Your favorite and least favorite fields of math?

Kyriakos

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Just a general question ;)

For me:

Favorite: Geometry, Limits, Probabilities, and (somewhat) Derivatives/anti-derivatives and optimisations there. Number relations too, of course, as with primes.

Least Favorite: Algebra. I dislike polyonymic analysis. (and i know very little about it, accordingly. But i inherently dislike the examination of n degree polyonyms as for solution types, and haven't yet felt inclined to read Galois on turning this into a symmetry field examination).

Curious/Neutral: Set Theory
 
Favorite: Discrete mathematics, Probability theory, Statistics, Number Theory, Analysis (derivatives, optimizations)
Less favorite: Linear algebra, diff. equations. Just more difficult to grasp intuitively.
 
Favourite: Trigonometry and Linear Algebra. I was decent with trigonometry, though I wasn't good at linear algebra all at it in college, but nowadays, I deal with those the most in my professional life and I have achieved most using those particular fields. I both cases, there is something vaguely satisfying about dealing with them.

My least favourite subjects would be probability and statistics. Those are boring, and hugely overrated.
 
My most favourite field of math is Combinatorics & optimization. I love that stuff. Got the highest mark in University in comb & opt. It's basically a class in which you learn how to count and work with theories involving graphs (not the usual types of graphs). A lot of people seem to hate it, because it's quite different from other types of math, so I guess people don't find it easy to get used to... and the connection between the two parts of it (comp - opt) is not readily apparent.. but my brain just seems to think in a way that makes it much easier to work in this field.

Linear algebra is something I always did well in as well - I just love proofs involving things doing things in multiple dimensions. I always found myself being able to visualise that stuff in my head somehow and make sense of it. Stimulated my mind. I will never forget calling up my grade 13 Algebra teacher and walking her through my work on the exam. She initially gave me something under 80%, but I noticed that I got 0 marks for a couple questions where something had to be proved. Well, see, I approach those types of questions from multiple angles, and not too infrequently end up with a completely different proof than what was in the textbook. Unless the question really steers you towards a certain method. But it was usually right - the logic flowed from one statement to the next and the body and soul of the proof was proper. Anyway, this teacher liked me in the first place and let me skip class ("as long as you understand", and I did), so that made it easier to walk her through my logic and get her to accept it.

My third most favourite part of math is Logic. Which in theory is not a part of math exactly, but in practice I took a couple courses that overlapped between Mathematical Logic and various types of Computer Science-related logic which always had a strong mathematical foundation. So they were basically math classes. And I guess the subject matter appeals to me as well.

My least favourite type of math is Calculus. Basically my introduction to calculus was as an applied math. That's how most people learn the subject, but I found the applications of calculus so esoteric that it did not interest me. Furthermore, the second half of the class which introduced me to the subject flipped it from applied to theoretical. We worked through the theorems from first principles.. which usually would excite me, but I found everything too abstract and at the same time specific - applicable to only a small subset of math problems/questions that I found interesting. I hated calculus in high school and I hated it in university. Instead of concepts I could base my understanding around, it seemed to be a subject where you base your understanding around formulas and "tricks". I prefer more pure maths, where everything "just clicks" and is based on some elegant set of ideas. I can then train my brain to accept those axioms and go from there. With Calculus that's a lot less intuitive, and so it always made me .. just feel bad.

I also never liked Statistics. I took a couple classes in university where the first two hours of the exam is just questions about different ways of birds flying into a forest and sitting on branches - and me then having to figure out the proper model and distribution for each scenario and the probability of various silly scenarios for each model.
 
God, your teacher had the worst approach to calculus. It's the same reason why I hated this one thermodynamics class.

Did you have to do delta-epsilon proofs?
 
I like arithmetic, because it's the form of math I'm best at. :(

I guess I'm okay with algebra and geometry too. I don't like any math when it has to do with Physics. Screw you Physics class.
 
I like geometry as presented by ancients who worked successfully without numbers.

I didn't like trigonometry, but I suspect that was just a matter of how it was taught when I encountered it. A lot of "memorize these identities" left me very disenchanted, as up until then math had always been something you understood, not something you memorized.
 
Favorite: not maths
Least favorite: Maths

Kidding, to a degree. My relation with maths is weird ; I like casually looking at numbers and figuring out relations (I figured out a few on my own before they were taught in school - basic stuff to actual proper maths, but not what they taught us), but I was never really good at it in an academic sense (and as such I lack the scholarly grounding to really follow high-end maths) because I never really got into the "write every step" mentality, or for that matter the "use the method we teach you, not an alternate method that also works" one so at some point I just gave up on school maths.
 
Favorite: not maths
Least favorite: Maths

Kidding, to a degree. My relation with maths is weird ; I like casually looking at numbers and figuring out relations (I figured out a few on my own before they were taught in school - basic stuff to actual proper maths, but not what they taught us), but I was never really good at it in an academic sense (and as such I lack the scholarly grounding to really follow high-end maths) because I never really got into the "write every step" mentality, or for that matter the "use the method we teach you, not an alternate method that also works" one so at some point I just gave up on school maths.

