Mathematics

[EyeSeeCold]

What is the highest level of math you have completed in school or personally mastered?

Why did you stop and what did you find most difficult?
If you haven't stopped, for what reasons do you continue?

Comments about your instructors' bad/good teaching methods?

 

[Black Rose]

~ Basic Math
~ Pre Algebra
~ Algebra
~ Geometry
~ Algebra 2
~ Geometry 2
~ Trigonometry
~ Pre Calculus
~ Calculus
~ Advanced Calculus

Why did you stop and what did you find most difficult?
If you haven't stopped, for what reasons do you continue?

what are proofs?

Comments about your instructors' bad/good teaching methods?

recursion seems more important for reasons unspecified
i dont know why they did not say anything about it

x = n(n-1)/2
y = f(x)
z=z^2+c

i wish math i knew what to use it for

 

[Cheeseumpuffs]

About to start my second year in college as a math major. Last year I took a advanced calc with applications(or something like that)[3B], linear algebra[4A], DiffEqs[4B], and the first of two vector calc classes[6A].

I took Calc in high school and my teacher for that was phenomenal. He was great at explaining concepts and actually getting people into the subject matter. His class went a little slow for my taste, but it was necessary for him to make sure everyone in the class got it before moving on. What I've noticed about college math courses is that they move a lot faster than high school. The professors aren't trying to drill things into your heads, they're trying to get all of the subject matter into your hands before the end of the quarter and it's up to you to make sure that you find a safe place in your head to store it. Generally I like the college method of teaching because they go at a good pace and it really isn't tough to follow if you go to lecture. The problem is that if you're unable to go to lecture for an extended period of time (I got super sick for a week and a half/two weeks during the quarter I took 4B and 6A) then you're coming back pretty far behind and have to play catch-up.

The class I had the most trouble with last year was 4A (linear algebra). It was a lot more memorization than the other classes, as we had to memorize rules for determining whether something was a vector space or subspace or whatever. These rules seemed nitpicky in my opinion (at least the way they were presented in our homework assignments was) and I'm (not?) ashamed to admit that I have forgotten basically all of them. I can row-reduce a matrix like a fucking champ, though.

3B and 6A were also fairly challenging, but in a good way. They were the classes that dealt most heavily with pure problem solving, which is what I really enjoy about math. As opposed to 4A where the tough questions were the ones that said "A is not a vector space because:" and then went on to list four options which seemed virtually indistinguishable as far as correctness goes, the tough problems in those two classes were more along the lines of "Here is what you have, here is what you need to find" and then it'd be a matter of using the right concepts and methods to find the right answers, like solving an incredibly fun puzzle.


Man, math is great

 

[EyeSeeCold]

@Animekitty

What did you mean by the question, "what are proofs?" ?

I've yet to understand general recursion from a mathematical perspective. I can't speak for other math classes, but for myself, I find it interesting that instructors rarely delved into the why or what of mathematics (only the how). That might be something reserved for philosophy or logic, but it seems a greater understanding could be had if there was much more context for math concepts.


@Chesseumpuffs

Math major?

A couple questions. Have you thought about a double major? I know several majors might have overlapping math requirements which you seem to grasp pretty well.

Also do you tend to see the world in numbers, or are your skills in math just a separate thing?

What I've noticed about college math courses is that they move a lot faster than high school. The professors aren't trying to drill things into your heads, they're trying to get all of the subject matter into your hands before the end of the quarter and it's up to you to make sure that you find a safe place in your head to store it.​

Yeah this has been my experience as well.

Since mathematics is largely cumulative, there is a strong need for repetition/memorization but there is a limit to how long an instructor can focus on a subject. Basically leading to "bursts" of learning. I've been wondering whether it's possible to teach(or learn) comprehensive mathematics under a holistic method instead of discrete increments.

 

[Black Rose]

@Animekitty

What did you mean by the question, "what are proofs?" ?

I've yet to understand general recursion from a mathematical perspective. I can't speak for other math classes, but for myself, I find it interesting that instructors rarely delved into the why or what of mathematics (only the how). That might be something reserved for philosophy or logic, but it seems a greater understanding could be had if there was much more context for math concepts.

in geometry they made us do this and i was wtf is a proof symbols for? no contexts just symbols?

i assumed proofs are not general purpose

now i guess they are to do with something like this:

the god problem peano axioms

computer games give contexts but i dont want to learn all the libraries. and watered down code academy.

