Favorite branch of math?

[danzibr]

I was sitting in the cafeteria with my son (he's in 1st grade) during breakfast recently, and the kids were talking about their favorite subject. My son said math, some kids said science.

And I got to thinking... man, science is pretty dang broad. Got Chemistry, Physics, Biology, Geology, et cetera.

Then I was thinking, man, math is pretty broad too. Which branch of math is your favorite? I'll list the ones that come to mind.

Arithmetic: playing with numbers and operations and stuff. Could be considered a subset of Algebra, or Number Theory I suppose. Also, could put counting techniques here, like combinations and permutations.
Number Theory: looking at properties of numbers, like prime numbers.
Set Theory: study of sets. This stuff gets pretty wacky and cool when you look at debatably esoteric sets, and especially topology.
Topology: study of... topologies! :P Open sets and continuity and whatnot.
Algebra: working with functions (tons and tons of types of functions), equations, etc. Probably think of graphing, too. I'd say graphing is a combination of Algebra and Geometry, though. I mean, a curve is a shape. Split into Linear Algebra (matrices) and Abstract Algebra (groups and rings and rngs and whatnot).
Geometry: here's another broad one. You might think like triangles and circles and discs and spheres and balls, area and volume and whatever, but then there are also metrics and, well, other things.
Statistics: in fact, a "statistic" is a numerical description of a sample, like mean, standard deviation, etc. Information related to collections of numbers.
Probability: likelihood of future events. Got basic stuff like rolling a sum of 7 to intermediate stuff like normal curves and Poisson distributions to advanced stuff (at least to me) like distribution of primes and the Euler-Riemann zeta function.
Trigonometry: angles, triangles, functions (sin, cos, tan, cot, sec, csc, inverses of these, sinh, cosh, tanh, etc).
Calculus: Algebra + Trigonometry + Limits. If Algebra is about what's happening for exact numbers, Calculus is about what's happening nearby. Split into Differential Calculus and Integral Calculus.
Differential Equations: Kinda falls under Calculus, but kinda not. The single biggest field of applied math, I would say.
Logic: dunno if math can really claim this. I took a logic class once, 2 math credits.
Distribution Theory: study of... distributions. The dual of test functions with the inductive limit topology (I think??? Been a while). It's like a generalization of functions, have some interesting and useful applications.

Probably forgot one or two.

For me, my two favorites would be Probability and Metric Geometry. Then probably Calculus.

What's yours?

[BWR]

SEP: Somebody Else's Problem(s) - the math that other people do so I don't have to.
Also, the stuff the Laundryverse uses to power magic. Just make sure that equation you're working on won't eat you.

[Algeh]

I liked Discrete Math a lot when I took it back in college, but I've never been able to take higher-level classes that would directly follow from it. I also really liked Abstract Algebra but never got to take any classes in it beyond the 300 level.

In terms of stuff I get to teach regularly (middle and high school math topics), I usually like teaching Geometry, although this year I have too many Geometry students and I'm getting burned out on trying to give them detailed feedback on their proofs. I just can't find an easy way to teach them proper proofwriting that doesn't involve a lot of time per student and allowing revisions after giving them a set of comments. (It would help if they did the reading, of course. When I asked them to prove that opposite sides of a parallelogram were congruent on their last test, many of them had trouble remembering what a parallelogram was despite the fact than an entire week of their online lessons were about various parallelogram proofs...I can understand not remembering the specifics of the various individual proofs later and needing to reason them out from scratch (which is good practice anyway), but if you recently spent an entire week looking at proofs about them you should be able to remember what a parallelogram looks like and not draw a trapezoid or triangle instead.)

[2D8HP]

For my trade, my Union's school taught "practical trigonometry" (for measuring pipe distances), but none of the theory of why it works (I never got to learn any in High School, and didn't have the privilege of a college education), they also re-taught algebra, which I found interesting, so algebra is my pick.

I really have to contrast how mathematics was taught in my Unions school to high it was taught in my California High School in the 1980's, my apprenticeship had me go to class twice a week for three to four hours at night (exhausting because it was impossible to get eight hours of sleep before going to work the next day, even if you slept in your car) with less then 25 other apprentices instead of high school which had 40 students in each class, and you'd go five days a week of five or six classes of about 40 minutes each.

I'm still very bitter about how education is rationed, with the biggest lesson "taught" being how to duck and dodge, my best grades came from my seeing an open door one day behind which textbooks were kept, quickly stealing some, and reading them during the long summer break.

What other "lessons" I got were from the library, and from reading my wife's college textbooks.

[Peelee]

I'm still very bitter about how education is rationed, with the biggest lesson "taught" being how to duck and dodge

Can you extrapolate on this? I went to private school, so while I'm a huge proponent of public schools in theory, I don't know how they actually work.

[eggynack]

My two favorite math classes were probably graph theory and mathematical logic. Logic had this really interesting test structure where some of the questions involved proving stuff that was entirely new to the class. And graph theory is just always great.

[Sajiri]

I'm going to admit, I really loved algebra. Not sure why, I guess I just enjoyed the problem solving of it.