In school I was always the smart ass who told the teacher "I did show my work, I just don't have to do as much as you expect, apparently." My goal was to do every problem in a single step, or at least as few as I could manage.

Then I was involved in a cheating program, where I took a calculus course for another guy by correspondence. Everything had to be copied over into his handwriting, and enough steps had to be shown to establish the validity of the work. Since we could not afford to have him miscopy a sign or something along the way, and then copy a subsequent step correctly and show that he wasn't actually working from one step to the next I did every problem as if it were a textbook illustration; every step laid out in full detail.

By the time he finished the course the absolute beauty of it had me totally entranced. It is very high on my "if I knew then what I know now" list. I wish I had approached math that way in my own schooling.
 
I liked geometry in high school. It was the only math class I did well in
 
Statistics I find fascinating and useful. Geometry seems to be neither.
 
Diff eq this last semester was probably my favorite math class. I liked that it explained stuff from other classes that never really made sense. For instance, no one ever explained the leap between F = -kx to an equation for simple harmonic motion. They just told us to know it. But now getting from Hook's law to an equation for a spring's position makes perfect sense, even with damping, other forces, etc. This is pretty much true for a lot of things in the physics and engineering classes I've taken so far.
 
I've never been able to grok topology, so that's probably my least favorite.
 
I really liked linear algebra when I took it in college. For whatever reason, I found it made sense, and corresponded well with my natural mathematical talents.

I spent a fair amount of time dealing with formal logic. The concept is interesting enough, although I don't think it's something I would like to deal with all the time - it gets rather dry beyond a certain point. But it does extend to real-life logical reasoning as well, which is a useful application.

On the not-so-great side, I never liked trigonometry very much. I think memorizing the identities, and subsequent confusion between them when I didn't use them for long periods of time, was a significant part of it - why an identity would be the square root of two over two didn't really click. The other part of it that never really clicked is the meaning of cosine and sine. From an academic standpoint of identifying which parts of a triangle constituted each, I could give a correct answer, but I had no idea why they were called cosine and sine. So again, if I went a long time without using them, I'd get them confused. Tangent was slightly less bad, not because I knew where the name came from etymologically, but because the word was enough different to remember more reliably.

I've also had negative experiences with calculus. It was so-so in high school - I didn't like it as much as algebra, statistics, or discrete math, but the places where it was useful in physics were kind of cool. In college, after taking a semester without calculus to do linear algebra, coming back to calculus was painful. A poor professor didn't help, but I think there were other factors such as not being able to relate to the applications since I wasn't taking physics or other science courses that used it at the time. The memorization issue likely also factored in - memorizing things such as Stokes' Theorem without really understanding why they worked wasn't something that played to my strengths.

Ultimately, I switched from a planned major in math to majoring in computer science midway through college. My grades were consistently high in compsci, and consistently decreasing in math, which was a factor. But I think a lot of the reason why I was doing better, and really was more interested in compsci as well, was that I could relate to the applications of what I was studying. Even outside of the areas mentioned above, I was moving more into theoretical math as I took higher-level courses, and relating to it could often be difficult. As I got farther into college, I was looking forward to making a practical impact, so the difficulty in answering the question of, "what would I do with theoretical mathematics outside of academia?" discouraged me from studying it farther. I think a more hybrid approach between mathematics and either hard sciences or compsci, while still teaching the "why" of how things work, could have kept me more interested. As an example, coding theory was an interesting, if challenging, area to study in the math department, but I probably would have enjoyed it a lot more and got more from it if we'd had some compsci exercises where implemented some of the algorithms we were studying in computer code.

All in all, mathematics went from my favorite or tied for it every year through 8th grade, to middle-of-the-road in high school, to an area I no longer had much interest in by the end of college. Better teaching elsewhere was part of it (the English/literature department was way better in college than high school, for example), but a general difficulty seeing how it translated to the non-academic world was a large part of it as well. Academics for academics sake was good enough for me through a good part of high school, but by the end of college, it wasn't anymore.
 
I found GSCE maths super easy.

Then I understood nothing and failed A level maths.

I don't even!
 
As someone half way through a PhD in Stats, favourite should be obvious.

I hate doing proofs of things. I have no interest in that, someone else has done it and others have verified it, I just want to utilise that knowledge not revisit it.
 
I'll be a math heathen and say partial diff eq or diff eq.

Something made me feel smart if I say, Bessel function of the first kind.

Least favorite is whatever vector algebra is with Hilbert spaces, because that junk was hard.

I unfortunately dont get to use any of the math I learned, and I'm super bad at doing things informally. Like I can't figure out permutations or something intuitively. I'd have to recall formal methods (i.e. look them up)
 
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