Basis of $\mathbb{R}$ over $\mathbb{Q}$ exists by Axiom of choice, but is it...
Is it hard or proven to be impossible to construct basis $B$ of $\mathbb{R}$ over $\mathbb{Q}$?Small question regarding the cardinality:(If some miracle happened and CH turned out to be false, then...
View ArticleAre mathematical journals generally readable for graduated students?
I'm an undergraduate-level self-taught mathematics student. I'm estimating I might be around the second year of the degree on mathematics in terms of general knowledge. While I love the subject, i'm a...
View ArticleWhy can't you add apples and oranges, but you can multiply and divide them?
What is the algebraic difference between arithmetic operations, that prevents entities with different units from being summed or subtracted, but allows them to be multiplied or divided?This looks more...
View ArticleHow to explain to my daughter that $\frac {2}{3}$ is greater than $\frac...
I was really upset while I was trying to explain to my daughter that $\frac 23$ is greater than $\frac 35$ and she always claimed that $(3$ is greater than $2$ and $5$ is greater than $3)$ then $\frac...
View ArticleIs there any Complex Analysis book that is very "analysis"?
I have learned Complex Analysis for once, and I'm trying to review it. Then I found out that most Complex Analysis books are not very "analysis". That is, for typical analysis books(elementary...
View ArticleBook Recommendations for Learning Python for Mathematics.
Lately, I've been finding that I often need to compute various things and graph some pretty complicated functions. I've realized that learning to program, especially in Python, could be really helpful...
View Articleconventional notations for subsets/super-sets and proper subsets/proper...
Background$A\neq B\quad \tag{1}$Notations:$\subset,\subseteq, \subseteqq,\nsubseteq,\nsubseteqq,\subsetneq,\subsetneqq,\varsubsetneq,\varsubsetneqq \tag{2}$$\supset,\supseteq,...
View ArticleWhere exactly are we using the fact that $f$ is an odd function in the proof...
Consider the proposition that:$f:S^n \to S^n$ is an odd map $\implies$$f$ has an odd degree.Which is essentially the proposition used in Borsuk-Ulam theorem's proof as given in Hatcher. Now one point...
View ArticleRelation between Arnold tongues and Virasoro algebra
My knowledge in many mathematics topics is far from completeness, so please consider my question as so-called soft question.I know that Viroso group is a central extension of group of circle...
View ArticleHow to accurately average a function with a nonlinear response?
I am a physics PhD student working in optics and I have a bit of a weird problem that I am trying to sort out and I'm hoping you math folks can help me with.Without boring you with the experimental...
View ArticleI'm turning 18 soon, and I don't know how to do anything regarding college...
I'm sorry for how long, whiny, and pointless this will feel. I have not been able to find anyone aside from therapists to discuss any of this with, and I need advice from people who actually know what...
View ArticleTranspose method for finding a basis for the row space
My linear algebra textbook outlines a method of finding a basis for the row space of a matrix by finding a basis for the column space of its transpose. Is there any point of using this method? It seems...
View ArticleAt what point does working memory and IQ become a problem when trying to...
It may be one of the most uncomfortable questions one can ask themselves, but after having been a math student for 6 years (currently I'm in my first year as a PhD student), this question seems to...
View ArticleComments on the book Topology by James Dugundji
This post asks for comments on the book "Topology" by James Dugindji.Before I was given a copy of this book, I never read it in detail. When I did, I think this is a very good book. However, it seems...
View ArticleReferences and suggestions for calculus-1 B.Tech
I have just cleared the entrance examination and am planning on doing Mathematics and computing (B.Tech). The semester has not yet started but I am planning to pre-initiate the studies to get a lead...
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Possible trajectories with time travel
First of all, I'm not a mathematician, so sorry if the question is in layman terms.In the following picture, there is a character traveling toward the right.If the character encounters another...
View ArticleWhy is the Daniell integral not so popular?
The Riemann integral is the most common integral in use and is the first integral I was taught to use. After doing some more advanced analysis it becomes clear that the Riemann integral has some...
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About $p$-filters with $p\in\beta X\setminus X$.
I was reading this article and the next underlined part took my attentionThe definition of $p$-filter sounds so different from the usual definition of a filter in a topological space. I know that maybe...
View ArticleHow to express the originals system of equation in terms of its Groebner bases?
As a network engineer I need to explain some mathematical stuff to my fellow coleagues. Particularly, I need to explain the fact the the Groebner Basis will create an equivalent system. One particular...
View ArticleHow Does One Improve Problem Solving Skill
I feel that learning higher level topics in Mathematics doesn’t translate to helping one improve his/her problem-solving skill.To better explain my point, I think it would be useful to explain my...
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