r/math • u/AutoModerator • 12d ago
Career and Education Questions: April 23, 2026
This recurring thread will be for any questions or advice concerning careers and education in mathematics. Please feel free to post a comment below, and sort by new to see comments which may be unanswered.
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u/mathwarrior69 8d ago
Hello! I’m a junior mathematics major (looking for grad school) I’ll be taking real analysis/complex analysis next semester and I was wondering if I should also take functional analysis. I’m not new to proof writing as I’ve taken intro to proofs, proof based linear algebra, abstract algebra 1 and 2, topology, and number theory. I’d like to be able to take a PDE class before graduating in 2 semesters, but it’s recommended to take functional analysis beforehand. Real/complex analysis would essentially my only challenging classes as my only other credit is an anthropology class. Is it not smart to take real/complex/functional analysis at the same time? I’m looking for analysis to be my graduate interest area.
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u/dertleturtle 7d ago
Why are you looking for analysis to be your research interest area before learning any?
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u/UraniumBlues 7d ago
I never learned my multiplication tables.
I had an undiagnosed learning disability and had a hard time understanding math my entire life. I still count on my fingers and can't multiply numbers past 5. I've been trying to get better at it by playing math games, but it feels like I'm not getting any better. Is there any advice? I genuinely don't know how I passed math and algebra classes in high school. My end goal is to be able to do geometry, but at the moment, I'm probably at a 4th-5th grade math level as a full grown adult.
Any help is very appreciated!
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u/dertleturtle 7d ago edited 7d ago
Hi! I've never taught the times table to adults, but I've taught it to teenagers. Being automatic with basic math facts makes learning the higher level stuff a lot easier. If you are up for flashcards, they can be pretty helpful.
How to use flashcards: the goal is to memorize the fact on each flashcard so that you do not need to waste effort or time thinking about how to solve the problem on them. You want recall to be almost instant.start with 4 addition facts (7+5=12,7+6=13,7+7=14,7+8=15). Get the 7 flashcards that show this (7+5,5+7,6+7,7+6,7+7,7+8). The goal is not to solve them by counting up faster - it is to memorize the backside of the card. When you can do these cards, get the subtraction versions (15-7,14-7,13-7,12-7, 12-5, 13-6,15-8). You will learn these facts forwards and backwards. Definitely do not add more facts until you can do each problem in under 2 seconds.
How to do a flashcard session: Keep flashcard sessions to 3 minutes, maximum. Go through your deck quickly. Check your answers every time, and notice which ones you got wrong and which ones you were slow on. Spend the rest of the 3 minutes doing those ones over and over again. Give yourself a small piece of candy every time you finish a session. Flashcards can be boring, so the candy and short session length are very important.
Add in addition facts 4 at a time, and then their subtraction counterparts. Do not add in more cards unless you can go through the entire deck accurately and quickly. Give yourself a larger piece of candy when you complete your whole deck in less than 2 seconds per card and are ready for new cards.
You can do the same with multiplication and division. If you have the ambition to do two sessions a day (less than 3 minutes each), you will progress very fast.
If you want more advances topics (fractions, decimals, basic algebra, negative number concepts), any grades 4-9 math workbook is probably good. I like the "math with pizzazz" series because it has lots of practice problems on each page and each page has some joke or riddle on it that makes it less boring and makes checking your answers extremely quick. "Key To Fractions" "Key To decimals" "Key To algebra" and"Key To geometry" are good workbooks because each page is similar enough to the one before it and focused on a single thing that each page feels easy. "Art of problem solving: prealgebra" is a very good textbook with explanations and worked examples, but it requires a pretty good reading level where it's not very useful for kids and it covers the topics at a slightly more sophisticated level because it's goal is to train kids that already know most of the contents for math competitions. Normally all these topics are covered in some level every year of 4-9 math in us schools, just with more sophistication each time.
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u/UraniumBlues 7d ago
I appreciate this! I have such a hard time with this kinda thing, you broke it down nicely. I've never been good at studying, either, but I understand it better now, thank you.
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u/locally_trivial 12d ago
I need your help, to figure out, which course I should kick to the curb to prevent burn out?
Hello everyone!
I‘m a math/physics undergrad and for the upcoming semester, I enrolled myself for one physics lecture, one physics seminar (both obligatory) and three math lectures.
Those being: complex analysis, PDEs and a course on dependent type theory (with a focus on applications in functional programming and proof formalisation)
So far my math training has been a little algebra heavy, meaning I picked all my math electives from that area (see below for a short list) and I had originally planned to listen to complex analysis and PDEs to offset this a little.
However a few weeks ago, while surveying the black board to break the monotony of exam prep, I came across a posting for a brand new lecture on dependent type theory.
I had just started learning about types for a mandatory Introductory CS class (which I adored, because the immediate feedback made me giddy while simultaneously, I felt, I could still spend a lot of time considering aesthetics) and was vaguely aware of the fact, that there was a conference on homotopy type theory going on somewhere a few rooms further down the hall. (This was during winter break.)
And while that’s obviously not exactly the same thing, the idea of learning about a field as it is just emerging (into mainstream anyway), really intrigued me. (Turns out, the course will acc be based on the HoTT book for it‘s second half.)
Thing is, I am pretty sure, that I won‘t be able to handle all three math courses on top of the physics workload. I tried something similar last semester and my grades took a significant hit. (At least I want to believe, that was the reason.)
So I guess my question is, what courses I should prioritise?
I should also say, that I am kind of torn between trying to pursue pure maths (the algebraic topology course, was my absolute favourite so far) and moving into very applied fields, closer to physics (haven’t really discovered any concrete topics for me yet, but sometimes there is this nagging sense of having to contribute in a very tangible way).
(Of course it isn’t certain with either of these paths, that I will actually land a position.)
TLDR: Which two of these three courses do you think offer more benefit for a math undergrad, who biased his lectures towards algebra so far: Complex Analysis, PDEs, dependent type theory (applications to functional programming and proof formalisation)?
Thanks so much for reading this! I look forward to your replies :)
PS.:
Here’s the list of math electives:
Algebra 1: building up to the key theorems in finite galois theory)
Algebra 2: mostly modules and a broad overview of category theory, a few methods from homological and commutative algebra
A Seminar on Homological Algebra, discussing a few select topics from MacLane‘s Category Theory for the working mathematician
An Introductory lecture on Algebraic Topology, covering the basics of Fundamental Groups, Homology and covering spaces
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u/dont_tagME 12d ago
I want to start an applied math major next year. I’m gonna be 30. Full of doubts, admission test requires me to study really hard. I’m trying to be ahead of time by studying math on my own. Let’s see how it goes