When I was in high school I was sorted into advanced mathematics classes, but in my senior year we were allowed to choose whether we wanted to do advanced or standard math classes. Because I had a lot of other heavy subjects, I went for standard, then realised I really missed advanced as this one didn't do algebra (and felt like the class was stuff I'd covered back at the end of primary/grade school)

Cant really claim any further education on it, since now I work with special-needs 6-8 year olds so really the most advanced maths I have to know is basic multiplication and division.

[Lvl 2 Expert]

Statistics.

Never was any good at it, but it's both the most relevant to my line of work (aside from maybe simple calculations of dilutions and stuff) and one of the parts of math I always liked best.

[2D8HP]

Can you extrapolate on this?....

.

Spoiler: off topic extrapolation

Show

My school years were in the 1970's and '80's, so I'm unsure if there much lessons to be drawn, as (I hope) things are different now, but basically elementary/junior high school I remember as lots of unsupervised time where they would set us loose, or "PE" which would be tennis and volleyball for the girls, and unsupervised "smear the queer" for the boys, you can "Google" the "rules", but I remember the "game" as being basically acting out a lynch mob posse against whomever brave/bold/unlucky guy had the ball, or every so often a circle would form with two guys in the center who the rest elected to have a fist fight, most of the time if you were elected both of you would try to play act it out just enough to not receive a beating for "fakin'" (so a narrow line), but at least once a year some scared or mean boy would fight enough to draw blood, and someone would go to the school nurse, I have no memories of adults every putting a stop to it, my solution during my last year of Junior High School was to leave school most every day, and walk a mile to go to the library (I was an avid reader).

Thankfully High School didn't have that kind of scheduled violence (unless you played football), the closest I got was when I was accidentally stabbed in the arm during fencing class (the rubber tip broke off the foil), I was quite proud of my "dueling scar" (I had parried the foil away from my chest), and I was sad when years latter the scar healed enough to be barely visible. My High School had over 3,000 students (that's more people than two of my Union Locals have had working members), and it had an "open campus" meaning you"d leave to go to lunch, so one day just outside of school I was knocked unconscious by a group of boys who I didn't recognize, I returned to class late and bruised (ironically the class was an "Elective" "Criminal Law" class that was taught by a teacher who had gone to Law School but never passed the BAR exam (I actually do remember his teaching us how he avoided being drafted by the Army, so I did learn something other than ducking and dodging after all). The teacher saw my condition, asked me what happened, and then told me, "That's what you get for walking alone".

My father was already pulling me out of school to work cement and hauling jobs with him anyway, and I had on my own gone to a night class at a "community college" (not a University, we'd call it "High School with ashtrays"), after I completed one semester of that class, I was told that I couldn't take another semester beacause I was under 18, unless I got permission from my High School, so I got an appointment with a guidance counselor who told me that to get permission to take anymore classes at the community "college" I would have to pass something called the "California High School Proficiency Exam", which I did one Saturday at a small office between the High School and the Library, the exam was long, but the questions were easy, after I passed it I did have permission to attend more classes at the community college, and I was told that legally I had just graduated High School early, and could no longer be a High School student as well, upon hearing the news my mother said "Your not living here just to go to a ghetto school", (she went to UC Berkeley, and had a low opinion of other colleges), and her boyfriend got a job at his work. In time I would get a different job, meet my future wife who was going to law school (she is a couple of years older than me), I moved in with her, she dropped out of Law school, and I've been the income earner ever since.

If I was to design an "education system" based on my desires as a youth, they'd be some adults keeping the schoolyard from becoming "Lord of the Flies" and I'd have more time to read and have questions answered, but the truth is my childhood hopes were to be an astronomer, astronaut, or librarian, but there too many others willing and better able to do those jobs, and the most utility that society could get out of me is to have me in my place, as people ask for plumbers more than poets or philosophers, come "Gattaca" it will be even more clear who goes where, and it will be better known to whom to give out rarions of educatiom so that more will know their place earlier and fewer will have false dreams of better things.

[Knaight]

I quite like calculus, differential equations, and probability. All are a lot of fun, all include a lot of really interesting material, all are really powerful tools.

Still, for my very favorite I have to jump back a bit, to some fairly basic math. I'm talking about algebra - not linear algebra in particular, not abstract algebra much at all, but simple workhorse algebra. So often the main practical use of calculus and differential equations is to derive algebra functions, and these huge sets of algebra functions end up supporting scientific and engineering model after scientific and engineering model. It's unglamorous, it's relatively simple, and it gets the job done.

[tensai_oni]

Game theory.

Complicated but has so many uses - the go to branch to show sceptics who say "but what practical use does it have anyway?" If they manage to understand any of it that is.

Also it has a lot of really cool task solving and makes you think outside the box.

[danzibr]

Great responses!

I just did some reading on Game Theory, only the basics, but I gotta say I like it a lot. Wish I'd taken a course on it.

[Fri]

Can't exactly think one from the top of my head but I do have one specific favorite math story. That is, the German tank problem, where the allied intelligence estimated the number off German tank using math more accurately than using spies.

https://en.m.wikipedia.org/wiki/Germ...em?wprov=sfla1

[NontheistCleric]

Geometry. I never liked any kind of math in particular, but geometry was the only branch I was at least good at.

[aspi]

I'll toss in combinatorics, which in my opinion is definitely one of the "one or two" that you forgot

Among the subfields of combinatorics, my favorites are definitely graph theory and formal languages - but since I'm a computer scientist that is probably not very surprising.