 

[loosechange]

What is the highest level of math you have completed in school or personally mastered?

I took a course in Tensor Analysis but thought it redundant Vector crap. The professor didn't tell us what it was for and I didn't have the imagination to ask.

Why did you stop and what did you find most difficult?

I stopped because everyone else in the class had horse blinders on and I didn't want to become one of them. I lost my creative motives.

If you haven't stopped, for what reasons do you continue?

I continue when the mood takes me. Who can resist beauty?

Comments about your instructors' bad/good teaching methods?

I had one perfect instructor. He sent me to grad school. That wasn't good enough and having stuff shoved down my throat afterwards was not conductive to wanting to remember. One must remember for minimum functioning.

 

[Cheeseumpuffs]

@Chesseumpuffs

Math major?

A couple questions. Have you thought about a double major? I know several majors might have overlapping math requirements which you seem to grasp pretty well.

I've thought about double majoring in Computer Science possibly. One of my major requirements was an intro CS course and I really enjoyed that, also it's been something I've always been interested in and wanted to be good at but I've just had no jumping-off point for actually getting into it. That said, my school's only CS major is in the college of engineering and not L&S, so it'd be tough to get into, since our engineering school is pretty competitive from what I've heard.

Also do you tend to see the world in numbers, or are your skills in math just a separate thing?

I think a degree of my math ability comes from the way my brain works, but to some extent it's just a thing I do. If you asked me to add some numbers or whatever, I'm pretty fast about it and I can never explain how I did it that fast. It's very intuitive/visual for me when I'm doing math in my head and I can't really verbalize it. Also when I see a number (most commonly the TV channel or some kind of volume number (car radio, TV, computer)) I often catch myself finding the prime factors of that given number. All that said, though, I wouldn't say that I see the world in numbers. Like if you put a Rubik's Cube in front of me I don't see the number of possibilities that it could be put in or the smallest number of moves to solve it or anything like that.

What I've noticed about college math courses is that they move a lot faster than high school. The professors aren't trying to drill things into your heads, they're trying to get all of the subject matter into your hands before the end of the quarter and it's up to you to make sure that you find a safe place in your head to store it.​

Yeah this has been my experience as well.

Since mathematics is largely cumulative, there is a strong need for repetition/memorization but there is a limit to how long an instructor can focus on a subject. Basically leading to "bursts" of learning. I've been wondering whether it's possible to teach(or learn) comprehensive mathematics under a holistic method instead of discrete increments.

I think, to some degree, there's always going to be those bursts. To teach a concept you need to introduce it and say "here's what you use it for" and then say "here's a method for using that concept" and then you do practice problems and all that. So most things you learn in a math class follow a pretty predictable pattern. The better teachers I've had have been able to keep a little better of a flow by connecting one concept to another. Like, when they introduce a concept and are explaining it they'll maybe compare it to another concept or talk about how it works with another concept. It's a great feeling when you have that moment learning something where you go "Ooohh, it's just like [this] but with a different part where you have to do [that] and then it comes out looking like [thing] which you can then do [stuff] to." I'm trying to come up with a more concrete example of just what I mean but I just woke up and I'm hungry and need to shower so I'll leave that for another time.

 

[BrainVessel]

Ever since long division I've had trouble with math. It's one of the few things that get me genuinely frustrated and on the verge of tears and I don't know why. I can barely handle Algebra, that's about it.

 

[Ex-User (9086)]

I had done on the highest level from the elementary up to:
Calculus and differential equations.
Analytic geometry, also called algebraic geometry.
Some mathematical-statistical analysis course connected with robotics.

What I will be doing in the future:
Discrete mathematics.

Why did you stop and what did you find most difficult?

I found the analytic geometry course the most difficult.
I spent a substantial amount of time learning integrals and differential equations as it required a lot of memorisation, sadly.

If you haven't stopped, for what reasons do you continue?

It is interesting, I want to learn new things, some of which may prove useful when I work on something else, some are just good to know and help me understand and become interested in other things.

