What are some tips for a Pure Math major?

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Discussion Overview

The discussion revolves around the considerations and strategies for a student transitioning to a pure mathematics major, particularly at the University of Waterloo. Topics include research opportunities, course selection, and the potential for a second major in computer science or applied mathematics.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant expresses a desire to engage in research before graduation and questions whether to focus on core areas of pure mathematics or explore papers in a field of interest.
  • There is a suggestion to maximize pure math courses in later years while also considering the balance between coursework and self-study.
  • Another participant raises the importance of differential equations in upper mathematics, noting their absence in the pure math major curriculum.
  • One reply advises sophomores to take introductory courses across various branches of mathematics to identify fields of interest for future research.
  • There are differing views on the value of a second major, with one participant suggesting computer science for better career prospects and another advocating for applied mathematics to remain closer to pure mathematics.

Areas of Agreement / Disagreement

Participants express differing opinions on the importance of differential equations and the best approach to selecting a second major. There is no consensus on whether to prioritize pure mathematics or applied mathematics/computer science for career outcomes.

Contextual Notes

Participants mention the absence of differential equations in the pure math curriculum, which may affect the understanding of their relevance in advanced mathematics. The discussion reflects varying assumptions about the relationship between pure and applied mathematics.

Who May Find This Useful

Students considering a pure mathematics major, those interested in research opportunities in mathematics, and individuals weighing the benefits of a second major in computer science or applied mathematics.

samspotting
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Hi, I have just finished first year in general math and am going to choose the pure math major at my university (uwaterloo). I have a few questions about undergraduate math education.

I wish to do research in math before I graduate, what should I be doing? I am currently learning analysis through rudin, and linear algebra through friedberg on my own. Should I focus my education on the core areas of Pure Math? Or should I be trying to get through some papers now of a field of interest?

What strategy should I take for choosing courses. Should I try and max out on pure math courses, and eventually in my 3rd and 4th year choose hard upper level courses like functional analysis, topology, measure theory, ... or choose a few and spend more time learning outside the classroom.

I am looking for a second major, I like computer science but am also interested in the applied math area. I would need to take a few physics courses and a couple courses in differential equations (ode, pde). Would applied math more than cs? CS would get me more and better coop jobs, while applied math seems more true to a mathematics education. For cs, I would have room for only the minimum needed to graduate with a cs second major.
 
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I am in no way a mathematician or even majoring in math, but just from reading your post it appears you might have answered your own question.

Computer science for a better career outlook

Applied math to be more of a mathematician
 
True, that was a minor question, I guess I was trying to ask how important are differential equations to upper mathematics? There are no diff eq courses included in my pure math major option. I am seeing them mentioned everywhere though.
 
For sophomores, most universities make you take one or two courses from each branch of Mathematics (Algebra, Analysis, Number Theory, Prob/Stats etc). Figure out which field (or two) you could see yourself doing research in, and then load up of those courses Junior/Senior year. Don't worry about research until you've taken some upper level classes.

Statistics is a great second major, as is Computer Science. Both are very employable.
 

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