[Jaxzan Proditor]

My favorite would probably have to be the one I’m struggling though now: Calculus. Then again, there are plenty of areas that I’d love to learn more about.

[Mith]

.

Spoiler: off topic extrapolation

Show

My school years were in the 1970's and '80's, so I'm unsure if there much lessons to be drawn, as (I hope) things are different now, but basically elementary/junior high school I remember as lots of unsupervised time where they would set us loose, or "PE" which would be tennis and volleyball for the girls, and unsupervised "smear the queer" for the boys, you can "Google" the "rules", but I remember the "game" as being basically acting out a lynch mob posse against whomever brave/bold/unlucky guy had the ball, or every so often a circle would form with two guys in the center who the rest elected to have a fist fight, most of the time if you were elected both of you would try to play act it out just enough to not receive a beating for "fakin'" (so a narrow line), but at least once a year some scared or mean boy would fight enough to draw blood, and someone would go to the school nurse, I have no memories of adults every putting a stop to it, my solution during my last year of Junior High School was to leave school most every day, and walk a mile to go to the library (I was an avid reader).

Thankfully High School didn't have that kind of scheduled violence (unless you played football), the closest I got was when I was accidentally stabbed in the arm during fencing class (the rubber tip broke off the foil), I was quite proud of my "dueling scar" (I had parried the foil away from my chest), and I was sad when years latter the scar healed enough to be barely visible. My High School had over 3,000 students (that's more people than two of my Union Locals have had working members), and it had an "open campus" meaning you"d leave to go to lunch, so one day just outside of school I was knocked unconscious by a group of boys who I didn't recognize, I returned to class late and bruised (ironically the class was an "Elective" "Criminal Law" class that was taught by a teacher who had gone to Law School but never passed the BAR exam (I actually do remember his teaching us how he avoided being drafted by the Army, so I did learn something other than ducking and dodging after all). The teacher saw my condition, asked me what happened, and then told me, "That's what you get for walking alone".

My father was already pulling me out of school to work cement and hauling jobs with him anyway, and I had on my own gone to a night class at a "community college" (not a University, we'd call it "High School with ashtrays"), after I completed one semester of that class, I was told that I couldn't take another semester beacause I was under 18, unless I got permission from my High School, so I got an appointment with a guidance counselor who told me that to get permission to take anymore classes at the community "college" I would have to pass something called the "California High School Proficiency Exam", which I did one Saturday at a small office between the High School and the Library, the exam was long, but the questions were easy, after I passed it I did have permission to attend more classes at the community college, and I was told that legally I had just graduated High School early, and could no longer be a High School student as well, upon hearing the news my mother said "Your not living here just to go to a ghetto school", (she went to UC Berkeley, and had a low opinion of other colleges), and her boyfriend got a job at his work. In time I would get a different job, meet my future wife who was going to law school (she is a couple of years older than me), I moved in with her, she dropped out of Law school, and I've been the income earner ever since.

If I was to design an "education system" based on my desires as a youth, they'd be some adults keeping the schoolyard from becoming "Lord of the Flies" and I'd have more time to read and have questions answered, but the truth is my childhood hopes were to be an astronomer, astronaut, or librarian, but there too many others willing and better able to do those jobs, and the most utility that society could get out of me is to have me in my place, as people ask for plumbers more than poets or philosophers, come "Gattaca" it will be even more clear who goes where, and it will be better known to whom to give out rarions of educatiom so that more will know their place earlier and fewer will have false dreams of better things.

Spoiler

Show

I would say that education should be well rounded in all respects, since one cannot find something that clicks until they learn it. Personally, I am of the opinion that barring learning disabilities, reading maths, basic science, logic, history and geography should all be within the reach of any student. In junior high, some form of shop and home ed. should exist to teach hands on work and how to actually cook if you don't learn at home to broaden the horizons of what you can do.

Perhaps being a plumber would be your best fit, but I don't think one can assign that choice to a person based on "natural aptitude". You have to give people knowledge and see where they go with it. Dreams of being an astronaut at the age of 6 may not be a strong dream. Refining that interest in the sciences over the years can put that kid as an adult in some really interesting fields.

[2D8HP]

Spoiler

Show

I would say that education should be well rounded in all respects, since one cannot find something that clicks until they learn it. Personally, I am of the opinion that barring learning disabilities, reading maths, basic science, logic, history and geography should all be within the reach of any student. In junior high, some form of shop and home ed. should exist to teach hands on work and how to actually cook if you don't learn at home to broaden the horizons of what you can do.

Perhaps being a plumber would be your best fit, but I don't think one can assign that choice to a person based on "natural aptitude". You have to give people knowledge and see where they go with it. Dreams of being an astronaut at the age of 6 may not be a strong dream. Refining that interest in the sciences over the years can put that kid as an adult in some really interesting fields.

.

Spoiler: for Mith

Show

Your "shoulds" sound like a wonderful dream, it's good if children get that, even better if more children get those "shoulds", great if all children get enough of a good ration of education and get to learn and thrive.

I wouldn't hold my breath waiting.

[Peelee]

.

