Pure Mathematics vs. Applied Math vs. Discrete Math

In summary, the conversation discusses the differences between pure math, applied math, and discrete math and the speaker's concerns about choosing a university for their undergraduate degree in mathematics. They are considering Georgia State and Georgia Tech, and while Georgia Tech has a better reputation, they only offer applied and discrete math degrees. The speaker is concerned about attending a Group I university and whether it would affect their chances of getting into a PhD program in math. They also mention reading "A Mathematician's Survival Guide" and seeking advice on how to evaluate a university's math faculty. The conversation ends with a suggestion to try sampling both pure and applied math to see which the speaker prefers.
  • #1
DarrenM
81
1
"Pure" Mathematics vs. Applied Math vs. Discrete Math

I'm approaching the point where I'm going to have to decide which four-year university I'm going to finish my Bachelor's degree at. I'm pretty much restricted to colleges in Georgia, and I am primarily looking at Georgia State and Georgia Tech.

I know that Georgia Tech has a better "reputation," but I'm a bit concerned about the fact that the only mathematics degrees they offer are Applied and Discrete, particularly since my goal is to eventually enter into a PhD. program for Mathematics. Georgia State has a Mathematics undergraduate degree, but (I can't find the rankings right now) I'm pretty sure that GSU is not a Group I school.

I've just finished reading Steven G. Krantz's "A Mathematician's Survival Guide," and it was an excellent source of information; I have no doubt that it will continue to be a valuable resource. However, Dr. Krantz suggested that a student attend a university where the math faculty are well-known in the field (because letters of recommendation are so important in applying to math graduate school programs); the problem I'm having, in applying that to my situation, is that I don't have the requisite knowledge or experience to even assess how someone is viewed in their field. I can look at the number of recent publications, I suppose, but I don't think that's the same thing.

Hmm. I suppose I've strayed a bit from the question I was asking, however it is a related inquiry. I feel that the pure Mathematics degree would better prepare me for graduate school, but I'm concerned that not attending a Group I university would hamper my future graduate applications.

Any help would be much appreciated.
 
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  • #2


I am not sure of the schools you mentioned but if you want to pursue a graduate program in math, your undergrad should be in math. Pure math and applied math are very different programs - there is some overlap in Calculus, Linear Algebra, and Differential Equations, but even in your second year, the difference is very noticeable.

As for not attending a top university - pure math doesn't require nice labs and facilities to do your work. As long as your school offers the basic undergrad math courses (real & complex analysis, group, ring, and field theory, etc) you should be in good shape as far as knowledge of the subjects are concerned. If you are worried about research experience, perhaps try talking to people in the department to see if there are opportunities to math undergrads.
 
  • #3


Try to sample both disciplines to see which you like. I'm in an applied math program, but I will take a full year of analysis, a semester of algebra, and an independent topics class in topology. This is together with my required dynamic systems, ODE, PDE, and numerical analysis classes.

Snobby pure-math types will tell you to avoid applied-math like the plague, but decided for yourself. I think the wave equation from PDEs is quite possibly the coolest thing I've ever seen, but yet I love talking about pure math too!
 

What is the difference between pure mathematics and applied math?

Pure mathematics is the study of abstract concepts and structures, often with the goal of understanding the underlying principles and relationships. Applied mathematics, on the other hand, is the use of mathematical techniques and models to solve real-world problems in various fields such as physics, engineering, and economics.

How does discrete math differ from pure math and applied math?

Discrete mathematics is a branch of mathematics that deals with discrete objects and structures, such as integers, graphs, and networks. It is often used in computer science and information technology. Unlike pure mathematics, which focuses on continuous objects and concepts, or applied mathematics, which is used to solve real-world problems, discrete mathematics is more concerned with the study of discrete systems and their properties.

Can pure mathematics be applied in real-world scenarios?

While pure mathematics is primarily concerned with theoretical concepts and structures, its applications can often be found in various fields such as physics, engineering, and economics. Many real-world problems can be solved using pure mathematical principles and techniques.

What skills are needed for each type of math?

Pure mathematics requires strong analytical and abstract thinking skills, as well as a deep understanding of mathematical concepts and theories. Applied mathematics, in addition to these skills, also requires the ability to apply mathematical methods to solve practical problems. Discrete mathematics requires strong logic and problem-solving skills, as well as the ability to think abstractly and work with discrete structures.

Which type of math is the most useful?

All three types of math have their own unique applications and are useful in different fields. Pure mathematics provides the foundation for many other branches of mathematics and has practical applications in various fields. Applied mathematics is essential for solving real-world problems and developing scientific and technological advancements. Discrete mathematics is crucial in computer science and information technology. Therefore, it is difficult to determine which type of math is the most useful as each has its own importance and applications.

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