Comments about your instructors' bad/good teaching methods?

I liked my lecturers, they were able to sustain my excitement and interest in mathematics, while not being able to explain it to me.
I tolerated my math instructors as they didn't discourage me and had a relaxed approach to the whole thing, which allowed me to learn everything on my own.

I really liked lecturers that provoked questions and created multiple tangents to their thoughts exploring as many possibilities as time allowed and not exhausting what they were supposed to do.

 

[Vrecknidj]

What is the highest level of math you have completed in school or personally mastered?

Graduate school course in mathematical logic.

Why did you stop and what did you find most difficult?

I found poor teachers to be the greatest obstacle. As far as the math itself, I found several topics challenging.

If you haven't stopped, for what reasons do you continue?

I do keep at it, when I find the time. Though I've been self-taught for 20+ years now.

Comments about your instructors' bad/good teaching methods?

Compassion and kindness are better than quite a few other traits, regardless of discipline.

 

[Pyropyro]

What is the highest level of math you have completed in school or personally mastered?

Calculus

Why did you stop and what did you find most difficult?

Because I finally finished all my math courses for my course.

I found it easier to use my voluminous Calculus book as a doorstop/impromptu pillow rather than reading it.

Comments about your instructors' bad/good teaching methods?

Nothing actually, I like the teachers but I hate the subject.

 

[Coolydudey]

Also studying maths, in the uk (you may even remember where!), what a great subject . Have covered (liberally re-named) basic number theory, DE, Analysis I, Introduction to groups, pre-linear algebra, vec calc, probability (lots of distributions), dynamics and special relativity, introduction to metrics and topology, calculus of variations. That's my first year.

I only ever had bad teaching at school. It never mattered there anyway, it was all just ridiculously easy for me...

As I said, maths is great.

 

[del]

Math major and took some graduate level real analysis, algebra, and probability.

I stopped because I finished my degree. I'd love to keep learning, and try to on the side a bit. I don't know that I have the single-minded obsession necessary to be a professional mathematician though. The reality is that to be a productive research mathematician, you need to live and breath your work, every second of the day, to an almost pathological level, and I just cannot sustain that level of dedication.

Also my professional life has led me into applied problems (control theory, probability) that I find just as interesting.

 

[crippli]

I took an engineering degree at one point. I think the math subjects was called calculus 1,2 and 3. There where also I think an own subject of linear algebra. And other courses like the element method, that consisted of mostly matrices and differential equations. Not really all that useful since computer programs set up these equations and calculate structural problems in 3 dimensions at a level that can not be done by one person manually. They said the idea was to understand the basics so one got a higher degree of feeding the program with correct data.

I don't really remember all that much from this stuff today. It was done over a few years. A lot of data fed into the system, and I suspect it went out with about the same speed as it came in. A teacher once said to me that the point was more to learn a way of thinking, rather then what one factually learned. Good times, I enjoyed the math classes, as I usually even turned up for the lectures.

 

[Polaris]

Basic math
Algebra
Trigonometry
Introductory and mid-level calculus for life sciences
Difference and differential equations
Statistics for life sciences

Threw myself into university level math after completing very basic level math at high school...many years later. Didn't sleep for two weeks during the intro-intensive bridging course to calculus - I had never done calculus before.

Teacher was okay at teaching although somewhat impatient, but excellent at identifying the students who really wanted to understand underlying principles and apply themselves. She realised my basic skills were missing and understood I had extreme anxiety. She did not make anything easier for me but she pointed out that I had the ability if I just got the basics covered, so I suddenly did not feel entirely stupid.

With respect to difference and differential equations and also statistics I got a real interest in mathematics. I would have continued with it if I hadn't changed degrees half way through due to my gypsy tendencies (I moved to a different town/university and had to change course structure).

The maths have been extremely useful in application to all other subjects I have done, as I have issues with focus if I cannot understand why we are using the different mathematical techniques. I have trouble with rote-learning because I cannot just plug a formula; I need to understand why that formula applies, otherwise I get so frustrated I cannot move on; I'll sit there for hours until I have found an answer. Some maths teachers did not like that and told me to just use the formulas unquestionably and forget about explanations, while others really appreciated it when I asked.