Spoiler: off topic extrapolation

Show

My school years were in the 1970's and '80's, so I'm unsure if there much lessons to be drawn, as (I hope) things are different now, but basically elementary/junior high school I remember as lots of unsupervised time where they would set us loose, or "PE" which would be tennis and volleyball for the girls, and unsupervised "smear the queer" for the boys, you can "Google" the "rules", but I remember the "game" as being basically acting out a lynch mob posse against whomever brave/bold/unlucky guy had the ball, or every so often a circle would form with two guys in the center who the rest elected to have a fist fight, most of the time if you were elected both of you would try to play act it out just enough to not receive a beating for "fakin'" (so a narrow line), but at least once a year some scared or mean boy would fight enough to draw blood, and someone would go to the school nurse, I have no memories of adults every putting a stop to it, my solution during my last year of Junior High School was to leave school most every day, and walk a mile to go to the library (I was an avid reader).

Thankfully High School didn't have that kind of scheduled violence (unless you played football), the closest I got was when I was accidentally stabbed in the arm during fencing class (the rubber tip broke off the foil), I was quite proud of my "dueling scar" (I had parried the foil away from my chest), and I was sad when years latter the scar healed enough to be barely visible. My High School had over 3,000 students (that's more people than two of my Union Locals have had working members), and it had an "open campus" meaning you"d leave to go to lunch, so one day just outside of school I was knocked unconscious by a group of boys who I didn't recognize, I returned to class late and bruised (ironically the class was an "Elective" "Criminal Law" class that was taught by a teacher who had gone to Law School but never passed the BAR exam (I actually do remember his teaching us how he avoided being drafted by the Army, so I did learn something other than ducking and dodging after all). The teacher saw my condition, asked me what happened, and then told me, "That's what you get for walking alone".

My father was already pulling me out of school to work cement and hauling jobs with him anyway, and I had on my own gone to a night class at a "community college" (not a University, we'd call it "High School with ashtrays"), after I completed one semester of that class, I was told that I couldn't take another semester beacause I was under 18, unless I got permission from my High School, so I got an appointment with a guidance counselor who told me that to get permission to take anymore classes at the community "college" I would have to pass something called the "California High School Proficiency Exam", which I did one Saturday at a small office between the High School and the Library, the exam was long, but the questions were easy, after I passed it I did have permission to attend more classes at the community college, and I was told that legally I had just graduated High School early, and could no longer be a High School student as well, upon hearing the news my mother said "Your not living here just to go to a ghetto school", (she went to UC Berkeley, and had a low opinion of other colleges), and her boyfriend got a job at his work. In time I would get a different job, meet my future wife who was going to law school (she is a couple of years older than me), I moved in with her, she dropped out of Law school, and I've been the income earner ever since.

If I was to design an "education system" based on my desires as a youth, they'd be some adults keeping the schoolyard from becoming "Lord of the Flies" and I'd have more time to read and have questions answered, but the truth is my childhood hopes were to be an astronomer, astronaut, or librarian, but there too many others willing and better able to do those jobs, and the most utility that society could get out of me is to have me in my place, as people ask for plumbers more than poets or philosophers, come "Gattaca" it will be even more clear who goes where, and it will be better known to whom to give out rarions of educatiom so that more will know their place earlier and fewer will have false dreams of better things.

Spoiler: Unrelated to the thread

Show

That.... sounds ridiculous. Like, how can a parent hear about that and not go and raise holy hell with the administration about it? Though I freely admit I have no idea how effective that would be in a large school like that.

[Mith]

.

Spoiler: for Mith

Show

Your "shoulds" sound like a wonderful dream, it's good if children get that, even better if more children get those "shoulds", great if all children get enough of a good ration of education and get to learn and thrive.

I wouldn't hold my breath waiting.

Spoiler

Show

I feel it is worthwhile to push for it. The way I look at it, if you get one generation there, then the work gets easier from there. Education begets education. We can not know what we lose when a person loses that interest. Also common issues such as the rise of diseases due to anti vaccination beliefs would end because people understand how things work.

For now though, alas it is just a dream.

As for favourite branch of maths, basic calculus is the easiest part of maths I ever learned once I wrapped my head around it.

[Algeh]

.

Spoiler: off topic extrapolation

Show

My school years were in the 1970's and '80's, so I'm unsure if there much lessons to be drawn, as (I hope) things are different now, but basically elementary/junior high school I remember as lots of unsupervised time where they would set us loose, or "PE" which would be tennis and volleyball for the girls, and unsupervised "smear the queer" for the boys, you can "Google" the "rules", but I remember the "game" as being basically acting out a lynch mob posse against whomever brave/bold/unlucky guy had the ball, or every so often a circle would form with two guys in the center who the rest elected to have a fist fight, most of the time if you were elected both of you would try to play act it out just enough to not receive a beating for "fakin'" (so a narrow line), but at least once a year some scared or mean boy would fight enough to draw blood, and someone would go to the school nurse, I have no memories of adults every putting a stop to it, my solution during my last year of Junior High School was to leave school most every day, and walk a mile to go to the library (I was an avid reader).

