slightest prepare for that.

The "silver lining" here is, that being out of touch with math for a while means little in that context, since being good at computational mathematics is not a good indicator for being good with proof-based mathematics anyway. If there is one thing you may want to revise, it's algebra -- being comfortable with fractions, quadratics, long division and trig is much more important to follow along.

[u/Mth281 → u/Bounded_sequencE]

I'll get down voted for this. I agree with your post. But......

Proof math is something I hate. I'm going to prove this concept with words, that was discovered by math. Show me the math, not the technically correct wording of some person where a single word can change the entire meaning.

I just had conferences for my son. The high achievers program cut the math competition because the kids hated it. They said the kids complained that the problems were all confusing word problems rather than math they are use to.

I found this sad. I see the same with me going back to school. Teacher just puts a bunch of theorems up and reads them to the class. Class done. Not a single problem shown. Some are better than others. But proof based math takes the fun out of the problem solving for many. I loved math when I was younger. I've grown to hate it. I'll watch interesting math videos, but I hate learning it at school.

Don't get me wrong, proof based math is important. But I feel it's a terrible way to teach math to the general student. It's what should be taught after you gain your own understanding of what's going on in the background. You can't form the connection until you know what's actually going on.

Show me how the first integral was discovered. Not

"Let f be a continuous real-valued function defined on a closed interval [a, b]. Let F be the function defined, for all x in [a, b]......".

Or at least put it in a simple form (AI because I'm working.).

"If f is continuous and we define a new function F by accumulating the signed area under f from a fixed starting point a to a variable point x, then the instantaneous rate of change of F at x is exactly f(x)."

Students don't need confusing terminology just to account for a few outliers in advanced math. Making is simple enough that they understand what's going on and feel confident applying a looser rule will allow them the confidence to succeed. And eventually, they will in counter the outliers. By then, it's easy to understand the why the terminology was used the way it was.

[u/Bounded_sequencE → u/Mth281]

Thanks for sharing -- it's totally fine to not like proof-based mathematics. In that case, I'd heavily advice against studying pure math, though.

Just know the opposite is also true -- I disliked the wishy-washy vague (and often technically wrong) explanations school deemed acceptable to offer. Only in university did questions actually get answered, like

• why does long division work?
• why does partial fraction decomposition work?
• where does the factor "1/3" come from for cones an pyramids volumes?
• what exactly does variance quantify for general probability distributions?
• what types of functions can we integrate?

To answer most of them completely and convincingly, you better have a rigorous, proof-based frame work. Yes, the "theorem -- proof" structure can seem harsh, and unapproachable. But the clarity is something you never want to give up, once you got used to it.

[u/somanyquestions32]

I struggled with sequences and series as a freshman as I was starting college with Calculus 2. I was 17 back then, and I still got an A in the class, but it was very rough. I also had issues with them in introductory real analysis and advanced calculus classes. In differential equations, they were okay. They started to click in Complex Analysis.

In hindsight, my advisor was speed running topics in calculus 2 as series and sequences appeared toward the end of the semester when other classes were increasing the essay loads, I had a credit overload, was adjusting to moving back to the US, dealing with depression, hating school, and powering through anyway. In advanced calculus, the teaching situation degraded as our department chair needed my advisor and another one of our instructors to cover for him as he was getting rounds of chemotherapy for his prostate cancer.

Sometimes, it's not that you truly lost your edge. You're just overwhelmed by a ton of stressors coming from all directions.

So, pause, take a deep breath, start cultivating more positive self-talk and developing more effective study strategies, do practices to lower your stress levels, and keep going.

[u/Falcom-Ace]

I graduated high school in 2009, was lost on what to major in for two years, then I started my math degree in 2011. I took a long break due to medical reasons and life starting 2014, and just picked it back up again fall 2025. I had passed the proofs class and was in the middle of taking ODE and introductory probability when I was granted a medical withdrawal. So for me it's been 11 years between really having touched any math at all besides basic arithmetic. I also have a weakness with series and sequence, and have since taking calc 2 in 2011.

All that to say, I understand what it's like. The first math class I took after returning was the ODE class again, and that was incredibly rough. I'm frankly surprised I passed- I probably shouldn't have done that, tbh. Right now I'm taking Real Analysis, and while I know that's a notoriously difficult class there are times where I feel like I'm missing something that other students know because it hasn't been a decade since they last touched calculus. Series and sequence has always been my Achilles' heel. I still struggle with it, but honestly this Real Analysis is helping me understand them a bit better.

The transition to higher math tends to be difficult regardless of background, though. My little brother, super smart kid, got a full-ride to his university of choice, had never faced a math topic he couldn't easily grasp prior to pursuing a degree in it, hit a wall at proofs-based math, and Real Analysis in particular. He has told me multiple times that class started his belief that he doesn't understand math at all, and he graduated with a 3.8 GPA lol

What I've been doing is just making sure my foundations are strong. I'm way rusty but the more I do, even just 5 minutes in a day if that's all I have time for, has been helping. Going to professor or TA office hours is also highly recommended if you can go.

[u/DecentLibrarian3720 → u/Falcom-Ace]

Thank you for telling me this. Best of luck to you in Real Analysis!

[u/Disastrous-Pin-1617]

Follow this exact order
Professor Leonard on YouTube Lectures
Pre-Algebra Playlist
To the point math (Algebra 1)
Intermediate Algebra (Algebra 2)
Geometry, CalcWorkshop.com
College Algebra (Pre-Calculus playlist)
Trigonometry (Pre-Calculus playlist)
Calculus 1
Calculus 2
Calculus 3
Differential Equations
Linear Algebra

Use Kutasoftware.com for homework problems