I appreciate absolutely everything I have learnt at university level. I see many people complain that they find their degrees useless. I find the opposite; it has given me skills and knowledge way beyond course curriculum due to a genuine interest in absolutely all systems and opened up many paths for potential careers. But then I usually research exhaustively which means I simply don't have a life outside of study/work. Not that I really care, it's what I like to do :/

 

[TimeAsylums]

Read:

"Mathematics for the Nonmathematican" - Morris Kline

Working on:

ftp://c-94-255-159-153.cust.bredban...on University Press, Princeton, NJ, 2008..pdf

 

[Architect]

Standard STEM though college (up to calculus, differential equations - the hard science track, not the soft bio track) plus statistics, advanced undergraduate math (mostly number theory). In graduate school was special topics like Tensor calculus and various other fields, also some specialized computer science math.

Stopped because I had learned enough, I use math as a tool, I'd love to explore it more but there's no time.

Worst teacher was in grad school where there are no seat belts. He talked about some things, then we'd get homework that might as well have been written in Greek, it was so unrelated. I had no idea how to tackle it.

 

[Coolydudey]

Standard STEM though college (up to calculus, differential equations - the hard science track, not the soft bio track) plus statistics, advanced undergraduate math (mostly number theory). In graduate school was special topics like Tensor calculus and various other fields, also some specialized computer science math.

Stopped because I had learned enough, I use math as a tool, I'd love to explore it more but there's no time.

Worst teacher was in grad school where there are no seat belts. He talked about some things, then we'd get homework that might as well have been written in Greek, it was so unrelated. I had no idea how to tackle it.

Couldn't help answering something could you?

 

[Architect]

Couldn't help answering something could you?

Old habits die hard. Unfortunately.

 

[JansenDowel]

Mastered: Calculus, Linear Algebra; Diff Equations, Multivariable Calculus; Abstract Algebra, Numerical Analysis.

By far, the hardest in this list was Abstract Algebra. I can not begin to describe how easy it was to pass every math paper after Abstract Algebra. I literally NEVER went to lectures or tutorials and passed with A's.

 

[EyeSeeCold]

@thread

I see a fair amount have taken higher level maths. Would you say your opinions have changed or stayed the same once you passed a certain level? At any point did the math seem radically different? (for better or worse)

in geometry they made us do this and i was wtf is a proof symbols for? no contexts just symbols?

http://dj1hlxw0wr920.cloudfront.net/userfiles/wyzfiles/91949ef6-cf8c-4bbe-9b81-21dac5012f47.gif

i assumed proofs are not general purpose

now i guess they are to do with something like this:

the god problem peano axioms

http://i1.ytimg.com/vi/OWkLJ8dCf20/0.jpg

computer games give contexts but i dont want to learn all the libraries. and watered down code academy.

I'm not familiar with the book or the axioms. Though the amount of symbols and theorems to remember in math definitely seems absurd, not to say they aren't interesting.

I've thought about double majoring in Computer Science possibly. One of my major requirements was an intro CS course and I really enjoyed that, also it's been something I've always been interested in and wanted to be good at but I've just had no jumping-off point for actually getting into it. That said, my school's only CS major is in the college of engineering and not L&S, so it'd be tough to get into, since our engineering school is pretty competitive from what I've heard.

Ah okay, I see that you've put some thought into it. There is also the departmental counselor(s) to get advice from if no one else has really encouraged you about doing CS simultaneously.

I think a degree of my math ability comes from the way my brain works, but to some extent it's just a thing I do. If you asked me to add some numbers or whatever, I'm pretty fast about it and I can never explain how I did it that fast. It's very intuitive/visual for me when I'm doing math in my head and I can't really verbalize it. Also when I see a number (most commonly the TV channel or some kind of volume number (car radio, TV, computer)) I often catch myself finding the prime factors of that given number. All that said, though, I wouldn't say that I see the world in numbers. Like if you put a Rubik's Cube in front of me I don't see the number of possibilities that it could be put in or the smallest number of moves to solve it or anything like that.

This is what draws me to typology, and why I think cognitive science seems fascinating. On a basic level the math ability is pretty cool, but then there's bound to be subtle differences in the way you approach things compared to others that are less numbers-oriented.

