# Tag Info

1 vote

### Vector analysis text book.

It is "Calculus: Early Transcendental Functions" by Robert T Smith and Roland Minton. I found it here on page 876. It seems to be a matter of luck whether Google shows this page on a preview ...
• 6,455
1 vote

### Where do i start learning recursion for mathematical olympiads?

Not sure if this is useful, but there is a textbook called "Further Pure Mathematics 2" published by Pearson, which is intended for high-school students studying Edexcel AS and A Level ...
• 333

### Realtionship between automorphism number of a graph and subgraph count

I think that a way to see $S'_{H,N}$ is just the set of all bijections (i.e., functions $f$ from an arbitrary subset of nodes of size $m$ of the graph $G$), that ''map'' on $H$. Therefore for each ...

• 3,367
1 vote
Accepted

### Finding References for known results about mixing time of a Markov chain arising from Gaussian elimination

There are at least $N=c2^{n^2}$ invertible matrices mod 2, where $c=1/2(1-1/4)(1-1/8)\cdots (1-2^{-k})\cdots>0$. Since there are less than $n^2$ possible moves in each step, after $t$ steps the ...
• 22.1k

### Topology textbook with a solution manual

Four other than Munkres (who benefits from fair-sized readership) come to mind (as a fellow self-student who appreciates solutions after over-extended attempts). Two introductory: Introduction to ...
• 325
1 vote

### Law of large numbers result for largest component in Erdos-Renyi

See Lemma 2.12 here: https://www.math.cmu.edu/~af1p/BOOK.pdf Essentially the limit you ask for is like $1/(p-1-\log p)$ (But you should use c, not p, since p is usually the notation for the edge ...
• 511
Accepted

### Law of large numbers result for largest component in Erdos-Renyi

With apologies, I will switch the notation, to avoid writing $\frac pn$ for the edge probability (which is almost always $p$, and $p = \frac pn$ would be silly). Let's say we are looking at $G(n,p)$ ...
• 144k
1 vote
Accepted

### References to study Clifford algebras

Only two of the six books I checked give an explicit proof that you can generate a basis for the entire Clifford algebra from an orthogonal vector basis: Ian Porteous in Clifford Algebras and the ...
• 7,100

• 4,302

### Find the Harmonic Mean Using Parabola

It seems that this method I'm talking about is just another version of the Cross ladder theorem.
• 2,518

### Thurston's metric on $\widetilde{SL(2,\mathbb{R})}$ is twisted. So is this paper "wrong"?

After taking a carefull read in P. Scott's The Geometries of 3-manifolds, I'm posting a (partial) answer myself. Basically, I just misunderstood concepts. Many sources call Thurston's model geometries ...
• 2,769
Accepted

### Calculating the n-th power of any 2×2 matrix

I found a reference, see McLaughlin, where the applications listed in the post have already been done. However, I did not find a reference of the above proposition, which was concluded independently ...

### Is there any online source for proofs than $(1+\frac{1}{n})^n$ and $(1+\frac{1}{x})^x$ is $e$?

This limit definition comes from the fact that $\frac{d}{dx}(e^x)=e^x$, so we can start by stating the formula for a slope with a really small $\Delta$, $\frac{f(x+\Delta)-f(x)}{\Delta }$ so this ...
Accepted

### How is the discriminant defined for $x^3+y^3+z^3+u^3+(ax+by+cz+du)^3+exyzu$?

I have good news & bad news. The good news is that there is a method to get the Discriminant. The bad news is that the eventual expression is going to be impractical & very hard to write out. ...
• 11k
For Weyl groups of type $A$, $B$ and $D$ GAP has built-in generic parameterized tables via ...