Does Math Get More Enjoyable Beyond Pre-Calculus?

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Discussion Overview

The discussion revolves around the enjoyment of mathematics as students progress beyond pre-calculus, particularly focusing on the transition to calculus and higher-level math courses. Participants share their experiences and perspectives on the perceived enjoyment and challenges of math at various educational stages, including high school and university.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification
  • Personal experience sharing

Main Points Raised

  • One participant expresses doubt about the enjoyment of math beyond pre-calculus, questioning whether calculus will be more engaging.
  • Another participant found calculus to be exciting compared to high school math, attributing this to differences in curriculum and teaching style.
  • A participant suggests that the experience of math varies significantly for math majors compared to high school students, recommending self-study of more rigorous math texts for a better understanding of the subject.
  • Some participants highlight the importance of exploring applications of math, such as in physics and engineering, to enhance enjoyment.
  • One participant shares a personal journey, noting that their interest in math grew through exposure to physics and engaging teaching methods.
  • Another mentions that multivariable calculus and topics like linear algebra can be interesting, but the teaching approach greatly influences this perception.
  • A participant recalls a moment of fascination with the Pythagorean theorem, indicating that personal experiences can spark interest in math.
  • Several participants emphasize the role of good teaching and collaborative learning environments in making math enjoyable.

Areas of Agreement / Disagreement

Participants generally express a range of opinions on the enjoyment of math, with some finding it more engaging in higher-level courses while others remain skeptical. There is no consensus on whether math becomes universally enjoyable beyond pre-calculus, as experiences vary widely.

Contextual Notes

Participants mention that the curriculum and teaching methods in high school may contribute to a perception of math as tedious, and that personal interests and experiences significantly influence enjoyment. There is also a suggestion that the transition to university-level math may present different challenges and opportunities for engagement.

Who May Find This Useful

This discussion may be useful for students contemplating their future in mathematics, those experiencing challenges in their current math studies, and educators seeking insights into student perceptions of math enjoyment.

ilii
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I am almost finished pre-calculus and I am wondering when math will become more enjoyable. I feel like everything about math up to this point seems like a chore. I absolutely can't stand graphing function after function, it just seems like such an incredibly mundane thing to do. I keep telling myself that everything will become more interesting the further I go, but I am having my doubts. Will math become more fun in calculus? I really don't know at this point. I have seen videos that go through a few calculus concepts, and they just seem like an extension of what I have already learned. Maybe after calculus, then ... how much further on? Maybe math is not for me, if this is all math entails.
 
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Calculus is when it started getting really exciting for me. Precalculus and Algebra (high school level) was extremely boring. Apart from the subject matter, the curriculum is at fault. In high school they made us do the same routine exercises hundreds of times. It isn't like that in university. Don't make a major decision in life such as majoring in math or not because of a bad high school experience. Take some math classes in university and then decide. Personally, I find math extremely fascinating and enjoyable.
 
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If you are a math major, it is highly likely that what you have experienced thus far is no where close to what you will be experiencing as a math major. (speaking in relation to the United States at least) Math is taught to be used computationally because that is how most people will use it, if they ever do. If you are understanding and performing well, but want to know what being a major will be like, I would recommend self-studying some real math.

I know as far as 'real math' goes, Serge Lang's Basic Mathematics was my first introduction. If you want a more rigorous introduction, I would go with either Apostol's or Spivak's calculus texts. These texts are very difficult, especially to self-study, but it is a real introduction to pure math.

Then again, if you don't enjoy any of the above treatments of math, then maybe pure math isn't for you. Applied math is still an option and you may enjoy the concepts introduced in calculus, but it really is just more of the same routine. The concepts are different, but the calculations are just calculations.

Edit: Again, all of this is if you are a math major. But, if all the math you have encountered so far hasn't interested you, why are you wanting to study it?
 
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ilii said:
Maybe math is not for me, if this is all math entails.

Many confuse the computational drudgery of mathematics with the art of mathematics. You simply can't get around the need for algebraic manipulation, or the application of theorems.

But there is hope. When I was beginning my study of calculus, I also would go off to explore the Mandelbrot set and observe the fractals at the edge. A friend and I tried writing programs to search for prime numbers as fast as possible. Learn about Laplace transforms.

Alternatively, consider studying the history of mathematics. The famous mathematicians of history were some impressive figures, facing daunting problems.

You are still in the drudgery stage. There is light ahead.
 
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You may find mathematics more enjoyable if you look at its application. Since you are learning calculus, reading some university physics and engineering books may inspire you. You will realize how interesting the application of calculus is in daily life.
 
I offer you a quote:

"If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy." ~ Paul Turan

If mathematics doesn't make you happy, then maybe your interests lie in a different field; Perhaps some form of art?

Although I must mention that math is arguably the most important tool-set to acquire if you intend to enter any form of science or engineering. In my own personal opinion, math is the most important subject in existence, and if you accept what it has to offer, then it can take you places.