Thankfully High School didn't have that kind of scheduled violence (unless you played football), the closest I got was when I was accidentally stabbed in the arm during fencing class (the rubber tip broke off the foil), I was quite proud of my "dueling scar" (I had parried the foil away from my chest), and I was sad when years latter the scar healed enough to be barely visible. My High School had over 3,000 students (that's more people than two of my Union Locals have had working members), and it had an "open campus" meaning you"d leave to go to lunch, so one day just outside of school I was knocked unconscious by a group of boys who I didn't recognize, I returned to class late and bruised (ironically the class was an "Elective" "Criminal Law" class that was taught by a teacher who had gone to Law School but never passed the BAR exam (I actually do remember his teaching us how he avoided being drafted by the Army, so I did learn something other than ducking and dodging after all). The teacher saw my condition, asked me what happened, and then told me, "That's what you get for walking alone".

My father was already pulling me out of school to work cement and hauling jobs with him anyway, and I had on my own gone to a night class at a "community college" (not a University, we'd call it "High School with ashtrays"), after I completed one semester of that class, I was told that I couldn't take another semester beacause I was under 18, unless I got permission from my High School, so I got an appointment with a guidance counselor who told me that to get permission to take anymore classes at the community "college" I would have to pass something called the "California High School Proficiency Exam", which I did one Saturday at a small office between the High School and the Library, the exam was long, but the questions were easy, after I passed it I did have permission to attend more classes at the community college, and I was told that legally I had just graduated High School early, and could no longer be a High School student as well, upon hearing the news my mother said "Your not living here just to go to a ghetto school", (she went to UC Berkeley, and had a low opinion of other colleges), and her boyfriend got a job at his work. In time I would get a different job, meet my future wife who was going to law school (she is a couple of years older than me), I moved in with her, she dropped out of Law school, and I've been the income earner ever since.

If I was to design an "education system" based on my desires as a youth, they'd be some adults keeping the schoolyard from becoming "Lord of the Flies" and I'd have more time to read and have questions answered, but the truth is my childhood hopes were to be an astronomer, astronaut, or librarian, but there too many others willing and better able to do those jobs, and the most utility that society could get out of me is to have me in my place, as people ask for plumbers more than poets or philosophers, come "Gattaca" it will be even more clear who goes where, and it will be better known to whom to give out rarions of educatiom so that more will know their place earlier and fewer will have false dreams of better things.

Spoiler: Unrelated to the thread

Show

That.... sounds ridiculous. Like, how can a parent hear about that and not go and raise holy hell with the administration about it? Though I freely admit I have no idea how effective that would be in a large school like that.

Spoiler: Education, advocacy, and diploma requirements

Show

I was told in 6th grade that I did not qualify for any accommodations for my learning disabilities because I was already meeting academic graduation standards so it didn't matter if I didn't learn anything in the next 6 years of school without services, they didn't have to provide any.

They did not offer to just let me graduate in the middle of 6th grade at age 11 (not sure if my parents would have gone for that or not), just made it clear they weren't going to do anything to help me succeed and that my problems were my problems rather than theirs.

Specifics about my disabilities: I have dysgraphia and to this day have trouble forming letters correctly sometimes ("p" is particularly hard for some stupid reason). The main accommodation I wanted was to be able to type rather than handwrite my schoolwork and to not have to try to take notes while I was listening, because I can either think about how letters work OR listen to what someone is saying, but probably not both. I also have an audio processing issue, a working memory issue, and some general left/right confusion that combine with my dysgraphia to make taking notes from lecture even more of a mess. On the other hand, I'm a very fast reader and learn really well from text, so I could pretty much teach myself most things from textbooks if left alone to do so.

My parents were NOT impressed with this answer, but the best they could do in the short term was to pull me out and put me in private school for a year while they argued more with the school district. After about a year of my parents having a lawyer send them a bunch of letters and such, they agreed to put me into a magnet school within the school district if it would get my parents to stop threatening legal action. They still wouldn't identify me as needing disability services, but they decided that I could have a "gifted student plan" that let me go to that magnet school, which was basically an hippy alternative school with a lot of student freedom to choose what you did with your studies. That in turn let me learn a lot of stuff by reading on my own, which worked out given that I learn well that way.

I graduated a year early by getting all of my credits in 3 years of high school instead of 4 because I kept finding independent study projects that interested me to work on. Because my parents knew a lot about colleges, they were able to steer me through which ones to apply to, and in college they FINALLY recognized my disability and let me type things (or have extended time on handwritten tests so I could waste testing time figuring out how to form letters) if I needed to.

It takes not only interested parents to do that, but also parents with a high level of social capital and knowledge of the system. We had multiple educators and lawyers in my parents' network of friends that they could consult if they had questions, and they had the money to pull me out and put me in private school as a stopgap. Not all parents can do that.

The main gap in my education due to all of that was that I never took a proper math class after 6th grade until college, where I placed into the lowest non-remedial class (elementary functions/precalc) due to not really having taken most of the middle or high school math curriculum in an actual class rather than just poking at some of the interesting bits on my own (the interesting parts to me at the time were mostly set theory and probability, which may not have helped matters with the college placement test).

Getting from there to proper math-major courses was an adventure in itself, but I kept trying because I really liked computers and my college's only computer-related degree was a "Computer Science and Mathematics" degree offered through the math department. Once I figured out that proofs meant there was a reason for everything and it wasn't just a bunch of disconnected memorizing I did really well at math, but it was a rough journey until I got through calc and hit the proof-based classes they only have math majors take.

[Goaty14]

My favorite math is calculator math -- the kind that I don't have to do

[Jay R]

Operations Research - game theory, scheduling, networks, linear programming. The mathematics of decision making.

