141–150 of 231 posts
Two caveats: first, it is obviously biased to the sort of math I find enjoyable, and second, many of the suggestions require the reader to have that elusive quality called "mathematical maturity". (I have no idea how one goes about gaining mathematical maturity, despite having gone through this process myself.)
But if you want to give it a go, why not start with the tried and tested "Euclid's Elements" and a book on the history and philosophy of mathematics. If you are still interested, then tackle a course plan laid out by MIT or any other reputable university.
Also, I suggest getting an exercises/solutions book because math is doing. You can read the theorems, corollaries, etc and think you understand it but until you try to solve a problem yourself, you really won't know if you really understood the topic. And in your down time, you can check out math related channels/videos on youtube or elsewhere. It's going to take a lot grit and determination. Best of luck to you.
Here is a proven approach for at least the first part, building foundations and being ready for graduate work. Many Berkeley Ph.D. students passed through this route. Get the book "Berkeley Problems in Mathematics." It contains historical problems from the Berkeley math prelim exam, and solutions. Now don't look at any solutions yet. This is the exam all Berkeley math Ph.D. students must pass within three semesters o…
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From what I've observed, most engineers are glad to be done with math when they finish college. Most engineering is qualitative: Organizing and arranging things, making things fit together, and troubleshooting. Maybe 10% of engineering is quantitative, and that work often goes to the handful of people in the department who have maintained an interest in it. Some of the engineers who attract quantitative work are peop…
When you refer to engineers, do you mean actual engineers (BSc in Engineering)? or your web designer with jquery skills who calls himself engineer?
When you're designing a real-world engineering project, the entire specifications are defined legally (through national, state and local laws) and technically in manuals/books. Many engineering specifications will describe the work done to a T before you even need to think about it i.e. "water main shall be constructed of 12'' coated DIP at depth no less than 2 ft". A lot of the challenges are managerial and logistical.
All of this is on purpose. "Traditional" engineering disciplines are more mature and have the constraint of being safe for the general public. There isn't much room at all to creatively deviate from what's already specified.
I've found software design to be a lot more technically demanding in regards to designing and building things. There's a lot less precedent, more moving parts and many different ways to do one thing.
As an alternative I would suggest a top-down approach. Start with the theorems/results you truly wish to understand and work backwards. There was a great quote from an interview of Peter Scholze (one of last year's Fields' Medallists), which has really changed how I view learning: At 16, Scholze learned that a decade earlier Andrew Wiles had proved the famous 17th-century problem known as Fermat’s Last Theorem, which…
Here's my personal opinion about how you should approach this. It's all well and good to want to cover undergraduate math courses. When you are actually enrolled in a university, you will have enough inertia and motivation to complete the courses. However, when you are self-studying you are doing it all on your own. It's hard to be as thorough and cover everything. And so I ask, what really is your goal here? You don…
Personally, I think this is bad advice, because without an undergrad+ background, the projects above will either be impossibly frustrating or you will make up some crackpot bullshit. Plus, the undergraduate curriculum is its own reward.
Links:
http://content.algebraicgeometry.nl/2017-2/2017-2-007.pdf
https://projecteuclid.org/download/pdfview_1/euclid.ecp/1508...
Look for my name (Thomas / Tom Price) on these pages:
https://web.archive.org/web/20170121000748/https:/wwwmath.un...
https://www2.math.binghamton.edu/p/seminars/arit/arit_spring...
https://www2.math.binghamton.edu/p/seminars/arit/arit_fall20...
https://www2.math.binghamton.edu/p/seminars/arit/arit_fall20...
There's a set of basics that you will want no matter which direction you go: calculus/real analysis, linear algebra, differential equations/dynamical systems, and sets, groups, rings, and lattices. Calculus: learn to extract qualitative information about a function (it goes up here, has a maximum there, goes down there, oscillates with an increasing period, goes to this value at infinity...) and to numerically comput…
Most engineers I know have not learned set theory or groups/rings/lattices. They still seem to be doing pretty well.
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Personally, I think this is bad advice, because without an undergrad+ background, the projects above will either be impossibly frustrating or you will make up some crackpot bullshit. Plus, the undergraduate curriculum is its own reward.
Not necessarily. I left undergrad after four terms and self-studied to the point of having published research, giving invited talks, and even being a visiting researcher for three months with my expenses paid. Links: http://content.algebraicgeometry.nl/2017-2/2017-2-007.pdf https://projecteuclid.org/download/pdfview_1/euclid.ecp/1508... Look for my name (Thomas / Tom Price) on these pages: https://web.archive.org/web…
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I think setting attainable goals and working towards it helps. It is very easy to lose motivation if you don't know what you are going for..
Depending on your background, you probably don't have enough information to pick a long-term goal anyway. I am afraid that sounds curmudgeonly, but I have also seen students shoot themselves in the foot because they decided they didn't need a class for their not very well informed goals.
Nah, it's totally possible for newbies to pick high-level long-term goals.
This can be something like "I want to teach my computer to tell apart dogs and cats", or "I want to create a website where people can buy and sell yarn." From there, Google searches can direct someone towards concepts and various methods of learning them.
I mean, you can disagree all you want, but this is in fact how many people learn things.
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Personally, I think this is bad advice, because without an undergrad+ background, the projects above will either be impossibly frustrating or you will make up some crackpot bullshit. Plus, the undergraduate curriculum is its own reward.
Not necessarily. I left undergrad after four terms and self-studied to the point of having published research, giving invited talks, and even being a visiting researcher for three months with my expenses paid. Links: http://content.algebraicgeometry.nl/2017-2/2017-2-007.pdf https://projecteuclid.org/download/pdfview_1/euclid.ecp/1508... Look for my name (Thomas / Tom Price) on these pages: https://web.archive.org/web…
As an aside, your work on numerical cohomology appears to have been useful for a new result pertaining to lattices. Given the authors of the followup work it's likely helpful for the study of lattices in post-quantum cryptography.