Don't let the remedial tasks of high school math offset you from the grandeur that mathematics has to offer. The rabbit hole goes a lot deeper than they let on.
 
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ilii said:
I am almost finished pre-calculus and I am wondering when math will become more enjoyable. I feel like everything about math up to this point seems like a chore. I absolutely can't stand graphing function after function, it just seems like such an incredibly mundane thing to do. I keep telling myself that everything will become more interesting the further I go, but I am having my doubts. Will math become more fun in calculus? I really don't know at this point. I have seen videos that go through a few calculus concepts, and they just seem like an extension of what I have already learned. Maybe after calculus, then ... how much further on? Maybe math is not for me, if this is all math entails.

I quite enjoyed it at school, there was lots of graphing and equation juggling, but for some reason I quite enjoyed it - most of my friends didn't. It became a bit more of a chore at university, but manageable. The programming jobs I did after that were also a bit of a chore, but paid very well, and that helped a lot! At school you have lots of other classes so really don't do that much graphing or algebraic manipulation - if you are finding it a chore now then expect it to become much more of a chore! Maybe Math isn't for you. What do you find isn't a chore? Do that!
 
I have a PhD in math, but I never liked it that much in high school. Physics is what caught my attention and made me like math more. As far as math itself, I would say multivariable calculus is where it starts to get interesting. Linear algebra and differential equations can be interesting, but it depends on how it's taught (speaking of which, even high school math could be more interesting if it were taught differently, though maybe the curriculum could be tweaked a bit, as well). Differential equations is usually taught in a really uninteresting way. Probability can also be cool, if it's taught well. After those courses, you get to the "real" math, like real analysis. That's the standard route, but if you are interested enough, there are subjects like graph theory that you could possibly study that don't really have any formal prerequisites at all, except mathematical maturity, which you could get from an intro to proofs type class/book, although something like calculus probably helps, too.

It definitely entails more much more than what you've seen. I ended up not liking modern research-level math, but the problem there is very different from those boredom issues of high school math. I did like undergraduate math and graduate level math.
 
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I remember, I became for a first time fascinated about math when I heard of Pythagorean theorem . To me it was like a magic that opens doors of geometry.
 
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  • #10
I am a university student of Physics, and math started to be interesting with multivariable calculus, you start to see that math is actually a door opener as zoki85 says. You need to choose a good teacher and think of math as a tool that impressively can be used to described and predict almost any phenomenon in the universe. It was helpful to think about a physical application every time I encounter a new topic in calculus. Studying why we can solve a differential equation with an homogeneous and particular solution was the first thing that truly captivated me in math.
I hope this is helpful :)
 
  • #11
I fell in love with math in junior college because of two professors who genuinely loved the subject and spent quality time with our small group of students - treated us like fellow-researchers. A big part of why I loved it was the group of students who studied together diligently every afternoon for two years. I was good at problem-solving, and the prospects were good (1980's), so I went the engineering route. But I went back for a Masters degree in math education recently and again enjoyed the higher level math I took - to a point. I got to some of the graduate-level courses and realized I could learn it with effort, but the younger kids were far faster in absorbing the ideas than I was, which added stress and took some of the fun out of it. Now I enjoy learning math at my own pace.

While you're young and still deciding on an educational/career pathway, go as far as you can with math if you think it's for you. Pick a mentor, a good high school teacher or college professor - or a great grad student, and ask them to show you what "turns them on" about the math they're doing. Help someone complete a proof to submit for publication, take notes for a professor who wants to publish. Know who the great teachers/professors are, and arrange your schedule around taking them. Get to know a mathematician closely. Look at taking the watershed college-level courses, such as Foundations of Advanced Mathematics, that are required to proceed further. Join a math club. It sounds hokey, but these are students who can help you find yourself, and the club's professor-advisor is usually a great resource.

By the way, when I was in high school, I hated geometry but loved algebra. In undergraduate college, I fell in love with calculus, but I didn't care for statistics. I think every mathematician has his or her favorite area. There are so many facets of math, that it's probable you haven't even found the general field you'll like yet. Hang in there, and best wishes!
 
  • #12
Simply said, calculus breathes life into math.

Also complex numbers are pretty interesting- imagine: numbers are two dimensional, and any expression you can possibly imagine needs only 2 dimensions for the entire domain and range to be complete. Truely amazing
 
  • #13
Here's an interesting video on the general topic (not calculus specifically, but mathematics in general):



There are more Numberphile videos:
http://www.numberphile.com/
They are targeted toward lay people; you don't need to be a mathematician to appreciate them. The emphasis is on number theory of course (calculus is within a different branch of mathematics called analysis). Some videos are just playful manipulation of numbers, but others are far more thought provoking. They're all good for gaining interest in math though, even if there isn't much calculus.
 

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