That's what my Ph.D. is in, and my patents are about telecom switch scheduling.

I also may have been the first to officially apply game theory to D&D, having written an undergraduate paper on the combat system in original D&D, back in 1976.

[Mith]

I also may have been the first to officially apply game theory to D&D, having written an undergraduate paper on the combat system in original D&D, back in 1976.

Interesting. Could you share the paper in any way for others to read?

[Jay R]

Interesting. Could you share the paper in any way for others to read?

Nope. I threw away my undergraduate files a long time ago. Pretty much it was putting the weapon choices into a large min/max matrix. The main result was that a halberd was the best overall weapon (which nobody used).

The professor's biggest comment on the paper was that the magic shouldn't have been left out; it could be optimized too. [I agree, but that would have been a much bigger project, and beyond me at that time.]

[pendell]

.

Spoiler: off topic extrapolation

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My school years were in the 1970's and '80's, so I'm unsure if there much lessons to be drawn, as (I hope) things are different now, but basically elementary/junior high school I remember as lots of unsupervised time where they would set us loose, or "PE" which would be tennis and volleyball for the girls, and unsupervised "smear the queer" for the boys, you can "Google" the "rules", but I remember the "game" as being basically acting out a lynch mob posse against whomever brave/bold/unlucky guy had the ball, or every so often a circle would form with two guys in the center who the rest elected to have a fist fight, most of the time if you were elected both of you would try to play act it out just enough to not receive a beating for "fakin'" (so a narrow line), but at least once a year some scared or mean boy would fight enough to draw blood, and someone would go to the school nurse, I have no memories of adults every putting a stop to it, my solution during my last year of Junior High School was to leave school most every day, and walk a mile to go to the library (I was an avid reader).

Thankfully High School didn't have that kind of scheduled violence (unless you played football), the closest I got was when I was accidentally stabbed in the arm during fencing class (the rubber tip broke off the foil), I was quite proud of my "dueling scar" (I had parried the foil away from my chest), and I was sad when years latter the scar healed enough to be barely visible. My High School had over 3,000 students (that's more people than two of my Union Locals have had working members), and it had an "open campus" meaning you"d leave to go to lunch, so one day just outside of school I was knocked unconscious by a group of boys who I didn't recognize, I returned to class late and bruised (ironically the class was an "Elective" "Criminal Law" class that was taught by a teacher who had gone to Law School but never passed the BAR exam (I actually do remember his teaching us how he avoided being drafted by the Army, so I did learn something other than ducking and dodging after all). The teacher saw my condition, asked me what happened, and then told me, "That's what you get for walking alone".

My father was already pulling me out of school to work cement and hauling jobs with him anyway, and I had on my own gone to a night class at a "community college" (not a University, we'd call it "High School with ashtrays"), after I completed one semester of that class, I was told that I couldn't take another semester beacause I was under 18, unless I got permission from my High School, so I got an appointment with a guidance counselor who told me that to get permission to take anymore classes at the community "college" I would have to pass something called the "California High School Proficiency Exam", which I did one Saturday at a small office between the High School and the Library, the exam was long, but the questions were easy, after I passed it I did have permission to attend more classes at the community college, and I was told that legally I had just graduated High School early, and could no longer be a High School student as well, upon hearing the news my mother said "Your not living here just to go to a ghetto school", (she went to UC Berkeley, and had a low opinion of other colleges), and her boyfriend got a job at his work. In time I would get a different job, meet my future wife who was going to law school (she is a couple of years older than me), I moved in with her, she dropped out of Law school, and I've been the income earner ever since.

If I was to design an "education system" based on my desires as a youth, they'd be some adults keeping the schoolyard from becoming "Lord of the Flies" and I'd have more time to read and have questions answered, but the truth is my childhood hopes were to be an astronomer, astronaut, or librarian, but there too many others willing and better able to do those jobs, and the most utility that society could get out of me is to have me in my place, as people ask for plumbers more than poets or philosophers, come "Gattaca" it will be even more clear who goes where, and it will be better known to whom to give out rarions of educatiom so that more will know their place earlier and fewer will have false dreams of better things.

I can attest to the accuracy of 2DHP's statement, because this is exactly what I went through in 1970s-1980s California elementary school (Placentia Unified School District - Ruby Drive Elementary School, Topaz Elementary School - 1977-1982).

Recesses were a nightmare for precisely the reasons he states. Gangs of children picking on the small and weak. I learned to hide in the library.

Things straightened up in Junior High, as the Vice Principal of Bernardo Yorba Junior High School was a very tough, strict man who tolerated no nonsense. It was even better when I moved to Northern Virginia, where rich parents and competitive private schools made Fairfax County public schools the envy of the nation -- at least in 1989.

Respectfully,

Brian P.

[2D8HP]

I can attest to the accuracy of 2DHP's statement, because this is exactly what I went through in 1970s-1980s California elementary school......

Spoiler: Response

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Such were the joys of a kinder, gentler time!.

Oh wait, what do you call the exact opposite?

The only way it makes sense to me is to think of it as a program to get children willing to accept and/or inflict pain and suffering, left over from times that desired warriors and workers, not scholars and scientists.

I am (obviously from many of my posts) still enchanted by a lot of 1970's and '80's (and earlier) media, but anyone who thinks "everything was better then" seems wackadoodle to me as I don't miss the fists and gunshots at all!

