What are some tips for a Pure Math major?

In summary, the individual is a first-year student at the University of Waterloo who has decided to major in pure mathematics. They have questions about undergraduate math education, including how to prepare for research before graduation, what courses to take, and whether to choose a second major in computer science or applied math. They are considering taking upper level courses in functional analysis, topology, and measure theory, and are also interested in differential equations. They may consider a second major in statistics or computer science for better career prospects.
  • #1
samspotting
86
0
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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  • #2
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
 
  • #3
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.
 
  • #4
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.
 

1. What is a pure math major?

A pure math major is an academic degree program that focuses primarily on the development of advanced mathematical theories and concepts. It is a branch of mathematics that deals with abstract, theoretical concepts and does not have direct applications in the physical world.

2. What courses are typically included in a pure math major?

Courses in a pure math major can vary depending on the university, but they typically include subjects such as calculus, linear algebra, real analysis, abstract algebra, topology, and number theory. Students may also have the opportunity to take electives in areas such as differential equations, mathematical logic, and geometry.

3. What skills are developed in a pure math major?

A pure math major develops analytical, critical thinking, and problem-solving skills. Students learn to think abstractly and logically, and to apply mathematical principles to various complex problems. They also develop strong quantitative skills and learn to communicate complex ideas and theories effectively.

4. What career options are available for pure math majors?

Career options for pure math majors include roles in academia, research, and industry. Many graduates go on to pursue further education in graduate school, while others find employment in fields such as finance, data analysis, cryptography, and computer science.

5. Is a pure math major right for me?

If you have a strong passion for mathematics and enjoy solving complex problems, a pure math major might be a good fit for you. It requires a high level of dedication and a strong background in math, but it can lead to a fulfilling and intellectually stimulating career in various fields.

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