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Mathematicians are chronically lost and confused (2014)
21–30 of 147 posts
Re: Mathematicians are chronically lost and confused (2014)
#22I have a great personal story that highlights how long the journey of understanding mathematics is. I took linear algebra my freshman year of college. It was the non-math major course, so it didn't require proofs. I got an A+ in the class. Not just an A, an A+. I was able to obtain such a high grade by taking tons of practice tests, and since the actual tests were basically mildly veiled calculations, I just had to m…
Math programs in general suck at telling you why a particular technique is useful in the real world, or more importantly, how to model. Lots of ways to solve an existing model, but very few touch the much harder task of building a model in the first place.
Re: Mathematicians are chronically lost and confused (2014)
#23I have a great personal story that highlights how long the journey of understanding mathematics is. I took linear algebra my freshman year of college. It was the non-math major course, so it didn't require proofs. I got an A+ in the class. Not just an A, an A+. I was able to obtain such a high grade by taking tons of practice tests, and since the actual tests were basically mildly veiled calculations, I just had to m…
Somewhat ashamedly, I have a 1st Class BSc Honours in Mathematics with much the same experience. It's fairly easy to fake an understanding of mathematics if you can understand that the exams paper will be a variant past exam papers.
Re: Mathematicians are chronically lost and confused (2014)
#24Does anybody know a good guide on where to begin? Resources are not the issue here, but usually the overwhelming amount of information regarding all those topics and areas of mathematics. I was always very interested but got discouraged rather quickly, even after a semester at university. So far my favorite access to math was through philosophy.
I made a 3-page overview of calculus as an extra section of some notes for a class I'm teaching. Mostly to see if it could be done.
Here it is. https://www.dropbox.com/s/yp8ijkzir4h8rz9/Calculus%20in%20e%...
I'm REALLY sorry for the picture quality. I'll use a proper scanner later. My phone's camera and app are terrible.
Re: Mathematicians are chronically lost and confused (2014)
#25I have a great personal story that highlights how long the journey of understanding mathematics is. I took linear algebra my freshman year of college. It was the non-math major course, so it didn't require proofs. I got an A+ in the class. Not just an A, an A+. I was able to obtain such a high grade by taking tons of practice tests, and since the actual tests were basically mildly veiled calculations, I just had to m…
I've had a similar experience several times. I feel like in college I was mentally much faster, but lacked insight (and probably curiosity).
There have been several times when I've picked up an old math or CS textbook and read something I never really fully understood in college -- it almost instantly makes intuitive sense to me now -- 20 years later.
There's an old saying that college is wasted on the young... in many ways I believe it is true.
Re: Mathematicians are chronically lost and confused (2014)
#26Earlier quoted context omitted.
Step 1: Read Lockhart's Lament: https://www.maa.org/external_archive/devlin/LockhartsLament.... Step 2: Download the Book of Proof: http://www.people.vcu.edu/~rhammack/BookOfProof/ You read through it and do all the odd numbered exercises (the solutions are at the end of the book). Step 3: Get a book called Real Mathematical Analysis by Charles Pugh and you work through that and attempt as many problems as you can, w…
I'd also recommend Hubbard & Hubbard for a beautiful and beginner-friendly mix of algebra and analysis. My preferred starter kit is Rudin plus Halmos or Axler, but treating Rudin as a summary. So a helper would be needed, like Counterexamples in Analysis. This is what Math 55 used to do.
I started with Hubbard & Hubbard. It is truly wonderful (and based on Spivak's other calculus book), but I couldn't imagine learning it without either significant background or a formal class. Even with a 2 semester class devoted to it in college, I ended up not understanding the most advanced concepts (eg. differential forms) until years later when it finally came up again in graduate-level courses. Of course, it was really an excuse to learn to think mathematically, not to learn calculus on manifolds.
Re: Mathematicians are chronically lost and confused (2014)
#27Does anybody know a good guide on where to begin? Resources are not the issue here, but usually the overwhelming amount of information regarding all those topics and areas of mathematics. I was always very interested but got discouraged rather quickly, even after a semester at university. So far my favorite access to math was through philosophy.
Since philosophy was your favourite, you might enjoy the novels of Greg Egan. As far as I can tell, he puts good mathematics in his stories.
I recently read my first Greg Egan and enjoyed it (Quarantine). Got any recommendations for specifically the ones he put good math into?
Re: Mathematicians are chronically lost and confused (2014)
#28Does anybody know a good guide on where to begin? Resources are not the issue here, but usually the overwhelming amount of information regarding all those topics and areas of mathematics. I was always very interested but got discouraged rather quickly, even after a semester at university. So far my favorite access to math was through philosophy.
If I were you, I'd start here (free book on the basics of math without which it's very easy to drown in the so called proof-based math):
Re: Mathematicians are chronically lost and confused (2014)
#29Earlier quoted context omitted.
Since philosophy was your favourite, you might enjoy the novels of Greg Egan. As far as I can tell, he puts good mathematics in his stories.
I recently read my first Greg Egan and enjoyed it (Quarantine). Got any recommendations for specifically the ones he put good math into?
Perhaps Incandescence, though it's less about mathematics and more about a society working out the physics of its environment. His website has more maths on it than I recall being in the novels.
Re: Mathematicians are chronically lost and confused (2014)
#30To me, this is about "mathematical maturity". My observation is that many programmers, especially those who have come of age by working in startups, tend to value ability and sometimes experience over formal education. This is a result, I believe, of noticing that they can outperform many people who have a classical education, and also seeing that many of the people to whom they look up also do not have much in the w…
I disagree that mathematics itself is difficult to engage with outside of academia.
There are some academic mathematicians who think mathematics has to be hard because it was difficult for them to understand. There are others for whom sharing their insights is more important than searching for new ones. I think that the set of mathematicians together have done a rather good job in the 20th century of producing mathematical literature and pedagogy that laypersons and the polymaths can understand.
I skipped university when I was young due to circumstance. I still had a love for maths but couldn't pursue formal training. When I came around to programming as a career instead of odd-loner-hobby it was as you say. I was quite impressed with my ability to code circles around CS graduates who, for all their theory and training, weren't prepared for "coding in the real world."
I never stopped studying mathematics. I've recently been going through temporal logics. If only more programmers were aware of the beauty of the proof of weak fairness. And its implications in system specifications.
Where I can see formal training being useful is exposing you to subjects you were not aware of in short order. My experience has been more akin to the mansion metaphor. Where I encounter limitations or difficulties in my programming I look to maths for the right tool to simplify the task and ensure it is correct.
So I agree about "mathematical maturity." I just don't believe it is exclusively acquired in an academic setting. I think some people have an inclination or awareness that pushes them to think this way.