Thanks B. P., and sorry to learn you remember the like.

[Aliquid]

I can attest to the accuracy of 2DHP's statement, because this is exactly what I went through in 1970s-1980s California elementary school (Placentia Unified School District - Ruby Drive Elementary School, Topaz Elementary School - 1977-1982).

Recesses were a nightmare for precisely the reasons he states. Gangs of children picking on the small and weak. I learned to hide in the library.

Things straightened up in Junior High, as the Vice Principal of Bernardo Yorba Junior High School was a very tough, strict man who tolerated no nonsense. It was even better when I moved to Northern Virginia, where rich parents and competitive private schools made Fairfax County public schools the envy of the nation -- at least in 1989.

Respectfully,

Brian P.

Out of curiosity... how big were these elementary schools? (you and 2D8HP). For me, Elementary was benign, and it wasn't until Junior High that things got rough. I had assumed it was because my Junior High had so many more students (probably about 7 times bigger), and it was easier for jerks to band together, rather than just be the "lone bully".


But I might have had a different experience because I wasn't in the US... We were never unsupervised in elementary school, except at lunch and recess, and even then there were a couple teachers patrolling the playground. Even PE was structured, where we were taught how to play specific sports, or just made to climb ropes and do long jump, or some annoying stuff like that.

[AsteriskAmp]

I was sitting in the cafeteria with my son (he's in 1st grade) during breakfast recently, and the kids were talking about their favorite subject. My son said math, some kids said science.

And I got to thinking... man, science is pretty dang broad. Got Chemistry, Physics, Biology, Geology, et cetera.

Then I was thinking, man, math is pretty broad too. Which branch of math is your favorite? I'll list the ones that come to mind.

Arithmetic: playing with numbers and operations and stuff. Could be considered a subset of Algebra, or Number Theory I suppose. Also, could put counting techniques here, like combinations and permutations.
Number Theory: looking at properties of numbers, like prime numbers.
Set Theory: study of sets. This stuff gets pretty wacky and cool when you look at debatably esoteric sets, and especially topology.
Topology: study of... topologies! :P Open sets and continuity and whatnot.
Algebra: working with functions (tons and tons of types of functions), equations, etc. Probably think of graphing, too. I'd say graphing is a combination of Algebra and Geometry, though. I mean, a curve is a shape. Split into Linear Algebra (matrices) and Abstract Algebra (groups and rings and rngs and whatnot).
Geometry: here's another broad one. You might think like triangles and circles and discs and spheres and balls, area and volume and whatever, but then there are also metrics and, well, other things.
Statistics: in fact, a "statistic" is a numerical description of a sample, like mean, standard deviation, etc. Information related to collections of numbers.
Probability: likelihood of future events. Got basic stuff like rolling a sum of 7 to intermediate stuff like normal curves and Poisson distributions to advanced stuff (at least to me) like distribution of primes and the Euler-Riemann zeta function.
Trigonometry: angles, triangles, functions (sin, cos, tan, cot, sec, csc, inverses of these, sinh, cosh, tanh, etc).
Calculus: Algebra + Trigonometry + Limits. If Algebra is about what's happening for exact numbers, Calculus is about what's happening nearby. Split into Differential Calculus and Integral Calculus.
Differential Equations: Kinda falls under Calculus, but kinda not. The single biggest field of applied math, I would say.
Logic: dunno if math can really claim this. I took a logic class once, 2 math credits.
Distribution Theory: study of... distributions. The dual of test functions with the inductive limit topology (I think??? Been a while). It's like a generalization of functions, have some interesting and useful applications.

Probably forgot one or two.

For me, my two favorites would be Probability and Metric Geometry. Then probably Calculus.

What's yours?

Calculus is not a branch proper so much as were universities lump up all of the real analysis for engineers they can muster. The branch should be Analysis, personally I find it a tedious abomination amalgamated with the refuses of topology but some people love it, some people are also masochists. The first might be a subset of the second. The delicate dance of the basic theorems and tools. A bit of topology on the reals mixed with elementary tools for function manipulation.

I wouldn't call Trigonometry a branch of math, it's either simple analysis or very weak geometry.

Differential Equations Not even close to calculus, the theory is far richer and deeper than what most are exposed to. It's closer to functional analysis and complex analysis than it seems from the rote memorization of the basic dumb solutions to the easy problems that are normally shown in the "Applied" versions of this sort of course. Not only that, it leads into the wonderful and terrifying world of Dynamic Systems, where Fractals goes from a meme from /sci/ and /r/iamverysmart to a serious point of discussion. The precise art of determining if dynamic systems have sensibility issues to initial conditions, solution uniqueness, stability and more importantly existence at all. The pure math side of it is a joy to behold and applied math has to dip in there as well because of how insanely delicate the problems are. My diffeq teacher used to say: "Other mathematicians laugh at DiffEq researchers. You change a single initial condition and you publish another paper. Yeah sure, but another initial condition might as well be an entirely different problem." Start the course laughing at the joke, finish the course crying because it's so right it hurts.

