What’s a tiny bit critical mistake you’ve made in a proof, either for an assignment or for research?

I hear sometimes of people making mistakes in research and what not, and I am curious as to what kinds of mistakes are being made by professional mathematicians, in particular the smallest mistakes made.

submitted by Nevin Manimala Nevin Manimala /u/SrVishi
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Different representations of common mathematical concepts?

I recently discovered there’s a matrix representation of conic sections, and I was wondering if we can ‘connect’ two different areas of mathematics in a similar way?

Like, for example, this connects algebra and calculus:

  • the derivative of a quadratic function = ±√(its discriminant) (don’t know how to handle complex numbers using this, though)
  • Cramer’s rule, n×n-determinant method for solving a system of linear equations, etc.
  • Calculus and geometry? Apparently setting ∇Q = [0,0] for any quadratic curve gives its center

Please keep in my mind that I’m still studying in school, so if you talk about fields and Lorentz transformations and fifth dimensions and eigenvalues, I’ll lose you.

I’m desperately in need of some way to crack the maths section in my entrance exam that comes in a week, and I don’t want to screw my life over, so I’d like the trusty tricks of mathemagical veterans.

Thanks! Your help is appreciated!

EDIT: Formatting, and added the ∇Q bit

submitted by Nevin Manimala Nevin Manimala /u/OrochimarusCthulhu
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Good morning reddit. Care to try a few problems on my new math website? It won’t be horrible, I promise.

The site is setup for people who already know the math so they can more or less do it like a crossword puzzle. The subjects are:

  • Algebra
  • Trigonometry
  • Calculus
  • Vector Calculus
  • Linear Algebra
  • Statistics

This is the first time I have really “advertised” the site so you will be the first users and obviously not everything will be perfect. But I’d love it if some of you tried a few problems. The site is here.

submitted by Nevin Manimala Nevin Manimala /u/Nobody271
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Alternate fields over ℝ²

I want to define a field over ℝ². I am free to choose the elements 0 and 1 and the operations + and *

The most common way is 0 to be (0,0), 1 to be (1,0), (a,b) + (c,d) = (a+c,b+d) and (a,b)*(c,d) = (ac-bd, ad + bc). This is the way we define complex numbers.

Is the complex numbers the only possible field? Are their any other way to choose 0, 1, + and * so that it is a field?

submitted by Nevin Manimala Nevin Manimala /u/whichton
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Thematic: A Math Poem

A poem I wrote inspired by the documentary series ‘Dangerous Knowledge’.

Thematic

Welcome to the world of mathematics

With laws that seem universally static

from calculus to geometry to the quadratic

ruled by a genius few, rather erratic

laid down this world with strange schematics

these pupils pure souls, rather unpragmatic

seized by its beauty, they turned fanatic

their life dramatic, their end traumatic

but to this day they remain enigmatic

their theories, their ideas rather problematic

ostracized by many, they remained dogmatic

and exiled themselves to a dark dingy attic

sometimes distressed, sometimes ecstatic

their work paradigmatic seemed axiomatic

which in the end, turned them into a lunatic.

submitted by Nevin Manimala Nevin Manimala /u/oblectoergosum
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Why does real analysis come easier to me than abstract algebra

I’m taking a year long course in Abstract Algebra and Real Analysis, it’s partitioned into two parts. I always find that the analysis concepts come really easy to me, but the abstract algebra concepts are always a up hill battle. It seems like in Abstract Algebra I have to memorize a bunch of theorems and definitions in order to do well on Exams, but in Real analysis I can get by with just using my analytic abilities and memorizing very little. I know you should not memorize, but how do you except me to properly apply a theorem if I don’t even know the statement and edge cases? Abstract Algebra to me seems like a dull subject that’s filled with jargon and symbol pushing, I know that’s not true but that’s how I feel because everything I learn about rings, fields, and such seem to lack intuition of any kind. I don’t see why someone would define certain things in a proof, the whole thing is just a blurry mess for me.

submitted by Nevin Manimala Nevin Manimala /u/E40BayArea
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Does anything remain of Euler’s Conjecture?

Speaking specifically about Eulers Sum of Powers Conjecture, which states that if you add n integers, each taken to the kth power, that there will never be a solution if kn, for n>2.

I understand that the most general version of it has been disproved, but does anything remain of it? It looks like from Wikipedia that counterexamples have been shown for k equals 3, 4, 5, 7 and 8, but has it been shown that counterexamples exist for all combinations k and n, other than where n=2? Or is there some new modified conjecture stating that this limitations may exist for certain classes of k and n?

It just seems hard to believe that when n=2, there are zero solutions, but when n>2>n, there are always infinite solutions? What’s the current state of our understanding here for all ks and ns?

submitted by Nevin Manimala Nevin Manimala /u/VStarffin
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