Intereting Posts

Show that $17 \mid 15! -1$
I understand what a division ring is, but cannot find any examples. Can anyone give me one?
if $A, B$ are open in $\mathbb R$ then so is $A+B.$
How to find the closed form of 10.3500574150076 with software/algorithm?
What precisely is a vacuous truth?
Size of a family of sets $F$ such that if $|A\cap X|=|B\cap X|$ for all $X\in F$, then $A=B$
The generators of $SO(n)$ are antisymmetric, which means there are no diagonal generators and therefore rank zero for the Lie algebra?
Computing $\int_{\gamma} {dz \over (z-3)(z)}$
Higher Ext's vanish over a PID
Deducing a $\cos (kx)$ summation from the $e^{ikx}$ summation
Compact operators and completely continuous operators
The general idea of prove openness.
Showing that $X^2$ and $X^3$ are irreducible but not prime in $K$
Entropy of a binomial distribution
If gcd$(a,b) = 1$, then I want to prove that $\forall c \in \mathbb{Z}$, $ax + by = c$ has a solution in integers $x$ and $y$.

I am a college student, at a community college and I am in the process of obtaining an associates degree in general science with a specialization in mathematics in hope of transferring to a university to major in electrical-computer engineering.

When I first started community college about 3 years ago I entered with little no knowledge of anything(I was an extremely lazy high-school jock and a mediocre one at that), I took every introductory course basically except for in English. My first math class was learning basic arithmetic and now I am entering a Differential equations and Calculus III class next semester.

Now that my background is out of the way I would like to get my question. I am looking for books to help me obtain a deeper understanding of lower level mathematics, basically everything from Pre-Calculus and down. While I know enough(of algebra, geometry, trig, precalc) to excel in the courses at my school, which I think is fair to say are watered down. I feel like at my school the courses have only touched the surface of lower level mathematics and I would like to delve deeper into them.

- What is the general equation of the ellipse that is not in the origin and rotated by an angle?
- Determine y-coordinate of a 3rd point from 2 given points and an x-coordinate.
- A Golden Ratio Symphony! Why so many golden ratios in a relatively simple golden ratio construction with square and circle?
- Is there a simple proof of Borsuk-Ulam, given Brouwer?
- Find the sum $a,b,c,d,e,f,g$
- Minkowski sum of two disks

I have done some research and *think* that the books I am looking for are Algebra, Trigonometry, Functions & Graphs, Method of Coordinates, Sequences-Combinations-Limits; all by Gelfand.

I am also looking for books, on geometry(Now I don’t know if I should find a classical Geometry book or a Euclidean Geometry book; *I think* the two are the same but I don’t know)

Also, I am looking for a book that teachers about the number system, like the difference between Real numbers and complex numbers, and how the Reals branch off between natural, rational, irrational, etc.

And a book on mathematical notation would nice.

Finally, I need to know what order would be best to read these books. Basically I want to know the order in which would provide the best flow or synergy with one another.

I am obviously not going to buy all these books at once and this list is by no means set in stone and is subject to change.

Another reason that I want to get a deeper understanding of these subjects is because I feel like my lack of depth is what hindered me in my linear algebra class this semester, I did okay overall but I had hard time because the book used a lot of notation and symbols with stuff that I didn’t know.

I eventually, after reading these books, is get better books for calculus, linear algebra, and discrete mathematics.

Thanks.

- Convergence in distribution of conditional expectations
- An ancient Japanese geometry problem.
- What can I do with proper classes?
- Given a helix, consider the curve of it's tangent. Express the curvature and torsion of such a curve.
- What REALLY is the modern definition of Euclidean Spaces?
- Different ways finding the derivative of $\sin$ and $\cos$.
- How can the angle be found in this triangle?
- Probability spaces over graphs: which area has focus on them?
- What is the connection between linear algebra and geometry?
- Group theory text

- Integral representation of Bessel function $K_v(y) = \frac{1}{2} \int_{0}^{\infty} t^{v-1} \text{exp}(-\frac{1}{2}y(t+t^{-1}))\text{d}t$.
- The preimage of a maximal ideal is maximal
- groups with infinitely many ends are not boundedly generated?
- Confused about notation “:=” versus plain old “=”
- Coin with unknown bias flipped N times with N heads, what is p(h)?
- Convergence in distribution of conditional expectations
- What is the simplest formula for activation / smooth step function?
- Pairing function for ordered pairs
- Alternative proof of $\sqrt{2}$ is irrational assistance.
- Completion of a Noetherian ring R at the ideal $ (a_1,\ldots,a_n)$
- Intuitive explanation of covariant, contravariant and Lie derivatives
- Irreducibility of $X^{p-1} + \cdots + X+1$
- Evaluating $\lim_{b\to\infty} \int_0^b \frac{\sin x}{x}\, dx= \frac{\pi}{2}$
- How does one evaluate $\sqrt{x + iy} + \sqrt{x – iy}$?
- Find all $A,B$ such that $AB-BA=0$.