Intereting Posts

How can I prove that all rational numbers are either terminating decimal or repeating decimal numerals?
Circle revolutions rolling around another circle
Dense curve on torus not an embedded submanifold
Asymptotic behavior of system of differential equations
Solving Cubic Equations (With Origami)
Finite projective dimension and vanishing of ext on f.g modules
Finding all matrices $B$ such that $AB=BA$ for a fixed matrix $A$
Simple series convergence/divergence: $\sum_{k=1}^{\infty}\frac{2^{k}k!}{k^{k}}$
If $a=\langle12,5\rangle$ and $b=\langle6,8\rangle$, give orthogonal vectors $u_1$ and $u_2$ that $u_1$ lies on a and $u_1+u_2=b$
Why does dividing a vector by its norm give a unit vector?
If $abc=1$ so $\sum\limits_{cyc}\frac{a}{\sqrt{a+b^2}}\geq\frac{3}{\sqrt2}$
how the Kronecker product is a tensor product?
In Fitch, is a symbol not in a specified language automatically free?
Why is $L^1(\mathbb{R}^n) \cap L^2(\mathbb{R}^n)$ dense in $ L^2(\mathbb{R}^n)$?
How can I find the possible values that $\gcd(a+b,a^2+b^2)$ can take, if $\gcd(a,b)=1$

I’m searching for some references that deal with topics from “elementary geometry” analysing them from a “higher” perspective (for example, abstract algebra, linear algebra, and so on).

- Existence of normal subgroups for a group of order $36$
- Good books and lecture notes about category theory.
- If $R$ is an infinite ring, then $R$ has either infinitely many zero divisors, or no zero divisors
- Divisible module which is not injective
- $(R/I)=R/I$
- Proving irreducibility of $x^6-72$
- How many cards do you need to win this Set variant
- Why do mathematicians use this symbol $\mathbb R$ to represent the real numbers?
- Question about Algebraic structure?
- Matrix Theory book Recommendations

The book *Algèbre linéaire et Géométrie élémentaire* by Jean Dieudonné is a highly formal presentation of elementary geometry using linear algebra. It’s the way the Bourbaki school might have taught geometry in high school.

Two books called *Linear Algebra and Geometry*, one by Kostrikin and Manin, the other by Shafarevich and Remizov, apply linear algebra to geometry, but don’t limit themselves to revisiting elementary topics.

Artin’s book *Algebra* uses many examples from geometry to illustrate the theory (groups, etc.).

Finally, Volume 2 of the book *Fundamentals of Mathematics*, edited by Behnke and Bachmann, examines geometry from various axiomatic perspectives which, while modern, rigorous, and at times quite abstract, are perhaps closer in spirit to Euclid than to an exposition of geometry through linear algebra.

Kaplansky’s *Linear algebra and geometry* does a nice readable overview of the connection with linear algebra. Artin’s *Geometric algebra* goes further in depth! but is a little less fun to read. Then there are Kaplansky’s references to Coxeter’s books which I imagine are great, but I haven’t had the time to read them yet.

Try Jürgen Richter-Gebert: *Perspectives on Projective Geometry*. It shows the classical material in a modern way, and is written in an excellent pedagogical style.

- Simple formula on $X_n^{(k)} = \sum_{1 \le i_1 < … < i_k \le n} Y_{i_1} \cdot \dots \cdot Y_{i_k}$ (to show $X_n^{(k)}$ is martingale)
- Cross product of the reals question
- Why not defining random variables as equivalence classes?
- Cohomology of projective plane
- Integral $\int_0^{\pi/4} \frac{\ln \tan x}{\cos 2x} dx=-\frac{\pi^2}{8}.$
- Prove that a continuous function $f:\mathbb R\to \mathbb R$ is injective if and only if it has no extrema
- Point reflection over a line
- Let $f:\mathbb{R}\longrightarrow \mathbb{R}$ a differentiable function such that $f'(x)=0$ for all $x\in\mathbb{Q}$
- A set with measure 0 has a translate containing no rational number
- Determining the rank of a matrix based on its minors
- What is the 90th derivative of $\cos(x^5)$ where x = 0?
- Difference between proof of negation and proof by contradiction
- Maximal ideal in commutative ring
- Is the shortest path in flat hyperbolic space straight relative to Euclidean space?
- Books in foundations of mathematical logic