Classes Definition and 592 Threads

How do you write in proper set theoretic notation that a set A = (x,x) where x is a non-negative real number? Also, (x_1, y_1) R (x_2, y_2) if x_1 ^2 + y_1 ^2 = x_2 ^2 + y_2 ^2 The equiv. classes are circles at (0,0), right? How do you write this formally (using set theoretic notation)?

I know zero about the characteristic classes of finite group representations and would appreciate a reference. specifically, if I have a faithful representations of a finite group,G, in O(n) what can I say about the induced map on cohomology, P*:H*(BO(n))-> H*(BG) ? I am mostly interested in...

Hi my name is David. I live in Canada. I wanted to know if anybody knew the policies/regulations/opportunities here in Canada regarding individuals sitting in on college/university classes. I am on a fixed income and can not afford to pay for school and I suffer from severe fatigue so full...

Hi I am new using pointers and i am having a hard time trying to figure out how to write a program in c++ using pointers and classes. The program can be used to translate whole dollar amounts in the range 0 through 9999 into an English description of the number. For example, the number 713...

Say two students both express interest in becoming experimentalists of some sort. They both have research experience with experimentalists, comparable GPA's and GRE's, even similar letters of rec. However, one of them took two computer science courses, and the other didn't. Would admissions...

i don't clearly understand that what are the real and imaginary numbers in c++ classes when defining operators. help me . thnx

Is there a way to figure out the number of equivalence classes for all graphs of order n, size k?

I'm talking about undirected simple graphs.

Homework Statement Is there a proof that the number of elements in a conjugacy class of a group has to divide the order of the group? Everyone seems to cite it left and right but I've not seen a proof of it anywhere. Homework Equations The Attempt at a Solution I'm guessing...

These two terms would be the simplest terms in the set theory as they are on the first chapter in my textbook. But why can't i understand it? In my textbook it says A relation R in a set is a set of ordered pairs, so any subset of a set of ordered pairs will be a relation. This includes the...

What are complexity classes (P, NP, etc) in terms of pure sets? ZFC, I mean.

I'm an undergraduate who will be going on to graduate school in physics. I only have two physics classes remaining after this semester, but I have a full year before graduation. Any recommendations for classes to take/things to do in the meantime. I've got a couple ideas myself. What do you...

I'm a junior as a mech engineer and i just feel so bad getting C's in my engineering classes so far. I mean do i deserve to become an engineer if all I can do is get C's? How will this impact me when i do get a job? I lost all confidence in myself right now and i don't know if i can concentrate...

Homework Statement Create a class that adds counts of letters or two Strings, and create an object which represents sum of the counts. Homework Equations n/a The Attempt at a Solution i am confused about how to construct objects in a class itself, and not in client code. as in...

Homework Statement Determine the set of similarity classes of 3x3 matrices A, over C, which satisfy A^3 = 1. Determine..etc etc...which satisfy A^6 = 1. Determine the set of similarity classes of 6x6 matrices A, over C, with characteristic polynomial: char(A,x) = (x^4 -1)(x^2 - 1)...

Will not taking math classes beyond what's required for the physics major hurt me when trying to get into grad school for physics? At my school the only required math classes for physics majors are calculus I, calculus II, multivariable calculus, and differential equations. Also I've taken a...

So this summer I'm thinking about taking some community college classes so my summer isn't a total waste. I've taken precalc, ap physics b, and ap chemistry. I'm just wondering if anyone has any ideas of which classes would be mo Applied Physics General Physics and Calculus 1 College...

This is a bit of an odd question, but it's been bothering me for a while. The graduate sequences at top universities (Algebra, Geometry/Topology, Analysis) have always been rather esoteric in nature. Most students entering top universities have a rather strong background in these topics and...

Suppose I had a lot of residue classes and I wanted to find the probability that a random integer (mod the product of the moduli) was in at least one of the classes. How could I calculate that? If the moduli were pairwise coprime, it would be easy: start an accumulator at 0 and for each class...

Can anyone explain/give a good reference for Stiefel-Whitney homology classes?

Homework Statement How would we find number of similarity classes for a nxn matrix over the field Fp (cyclic of order p) for n=2,3,4? Homework Equations A and B are similar iff they have the same monic invariant factors The Attempt at a Solution I would say 4 classes for n=2, since...

Hello, I am trying to brush up on some mathematics and realized that I have to start from the very bottom. I keep getting confused by the symbols and it has been an ardeous last few days! Anyway, going through some stuff on set theory and came across the concept of equivalance classes. Let...

C++ -- Nested Classes A post or two I have been working with appeared to be associated with students in a C computer language programming course. In other words, the class may have not been object oriented. Also, mentioned in one post was the concept of housekeeping being less important than...