You may have missed:
Complex Analysis: The complex plane is wonderful and magic. If you pick the right family of functions (Holomorphic) your life is perfect. Define it in a small section and its unique for the rest of the space? Check. You can plug holes nicely? Check. Angles are preserved? Check. Easy to check if it's in the family? Check. Everything is SUPER WELL BEHAVED. Tons of analysis theorems are trivial with holomorphic functions! (Granted asking a function to be holomorphic is a ton). Different enough from Real Analysis to warrant a name on its own, deep enough to make a career out of it (combine liberally with Algebraic Topology and Dynamic Systems). Complex analysis deals with functions on the complex plane (duh), a specific family of functions in most cases. It might seem a ton of work for something so specific but holomorphic functions are everywhere and the theory is an odd case where historically you had TONS OF BRANCHES and then they realized that either they were actually just studying holomorphic functions or worse, just a subset of them. The fact that conformal maps end up being holomorphic, that a ton of derivative properties one could ask are just equivalent to being holomorphic and so on are simple natural proofs for a first course.

Category Theory: Doing the math, the monster math. What happens when you want to generalize math itself? A student travels to Argentina for a mysterious operation. Returns with a large cranial scar, speaks nonstop about the grace of Yoneda, the Universal Property is declared Dictator for Life by legions of followers, and announced to the world that "Ein Volk, Ein Tool, Ein Property". Poland becomes nervous. Joking aside Category Theory deals with Monads and Functors, and Arrows TM. It abstracts away as much as it can to try to express things in the most elegant language. It manages to represent and explain properties that spuriously appear all over math, it has extremely "weak" tools for itself which are able to prove stupidly strong results elsewhere. A personal favourite, though a layman explanation is beyond my means.

Algebraic Topology: More than the union of Algebra and Topology. A way of dealing with geometry without having to deal with all the grime, cruft and disgusting bits of analysis sticking to it, amongst other things. Algebraic Topology allows us many pipe dreams of mathematics... TODAY. Want to talk about holes? Homology. Want to talk about an 8 figure OBVIOUSLY being different than a circle? Homotopy. Want to calculate those complicated properties? Surgery. The joy of performing algebraic topology includes the ability to claim you are doing surgery on the sphere. The terminology is great, the applications are insane and it's an utter delight after you pass the initial pains of understanding CW Complexes and the proofs involving the Universal Lifting.

Computability Theory: Mainly applied math to CSci. Involves functions that are computable, a definition that takes half a semestre to pin down properly. It's basically Theoretical CSci which is VERY APPLIED MATH.

Convex Optimizatrion/Operations Research: Optimization of functions, finding extrema and minima. Useful for machine learning, economics, industrial processes... literally everything. It's just finding convex hulls 90% of the time.

Measure Theory (Probability should be inside here, not the other way around): Finding ways to split a sphere in twain while preserving volume. Measure theory expands the definition of what's a volume to arbitrary sets, and in the process finds an entire extremely fertile area of mathematics research. Related to what does it mean to say A LOT or ALMOST ALL or THE AVERAGE REAL. Has a massive amounts of useful tools, which appear in a lot of other areas.

Functional Analysis: Linear Algebra to the infinite power. Literally. Vector Fields of infinite dimension and more. Makes Dynamic Systems and Differential Equations bearable by excising the tumour of analysis from them and replacing it with far more elegant tools such as Sobolev Spaces.

And I'm still missing a ton I don't really have the time and in the case of several knowledge to go into.
Knot Theory, Lie Groups, Formal Languages, Galois Theory (which while technically algebra is wide enough to start eating away more things), Discrete Analysis, Representation Theory, Control Theory(you could chuck it in operations research). And the ignored stepchild no one really wants, philosophy of mathematics.

[2D8HP]

Out of curiosity... how big were these elementary schools? (you and 2D8HP).......

Spoiler: How many students

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35 to 45 years ago?

No idea.

A quick websearch tells me that the same school had 445 students in 2016, my old Junior High 561, and my High School 3,417.

My son who went to elementary school in an adjacent district this last decade that had 523 students in 2016, and his classes had 35 to 40 students each.

My son's elematary school had two lunches and recesses so only half would be out at the same time, I don't remember that for me but who knows?

Just like @pendell I would go to the library to escape, but I didn't go to the school library, I went to the public library, except on the rare occasions that I had some cash in which case I went to "Best of Two Worlds", "Comics & Comix", "Dark Carnival", "Gambit", "Games of Berkeley", or "The Other Change of Hobbit", so books, comics, ot games, and I stopped going to class after lunch or recess,there were no "truant officers", and I don't remember anyone mentioning that I was skipping school, I do remember that around age nine or ten I was told that I had to take a test adminstered by some adult who was not my teacher, maybe a social worker? And I was told that my arithmetic and writing skills were at or slightly below grade level, but my reading comprehension was already college level, which is ironic because the only college I attended was sneaking into the Doe Library, and Morrison Reading Room at the University of California, when I was a High school student, and also, no joke, me, my brother, and my DM actually for real explored the University steam tunnels (like the Tom Hanks movie) and we found bedding and sketch books of people who lived in them.

My schools were mostly close to the University, and in the 1970's and '80's there were demonstrations and riots, I remember seeing a mob being chased by police with billy clubs, another time I saw a police car on fire that was surrounded by a crowd, and once (this one I don't remember, my mother told me this) the wind actually carried tear gas to my pre-school/kindergarten.

My son doesn't understand when I tell him he's lucky to be bored.