Why do you like your chosen math field?

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In summary, the conversation discusses the individual's preferences in mathematics and how they may be influenced by their strengths and interests. They enjoy topology, differential topology, set theory, and differential geometry due to their visual and geometric aspects, as well as their focus on continuity and smoothness. They do not enjoy group theory or ring theory, which they find too abstract and lacking in continuity and smoothness. The individual also mentions their increasing enjoyment of different fields of mathematics as they age and learn more. They also mention the influence of algebraic geometry in changing their perception of algebra.
  • #1
andytoh
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I like topology, differential topology, set theory, differential geometry. But I ask myself why, and I can't give a good answer.

I know that I like abstraction and proofs, but yet I don't like group theory and ring theory, which are quite abstract and deals mainly with proofs. Perhaps I like dealing with derivatives, and hence my preference for differential topology and differential geometry. But yet I don't like differential equations or plain calculus. Do we like something just because we are good at it? Not in my case. I got my highest grade in group theory, ring theory, and number theory, all of which I don't like. Perhaps it's a genetic thing? I don't think so. So what is it then? And why don't I like group theory and ring theory? I don't know.

Can someone explain why you have chosen your math field?
 
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  • #2
well i think i alsoiked your chosen fields because of the geometric and visual aspect. also they involve smoothness and continuity, whidch are evry intuitive things to me, unlike finte reasoning in group theory, and the ugliness of the way calculus is often aught.

the older i get the more fields i like. it helps to teach them and learn them better.

if you want to enjoy diff eq, instead of those books like boyce and diprima, read arnol'd.
 
  • #3
mathwonk said:
well i think i alsoiked your chosen fields because of the geometric and visual aspect. also they involve smoothness and continuity, whidch are evry intuitive things to me, unlike finte reasoning in group theory, and the ugliness of the way calculus is often aught.

hmmm... I think you explained it pretty well. I like visual, geometric, continuous, and smooth objects. Group theory, ring theory, and number theory lacks the continuity and smoothness that I lust for. Differential Equations and calculus are too ugly in the sense that there is too much analytic calculation for my taste. I think I got it now.
 
  • #4
I used to hate algebra, until I learned some algebraic geometry, which made it seem much more down to Earth to me.
 
  • #5
i also began to l;ike algebra more afgter learning algebraic geometry. IN AG, one l;earns to vieew every ring as the ring of functions on some geometric space. this adds a lot to the intuition of the dioealas tructure of the ring, i.e. ideals become like (functions vanishing on) subvarieties of the geometric variety.
 

1. Why did you choose your specific math field?

I chose my specific math field because it aligns with my research interests and allows me to explore and solve complex problems that I am passionate about.

2. What do you find most interesting about your chosen math field?

What I find most interesting about my chosen math field is the application of mathematical principles to real-world problems and how it can lead to innovative solutions and advancements in various industries.

3. How does your chosen math field contribute to society?

My chosen math field contributes to society by providing a deeper understanding of different phenomena and helping to develop more efficient and accurate models for predicting and solving problems in various fields such as engineering, economics, and science.

4. What skills are necessary to excel in your chosen math field?

To excel in my chosen math field, one must have a strong foundation in mathematical concepts, critical thinking skills, and the ability to think abstractly. It also requires patience, perseverance, and the willingness to continuously learn and adapt to new methods and technologies.

5. How do you see your chosen math field evolving in the future?

I believe my chosen math field will continue to evolve and become more interdisciplinary, integrating with other fields such as computer science and data analytics. With the advancements in technology, there will also be a greater emphasis on computational methods and data-driven approaches in my field.

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