Undiscovered Abstract Algebras
I'm a layman when it comes to abstract algebras, so I hope this question gets well-received and makes sense. I know some basic Clifford Algebra, Kac-Moody Algebra, Lie Algebra, etc but nothing too...
View ArticleHow to motivate and deal with speculation?
I hope/think that this is an appropriate soft-question.I am a student of mathematics and have been increasingly feeling doubtful about whether or not I really understand the theory. What I mean by this...
View ArticleHow can I motivate and deal with speculation?
I am a student of mathematics and have been increasingly feeling doubtful about whether or not I really understand the theory. What I mean by this is highly attributed to the style of textbooks in...
View ArticleHow to understand Galois Representations as an undergraduate? [closed]
I am looking to doing my undergraduate thesis on Galois Representation Theory.I am currently taking a class in Galois Theory and learning Algebraic Geometry independently.Are there any resources that I...
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Wrong Answers - Excel Imprecision question for $\pi$ from letters
I probably should have posted this yesterday on 3/14...I'm working through a puzzle I became aware of and I think I may be getting a wrong answer as a result of Excel and its precision. My question is...
View ArticleMathematical places to visit [closed]
There are certain buildings and places on this planet where mathematicians can find delight because of the history, the art, the architecture, and for other reasons. For example, the Alhambra with its...
View ArticleCan epsilon be a big positive number?
This is a bit of a soft question, but I was just wondering, in the real analysis epsilon-delta definitions of limits and continuity, can epsilon be a very big positive number, like a googol, or a...
View ArticleFinitists reject the Axiom of Infinity - are there groups who reject the others?
I've seen rejections of the Axiom of Infinity. This is called finitism. Some ultrafinitists even add the negation of the Axiom of Infinity. Definitely doable.I've seen rejections of the Axiom of...
View ArticleUnderstanding the Round Metric and various other Metric Tensors on $S^2$.
Suppose we are dealing with a $2$-dimensional sphere.For simplicity we consider $S^2\subset \mathbb R^3$.Now we can give a parametrization on the sphere via the map $\varphi:(0,2\pi)\times(0,\pi)\to...
View ArticleWhy isn't finitism nonsense?
This is a by product of this recent question, where the concept of ultrafinitism came up. I was under the impression that finitism was just "some ancient philosophical movement" in mathematics, only...
View ArticleHow do I sell out with abstract algebra?
My plan as an undergraduate was unequivocally to be a pure mathematician, working as an algebraist as a bigshot professor at a bigshot university. I'm graduating this month, and I didn't get into where...
View ArticleSolving equations in the moduli and conjugate of complex numbers
I've been working on solving some equations in the moduli and conjugate of complex numbers and it always seems to take me awfully long to arrive at an answer.For example, solve $1+2|z|^2 =...
View ArticleOrder of the differential equation: [closed]
After reading the book, I am having confusion to calculate the degree of the following differential equations:\begin{align}&\frac{d^2y}{dx^2}+ x\sin{y}=0 \text{...
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Organizing the content of Euclidean geometry with pictorial mind maps
There is an idea that has been on my mind for a while, and I would like to share it so that it turns into a snowball. Perhaps it will be useful and attractive to engineering enthusiasts. I ask you to...
View ArticleIs there any difference between mapping and function?
I wonder if there is any difference between mapping and a function. Somebody told me that the only difference is that mapping can be from any set to any set, but function must be from $\mathbb R$ to...
View ArticleHow can one compute rounding preservant integrable functions?
Background & Context : The background of the question is an engineering problem.I want to efficiently represent a set of integers as rounded real valued functions and quickly be able to calculate...
View ArticleHow one can notice when a famous formulas is extended?
This integral: $\int\left( \frac{x^2}{1+x^2} \right)\frac{1-x\tan(x)+ \tan(x)-x}{1 -x\tan(x)-\tan(x)-x}dx$ seems to be complicated even Wolfram Alpha can't solve it, but it can be easily solved if one...
View ArticleConfidence interval construction for $f(p)$ of categorical distribution...
Let $X_1, \dots, X_n$ be i.i.d. random variables from a categorical distribution with parameter vector $p = (p_1, \dots, p_k)$.Suppose we’re interested in the estimating $\vartheta := f(p)$ for some...
View ArticleWhy is the exponential function the most important?
In the prologue to his Real and Complex Analysis, Walter Rudin states matter-of-factly that $\exp$ is the most important function in mathematics (take note, not merely in analysis). This looked so...
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