I think, to some degree, there's always going to be those bursts. To teach a concept you need to introduce it and say "here's what you use it for" and then say "here's a method for using that concept" and then you do practice problems and all that. So most things you learn in a math class follow a pretty predictable pattern. The better teachers I've had have been able to keep a little better of a flow by connecting one concept to another. Like, when they introduce a concept and are explaining it they'll maybe compare it to another concept or talk about how it works with another concept. It's a great feeling when you have that moment learning something where you go "Ooohh, it's just like [this] but with a different part where you have to do [that] and then it comes out looking like [thing] which you can then do [stuff] to." I'm trying to come up with a more concrete example of just what I mean but I just woke up and I'm hungry and need to shower so I'll leave that for another time.

I suppose I understand what you mean. I would describe it as a fluid and clear understanding of a concept, how & why the inputs/outputs relate to the formula, and the operating logic that is in place that allows a connection it to another concept. I guess what I was trying to say about the learning bursts was that they aren't conducive to those moments of deep mathematical clarity. I guess that's what tutors and self-study are for though.

Ever since long division I've had trouble with math. It's one of the few things that get me genuinely frustrated and on the verge of tears and I don't know why. I can barely handle Algebra, that's about it.

This right here is what I'd like to get into more of. Why does this happen? There have been times when my brain hits a wall and I'm utterly overwhelmed. Yet it makes so much sense when you watch someone else who understands the problem work through it.

It's unfortunate that math is to some extent "you either get it or you don't" in classrooms. I feel like math can't be taught, but one can learn it, because the mind has to personally understand the underlying logic/patterns.

I'd agree with what Polaris said: "otherwise I get so frustrated I cannot move on; I'll sit there for hours until I have found an answer."

Read:

"Mathematics for the Nonmathematican" - Morris Kline

Working on:

ftp://c-94-255-159-153.cust.bredban...on University Press, Princeton, NJ, 2008..pdf

That looks interesting based on the ToC, might take me a while to get to it, but I'll check it out, thanks.

 

[del]

@thread

I see a fair amount have taken higher level maths. Would you say your opinions have changed or stayed the same once you passed a certain level? At any point did the math seem radically different? (for better or worse)

It changes very radically during late freshman/sophomore year when you transition into proofs. Math courses stop being about doing exercises and examples and more about argument, logic, and proving the existence of solutions to a problem in general and what properties the solutions would (or would not) share.

I loved the transition, but many do not. The first proofs class is typically the class that makes the most people switch majors.

 

[nexion]

In my experience there has not really been a case of maths classes being progressively harder or higher in terms of material, but instead one of many disciplines and methods of problem solving existing in a sort of concurrency, as all of these disciplines share core definitions, formulas, and ways of approaching some problem.

It is interesting that one goes through school learning relatively high-level mathematical operations and then more of the framework is revealed as one moves through different branches of mathematics. Even in my limited understanding of stable truths across disciplines within the field of mathematics, I occasionally see implications of grander and much more basic systems. I understand that grade-schoolers have virtually no chance of comprehending set theory and logical axioms, but I would much rather learn such a diverse field starting with that which is true in all mathematics (the axioms) and work into various fields (algebra, geometry, calculus) from there. Now it becomes necessary to have flows in two separate directions: increasing both breadth in specialized mathematics and increasing depths in picking up similarities among them and going more towards the roots of all of mathematics. What I would prefer is a more holistic view that allows one to understand how these concepts build new systems and creates a sort of divergence from the entire field into distinct disciplines.

I consider math to be in my long-term peripheral interests, which means I generally find it interesting and will put more time into its study so long as this study manages to further my understanding and goals of primary interests.

 

[BrainVessel]

@thread

This right here is what I'd like to get into more of. Why does this happen? There have been times when my brain hits a wall and I'm utterly overwhelmed. Yet it makes so much sense when you watch someone else who understands the problem work through it.

It's unfortunate that math is to some extent "you either get it or you don't" in classrooms. I feel like math can't be taught, but one can learn it, because the mind has to personally understand the underlying logic/patterns.

I'd agree with what Polaris said: "otherwise I get so frustrated I cannot move on; I'll sit there for hours until I have found an answer."

