Abstract math Definition and 20 Threads

Please, I have a question about automorphism: Let ##\mathbb{K}## be a field, if ##\operatorname{char}(\mathbb{K})=p ##, then the order of automorphism ##\phi## is ##p##, i.e. ##\phi^p=\operatorname{id}##, where ##i d## is identity map. Is that right? please, if yes, how we can prove it, and...

I got bored a while back and deiced to create a table of the integer inputs of f(x)=(1+i)^x and I noticed quiet a few patterns which I am trying to catalog here, although most of my work so far deal with Natural inputs, all patterns continue into the negative, see here, I was wondering if anyone...

I'm currently a first year MathPhys student, and next year I have to decide my stream. I can pick a combination (pure) Mathematics, Applied & Computationtal. Mathematics, Statistics, MathSci, Physics, Theoretical Physics or Physics with Astronomy & Space. Naturally there are restrictions, and I...

Homework Statement Express the following statement using only quantifiers. (You may only use the set of Real and Natural Numbers) 1. There is no largest irrational number. Homework Equations ##\forall=## for all ##\exists##=there exists The Attempt at a Solution I express the existence of...

I'm taking an abstract algebra course that uses Hungerford's "An Introduction to Abstract Algebra" 3rd Ed. And while I feel like I'm following the material sufficiently and can do most of the proofs it's hard to learn and practice the material without a solutions guide. How am I supposed to know...

Homework Statement Simplify the following statement as much as you can: (b). ##(3<4) \wedge (3<6)## Homework Equations ##\wedge= and## The Attempt at a Solution I figured that I could just write this as ##3<4<6##, but then I considered what if I didn't know that ##4<6## If it was just...

I'm good at math like stats calc and others that r more process based. But I suck at things like abstract math, pure math , proofs etc. Am I an idiot? I'm OK with being stupid, I know it does not define a persons worth..

See attached picture. The question asks to prove that the statement which I have written on the first line is true. But I somehow proceeded to proving it is false. Basically what I did was simplify the given expression into the form (P or Q) => R and said this is equivalent to (P=>R) ^...

Homework Statement Let f: Z to ZxZ be the function defined f(t)=(3t, 3t+1) . Let B denote the subset of ZxZ defined by B={ (5m, 5m+1) : m is an element of Z}. Determine f^-1(B). This means that you should define set S with a property of S=f^-1(B). In addition, your definition of S should make...

Homework Statement If A is a set that contains a finite number of elements, we say A is a finite set. If A is a finite set, we write |A| to denote the number of elements in the set A. We also write |B| < ∞ to indicate that B is a finite set. Denote the sets X and Y by X = {T : T is a proper...

Homework Statement Let p(x)=xx+x+4 Determine a set S such that S ={p(n), n is an element of Z). Your defition of S should not refer to the polynomial p(x). Homework Equations S={n is an element of Z: p(n)=nn+n+4) The Attempt at a Solution I know that we can't take roots of p(x)...

A good book on Abstract Algebra that covers major undergraduate and graduate topics? Something rigorous professional and for mathematicians. Not Hungerford please, or any n x $100 book.

Homework Statement Let Ts denote the set of points in the x; y plane lying on the square whose vertices are (-s; s), (s; s), (s;-s), (-s;-s), but not interior to the square. For example, T1 consists of the vertices (-1; 1), (1; 1), (1;-1), (-1;-1) and the four line segments joining them...

(1)Assume a, b and n are nonzero integers. Prove that n is divisible by ab if and only if n is divisible by a and n is divisible by b.I'm wrong and can't remember why. I spoke to the professor about it for ~ 1 minute so it seems to have slipped my mind, it was because in one case it's true and...

Homework Statement Find a statement for , S, equibalten to ~(P v Q) and show that it is logically equivalent by construction the truth table for "S if and only if ~(P v Q)" and showing that this statement form is a tautology. Homework Equations The Attempt at a Solution My...

Man I've become desperate. I just signed up needing help on this homework. Can anyone help me with these two problems? Let A be the set {1,2,3,4}. Prove that a relation R on A with 15 ordered pairs is not transitive. I've got no clue on that one. And this second one, which I know...

Homework Statement If x_n\rightarrow L and y_n \rightarrow M prove that x_n - y_n \rightarrow L-M Homework Equations Definition of Limit The Attempt at a Solution I followed and stayed within the definition of limit of a sequence, but I got 0 for x_n - y_n.

Category theory is considered extremely abstract. What are some other branches of mathematics which are considered as abstract or even more abstract then category theory?

I had some colleagues in College who took a degree in Math on their first two years. After finishing their second year, they shifted to a different course. They already finished from Algebra to Calculus and they were in an even higher math. They were asked to prove that 1 + 1 = 3 This is...

I'm giving a talk entitiled "concrete analogies of abstract concepts", where I give examples of concepts in mathematics that might have arisen in things found in every day life. I already have "chess" for isomorphism and "acronyms" for homomorphisms, but I'm running a bit dry. Anyone got any ideas?