Importance to me as a pure maths major?

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Discussion Overview

The discussion revolves around the importance of various mathematical concepts and subjects for a pure mathematics major, including integration of parametric equations, set theory, and first-order logic. Participants also explore the differences between BA and BS degrees in mathematics and share resources for self-study.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant questions the significance of integrating parametric equations for a pure math major, noting that it is rarely needed in practice but could be learned if necessary.
  • Another participant suggests that reviewing parametric equations could be beneficial for understanding line integrals in future calculus courses.
  • Participants discuss the availability of resources for self-study in set theory and first-order logic, with specific book recommendations provided.
  • There is a discussion about the differences between BA and BS degrees in mathematics, with one participant noting that the BS typically requires more rigorous science courses while the BA includes more language courses.
  • One participant expresses a preference for the BS degree due to their struggles with language courses, despite concerns about the difficulty of chemistry.
  • Another participant offers a perspective on chemistry, suggesting that balancing equations is not the main focus and that systems of equations can aid in understanding chemical processes.
  • There is an acknowledgment of the challenges some participants face with applied sciences compared to mathematics, with a note on the potential for sarcasm to be misunderstood in the discussion.

Areas of Agreement / Disagreement

Participants generally agree on the value of learning parametric equations and the importance of self-study resources. However, there are differing opinions on the relevance of chemistry and the perceived differences between BA and BS degrees in mathematics.

Contextual Notes

Some participants express uncertainty about the necessity of certain mathematical topics and the implications of degree choices, indicating a lack of consensus on the best path forward for a pure math major.

Enjoicube
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Ok, I have a few questions here, so hopefully everyone will help me find an answer to these.
1. Firstly, I have just finished my second semester of calculus 2, and am now in the process of teaching myself a semesters worth of multi variable/ intro vector calculus, however, I noticed that we skipped over integration of parametric equations: Is this going to be of great importance to me as a pure maths major? I have taught myself the formulas, and could derive them, but I haven't been over any applications.
2. I have hardly had any introduction to set theory, but from what I have seen on wikipedia (very little) I am really in love with the subject. Does anyone know of any very basic books on set theory which I could use to teach myself?
3. Are there any recommended books on first order logic? I honestly have had no experience except for learning all the symbols I come across in readings.
my summer looks pretty bleak so far, and I really want to learn as much math as possible, so there is a lot of time for this.

One more thing, the school I will be attending has both a BA math and A BS maths. Anyone know about the difference? I am unsure about which to choose. I came into math for its beauty, like art, but at the same time I like eveything to be as rigorous as possible.

Oh yea, I have a limited budget :frown: (meaning nothing over $100) , sorry about this restriction.

Thank you all for any answers.
 
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1) No one on this board is going to tell you to not learn something. That said, I've had to integrate parametric equations close to zero times in the years since Cal II. Though, I feel confident that if I ever need to I could pick it up quite quickly. You're not going to have a gun pointed at your head and be told that you need to integrate a parametric equation NOW w/o looking at a text. If a future course requires you to use a particular method, you'll generally be able to see it coming and be able to study accordingly.

2) https://www.amazon.com/dp/0486638294/?tag=pfamazon01-20 book on set theory is simply fantastic in it's breadth.

3) https://www.amazon.com/dp/0486683702/?tag=pfamazon01-20 book on first order logic is a classic in my opinion, but requires that you have a bit of knowledge about sets.

Both of the above books should keep you occupied for the summer with a combined cost of < $25 (I really don't know how Dover does it).
 
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It won't hurt to go over parametric equations. It will help when you start doing line integrals in Calc III. Also, from my experience with the BA vs the BS in math, there is no real difference between the mathematics curriculum of the two degrees. The BS, however, usually requires more rigorous science courses, while the BA requires more language courses.
 
Aha, then BS it is, i just barely got an A in French this year, and it doesn't seem like it will get any better in later years. Although I might have to reconsider, going through chemistry again will be painful. Regardless of how good I am with algebra and calculus, I cannot stand balancing equations which is mostly arithmetic and common sense (something which I desperately need).

Oh, yeah, I though parametric eq. would help with line integrals. one of the reasons I asked. I can't wait to learn this stuff.
 
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Balancing equations isn't really what chemistry is about. Also, if you know how to solve systems of equations, voilà an algorithm for balancing equations.
 
I didn't think that that is what it was about, but intro chem is a lot about things I am terrible with (especially preparing solutions, molarity, stoichiometry etc.). Honestly, Math is a very random gift of mine, besides Math I am pretty bad with applied sciences (not that every science is applied). It sort of reminds me of Math, before the interesting stuff, you have to learn arithmetic. Sorry if I offended you by making a generalization, this is NOT what I intended, and my sarcasm is often lost on others (just like others' sarcasm is often lost on me).
 
I wasn't offended :-) Just pointing it out.

I liked the two years of high school chemistry I took a lot and I did very little balancing of equations, especially in the second year.
 

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