Yep. If it's something I haven't been meticulously taught to do I'll hardly be able to read it. I'll just see it as this giant lump of unsolvable problem in front of me, get very frustrated, and lose my patience with it.
I've been looking around regarding it and there appears to be a disorder called Dyscalculia. I haven't looked into much and examined its validity but here's a link for those interested: http://en.wikipedia.org/wiki/Dyscalculia

 

[EyeSeeCold]

It changes very radically during late freshman/sophomore year when you transition into proofs. Math courses stop being about doing exercises and examples and more about argument, logic, and proving the existence of solutions to a problem in general and what properties the solutions would (or would not) share.

I loved the transition, but many do not. The first proofs class is typically the class that makes the most people switch majors.

What classes/fields of math would those be? I can't find any names.

In my experience there has not really been a case of maths classes being progressively harder or higher in terms of material, but instead one of many disciplines and methods of problem solving existing in a sort of concurrency, as all of these disciplines share core definitions, formulas, and ways of approaching some problem.

Indeed the various mathematical fields do share fundamentals, but as for passing a math class, that is bound to be a relative experience with respect to difficulty.

It is interesting that one goes through school learning relatively high-level mathematical operations and then more of the framework is revealed as one moves through different branches of mathematics. Even in my limited understanding of stable truths across disciplines within the field of mathematics, I occasionally see implications of grander and much more basic systems. I understand that grade-schoolers have virtually no chance of comprehending set theory and logical axioms, but I would much rather learn such a diverse field starting with that which is true in all mathematics (the axioms) and work into various fields (algebra, geometry, calculus) from there. Now it becomes necessary to have flows in two separate directions: increasing both breadth in specialized mathematics and increasing depths in picking up similarities among them and going more towards the roots of all of mathematics. What I would prefer is a more holistic view that allows one to understand how these concepts build new systems and creates a sort of divergence from the entire field into distinct disciplines.

I consider math to be in my long-term peripheral interests, which means I generally find it interesting and will put more time into its study so long as this study manages to further my understanding and goals of primary interests.

I don't find much enjoyment in completing required math classes as part of a curriculum, yet, developing a strong logical-mathematical worldview over the course of life seems like it would offer some profound personal realizations. I feel like there is no time for that in today's world however.

Yep. If it's something I haven't been meticulously taught to do I'll hardly be able to read it. I'll just see it as this giant lump of unsolvable problem in front of me, get very frustrated, and lose my patience with it.
I've been looking around regarding it and there appears to be a disorder called Dyscalculia. I haven't looked into much and examined its validity but here's a link for those interested: http://en.wikipedia.org/wiki/Dyscalculia

Well I have identified one important fact of mathematics and that is that it's cumulative. If I don't understand what is in front of me, it's probably because I forgot/never learned the preceding material. Other than that my mind can occasionally use an extra pair of eyes/thoughts to help me see things I can't see when it comes to math.

I wouldn't go so far as to say that this would make you, me or anyone else likely to have dyscalculia (note it seems to be a model that suggests general life difficulties with numbers/quantities). Personally I do enjoy problem solving, but I don't enjoy having to work with sparse information (especially if my grade is dependent on it), that is what makes mathematics frustrating for me. Books have helped me to learn concepts more than instructors but I think a personal tutor/mentor would be ideal for the reason of communication.

 

[nexion]

What classes/fields of math would those be? I can't find any names.

While I am not personally majoring in math, I ran into proofs in high-school geometry and haven't heard anything about them since. I imagine university-level proofs and quite a bit more rigorous and detailed.

I don't find much enjoyment in completing required math classes as part of a curriculum, yet, developing a strong logical-mathematical worldview over the course of life seems like it would offer some profound personal realizations. I feel like there is no time for that in today's world however.

I think it really depends on what you do with your time. Certain fields afford one the opportunity to both increase knowledge about mathematical underpinnings and become better able / more knowledgeable in that field. Also, I think that a lot of people in today's world are oftentimes enormously busy doing nothing.

 

[Absurdity]

What classes/fields of math would those be? I can't find any names.

Haven't taken it myself but I know at my alma mater math majors are usually introduced to the higher-level, abstract stuff in real analysis. Some schools have a sort of preparatory course on proofs that's taken after the calc sequence + linear algebra and differential equations and before stuff like real and complex analysis, abstract algebra, etc.

