28 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

I think a more correct view is that proof is the LAST of several stages involved in researching something in math. What follows is a quickly sketched out scenario of what is often the case. Before ...
14 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

With the technological advances of the past couple decades, computational mathematics is now somewhat accessible to undergraduates. The wikipedia entry for computational mathematics lists out the ...
  • 6,579
14 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

I have taught Discrete & Computational Geometry to US undergraduates project-based, as opposed to assignment- and test-based. Some of the projects do involve proofs, but others are more ...
11 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

In other words, "knowing" math meant pretty much diddily-squat unless I could formally and rigorously write out proofs for everything I thought I knew. You appear to believe that somebody ...
  • 231
10 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

When I describe undergraduate research to students majoring in mathematics, I ask them to browse the abstracts of the most recent MAA undergraduate poster session. Here is a link: Abstracts for the ...
  • 8,133
8 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

Not quite an answer to your question, but if you have students who are interested in mathematics but not interested in (generating their own) proofs, encourage them to go into mathematics ...
  • 2,607
8 votes
Accepted

Is the Wronskian still assumed for graduate education?

I would say the assumption is that people heading to mathematics graduate school know about the Wronskian, but this assumption isn't universally true. Certainly, anyone who has studied a semester of ...
7 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

No. By definition, mathematics is the study of what can be formally proved, so if someone is not at all concerned with proofs, they are not doing mathematics (but possibly some math-related subject). ...
7 votes

What are some ways that one can progress from stage 2 to stage 3 of the rigor stages that Terry Tao has described?

This is not as much to answer the original question (to which the answer is just that you develop any skill by trying to practice it and evaluating the results) but to tell what my understanding of a &...
  • 851
6 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

Especially with the advent of relatively very fast numerical and symbolic manipulation software/computers, giving numerical evidence for various things is an eminently feasible, and interesting, ...
  • 13.7k
5 votes

Which books on geometry and topology are best for teaching an intro graduate course?

Disclaimer: I haven't taught the kind of course you describe, so please take my recommendations below with a grain of salt. Nevertheless, I hope they're helpful. John M. Lee's Introduction to ...
  • 4,502
5 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

IF you have kids that like math, but not proofs, I suggest modeling financial systems (e.g. actuarial issues) or the like (e.g. refinery operation) is a good activity for undergrad math majors. Data ...
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4 votes

Is the Wronskian still assumed for graduate education?

It is discussed in all the introductory DEqns texts of which I've used. It's needed to complete the discussion of linear independence of solution sets. Together with Abel's formula it provides some ...
2 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

Digital signal processing would seem like a good avenue. The colors on this monitor, the audio and video, the compression, the encoding, the timing, everything digital is passing in and out of digital ...
2 votes

What are some good examples to motivate the implicit function theorem?

I assume your students have seen Linear Algebra. Remember in Linear Algebra how you sometimes have to solve $Ax = b$ for a matrix $A$ with more columns than rows? You usually get free variables, right?...
  • 349
1 vote

Is it weird for an undergrad or grad quant/applied maths(/even pure maths) programme to not teach that probabilities of 0 or 1 will never change?

It's not weird. The institutions are busy teaching the bulk of their topics. Busy with conveying (what is at the end commercially important) knowledge to imperfect recipients, with limited time. ...
  • 11

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