My understanding is that the first course in real analysis is usually where you go back and prove all the stuff in calculus that the professors glossed over because it was too heady for most of the people in the class.

 

[Grayman]

Calculus was the highest math I have obtained. Math has been useful in so many things in my life. The thing is that I did not see it's true potential until I got into physics. It eventually became a language that helped define the workings of the universe.

The only thing I had issues with was proofs. It seems odd that I had issues considering most of my time in math was spent alone figuring out how to solve problems in different ways and seeing how everything fit together and supported each other. The thing was that I never learned the definitions or had much concern for definitions or procedures. I only cared for the patterns and this indescribable understanding I had for math.

Substitution for example lacks a definitive asnwere to what is being done. It is not, to me, accurate in proving anything.

To me I am not substituting something for something else, I am just looking at the same thing in a different way. 2 + 2 or 1 + 3 or 4 are all the same thing just being looked at differently.

x+Y =z Z= 1/G so x+Y=1/G To me this is not substitution and there is no rule, I am just viewing the 'z' from a different angle. Seeing more of it and more of how it works.

 

[del]

What classes/fields of math would those be? I can't find any names.

The first course is usually real analysis (which is basically fancy calculus), but it can be anything. At my school, it was number theory.

The point is, the new approach to math, where the focus is on proving statements in general rather than solving specific problems, encompasses all fields of math. That is probably why the transition to proofs causes so many to drop the major.

Absurdity is right, the first analysis course you typically prove things you already learned in calculus, albeit more rigorously. You go on to prove new and surprising things that you wouldn't have guessed from normal discussions on calculus.

 

[EyeSeeCold]

Haven't taken it myself but I know at my alma mater math majors are usually introduced to the higher-level, abstract stuff in real analysis. Some schools have a sort of preparatory course on proofs that's taken after the calc sequence + linear algebra and differential equations and before stuff like real and complex analysis, abstract algebra, etc.

My understanding is that the first course in real analysis is usually where you go back and prove all the stuff in calculus that the professors glossed over because it was too heady for most of the people in the class.

The first course is usually real analysis (which is basically fancy calculus), but it can be anything. At my school, it was number theory.

The point is, the new approach to math, where the focus is on proving statements in general rather than solving specific problems, encompasses all fields of math. That is probably why the transition to proofs causes so many to drop the major.

Absurdity is right, the first analysis course you typically prove things you already learned in calculus, albeit more rigorously. You go on to prove new and surprising things that you wouldn't have guessed from normal discussions on calculus.

I see, it looks like those are junior+ classes, which is why I couldn't find any information.

You said you liked the transition from the lower level math to proofs so I assume you have experience with the subsequent fields? Basically I'm curious whether the mindset and approach to math becomes so different, everything that made the other fields difficult, enjoyable, tedious etc no longer applies?

While I am not personally majoring in math, I ran into proofs in high-school geometry and haven't heard anything about them since. I imagine university-level proofs and quite a bit more rigorous and detailed.

I think it really depends on what you do with your time. Certain fields afford one the opportunity to both increase knowledge about mathematical underpinnings and become better able / more knowledgeable in that field. Also, I think that a lot of people in today's world are oftentimes enormously busy doing nothing.

Maybe. Kudos to anyone who has learned higher level maths on their own free time though. Seems like one's ability to focus would also be a factor.

Calculus was the highest math I have obtained. Math has been useful in so many things in my life. The thing is that I did not see it's true potential until I got into physics. It eventually became a language that helped define the workings of the universe.

Physics I can understand but how else has it been useful?

 

[Grayman]

Physics I can understand but how else has it been useful?

Industrial Automation:

A simple example is setting up a program in an industrial computer called a PLC. The PLC can measure the weight of the liquid in a completely sealed tank that is shaped like a can and is laying on its side. Like the ocean the pressure of the liquid increases from teh top to the bottom of the liquid. A device is installed that measures the pressure at the top of the tank which may be higher than the atmosphere and then takes a read at the bottom of the tank and figures the difference. Based on the density of the liquid it can determine the height of the liquid based on this difference of pressure using a calcluation. Since the tank is not round knowing the hieght does not tell you how much volume of the liquid you have. You have to then calculate what part of the can is filled with liquid and then determine the volume. The volumeis then sent to a display in a controll room with an alarm that goes off if it gets too low or high and the operators will have a truck fill the tank when it gets low.

Field of Measurement:

Natural gas for large volume customers can be measured using a plate taht restricts the flow of the gas and causes a difference of pressure before and after the restriction. Reads of this pressure can be taken to determine the flowrate. As the flow increases the restriction causes a greater drop of pressure after the restricting plate and the computer with the proper calucation can then determine the actual flow.

P/T = V The volume of gas is affected by temperature and pressure. All gas has to be measured at atmospheric pressure and 60 deg F. Since outside conditions and customer requirements for gas pressure do not allow for this we have to calculate what the volume of 600psi 35 deg F gas would have been had it been atmospheric pressure at 60 deg F. A device where the gas enters the pipe can measure how much actual heat 'btu' the gas can produce based on standard conditions. We charge the customers for the actual heat the gas can ideally produce and not the actual volume of gas we give them in case the gas contains impurities. So to calculate that you get a factor from this device that measures the heat of a standard cubic foot of gas and multiply that factor into the standard volume estimated based on non standard condiations to get a number that we use to charge the customer for the heat we provided them.

Speed control:

PID Proportional Integral and derivative, This is the calculation to determine the speed and the rate of change of speed to obtain a setpoint. An engine the size of a truck, not the engine in the truck, hooked up to a compressor that is the size of another truck compresses gas for a town. The engine has to keep a certain pressure as to not blow the pipe open or cause damage down stream or lose refineries due to under pressure conditions. PID controls the rate at which the compressor can ramp up and slow down in order to maintain the correct pressures. If it is off the compressor will not catch the pressure in time and it could blow safety devices that are set to keep the town safe and possibly cause an emergency shutdown. Or it could cut the supply to the refineries and cost millions of dollars in lost goods do to their own shutdown and issues caused by our inability to keep them supplied with gas.

GAMES:

I like to figure them out more than play them I build excell sheets like for D3 that calculates the leech, amor and damage blocked by armor etc..
I create a chart that can determine based on how much armor how much damage I would be able to block and how much damage I can take in a single hit before dying. This chart gives me an idea of a balanced and efficient build would be considering life, armor, leech, damage etc...
I also made a chart for POE that can estimate mana costs and the various methods of getting more mana regen in order to maintain certain skills. Once I know how much mana I need i can get just the right amount in my stats so I don't have to overdo it. To make the chart I had to use substitution so I can solve for different variables and determine how the affect eachtoebr and how they best work together.


Programming:

I was replicating a communication protocol between a device and my computer. I wanted to build my own software to control the device. The commuication had an error check code called a CRC which is an algorithm that can determine if there were any errors in transmission. I could not be certain of the divisor used. CRC is basically taking the binary representation fo the string and dividing it through the string and then recording the remainder. This remainder is then attached to the communication packet during transfer. The other computer then uses the known divisor against the string and sees if it gets the same remainder. IF the string was sent over the commuication lines intact both computers would have the same remainder. The recieving computer then accepts the communication packet as valid. if invalid it requests the packet again. Without the proper divisor I could not send the right error code and none of the commands would be accepted so I built a program that tested a number of divisors against a known string to receive a known remainder/error code. Basically hack the CRC algorithm. The program took 4 core processors and ran a month trying every number and it had barely gotten through a small peice of it and had not given me any good results. I stopped the program and set it up with commonly used divisors and had it test just those and got a valid divisor within a day.

Anyways I managed to replicate the protocol and have built a program that can control and configure the device.

But these are my more fun experiences. I did not includ the everyday tips calculations, taxes, making sure the right number of people are on the bus, or counting how many times someone can irritate me in a day.

 

[EyeSeeCold]

Thanks Grayman, those sound like they would be complicated in action. But I can sort of see how the math helps.


I am grateful for all the responses, I'm just trying to re-evaluate what I want mathematics to mean for me. Like programming, it's a gateway to many other roads.

 

[pjoa09]

Taking Discrete Math with Calculus right now.

I'd say by the time you do induction proofs and such, it'll get a lot more intriguing while being a lot more time consuming.