Hi, I'm a high school senior that's just been admitted to Caltech. They sent me their course catalog in the mail, and I've been looking over it this week. I want to major in physics, and someday study elementary particles, gravitation, and string theory. What math should I take? Caltech...

So, I've decied to major in Computer Science w/ a minor in Mathematical Sciences; however, I'm in a dilemma. I need to choose 3 more classes (out of the list below; I've already chosen the other 4 classes) and I'm not sure which ones I should take to make myself more "marketable" and a better...

Somebody told me recently that taking too many class looks bad because "it seems" that taking fewer classes shows that the student is concentrating more in depth. I want to take 5 this coming semester. I naturally would think that this is helping me become more qualified (taking a harder...

I am signed up to be a ME major at the University of Kentucky but I've always loved physics, especially quantum physics. Am I going to be able to take some advanced physics classes without majoring in physics? I know there is a lot of physics in ME but not the kind I want to take. Is a double...

Homework Statement To compute the conjugacy classes of D20 Homework Equations The class equation, center of the group, group order, Lagrange's theorem that number of elements in conjugacy classes divides order of group The Attempt at a Solution i'm struggling to understand how to...

so here's the thing, i basically have a physics minor and decided to go to applied math grad school since i think it'll open up more options and involves more math and won't involve experiments than engineering. i don't want to do theoretical physics since I'm concerned about job opportunities...

I have never taken calculus or physics, but for my major I require both. I am wondering if it is reasonable to take calculus I and physics with calculus I at the same time. Thank you.

In C++ what is the difference between an object and a class? I'm confused, is an object always a class?

Hi, I am currently attending a community college, but I will transferring next fall. One of the universities I am looking at offers calc 1,2,3&4 as well as advanced calculus of one variable and advanced calculus of several variables both of which have calc 4 and linear algebra as...

Hi all. Over here (New Zealand!), a BE is 4 years long (although it's hons). The first year is not specialized, it is just general engineering. All engineers do the same first year, before choosing their specialization. I all ready know what specialization I want to do, mechatronics. I also...

Hi guys, I am a sophomore in college right now intending to major in physics. The thing though is that I am fairly certain that I want to go to medical school and thus am just pursuing the major for my own intellectual curiosity. I am taking junior level mechanics and electrodynamics courses...

Homework Statement There's this one exam problem that I cannot solve... Here it goes: Consider the set Z x Z+. Let R be the relation defined by the following: for (a,b) and (c,d) in ZxZ+, (a,b) R (c,d) if and only if ad = bc, where ab is the product of the two numbers a and b. a) Prove that...

i'm almost done with my pure math major. i'll likely go to grad school to get phD, but I'm very concerned with job opportunities should i later decide i want to go into industry rather than academia. I've already completed the physics minor, but i doubt having a physics background helps that...

What is the mix of men and women in your physics classes at uni? I am right to expect a sausage-fest?

Hey everybody. I hope I posted this in the right section; it was either here or in Diff. Equations.. Anyway, here's the deal: I'm currently a sophomore at a community college, planning to transfer to a University in Fall of 2009 to finish my BS. By the end of next semester (Spring '08), I...

i'm about to enter my 3rd year, and i have been planning for a physics major during my entire college career, until recently, where i have decided to pursue pure math instead. i may decide to switch back to physics, or pursue mathematical physics, however i plan to take for sure this...

The stupid question of the day: The existence of proper classes is often proven by contradiction: assume that some object is a set, you'll find a contradiction, therefore it is not a set. We baptized those as "classes". Will (can) this even happen to classes? To find some object, assume it...

EMIII (EM waves in particular) REAL ANALYSIS II ABSTRACT ALGEBRA TOPOLOGY CLASSICAL MECHANICS (via Herstein) ... is this possible in a semester?

Hey all, This question stems from Scorpan, "The Wild World of 4-Manifolds", pg 302 (and all through that chapter). He states that a random homogeneous polynomial of degree d in CP^2 with coordinates [z_0:z_1:z_2] defines a complex curve C, with homology class [C]=d[CP^1]. So I understand...

For my undergraduate mathematics program the required classes are Calculus 1,2,3, Linear Algebra, Differential Equations, Introduction to Advanced Mathematics, Advanced Calculus, Algebraic Structures, and Mathematical Statistics I. Then I am told to choose 3 classes from each of the lists below...

Ok, I plan on changing my schedule so that I can get some work time in. I'm thinking of taking 2 Junior level and 1 Senior level math classes back to back. Abstract Algebra, Differential Equations, and Advanced Linear Algebra. Anyone have personal experience? I'm in pretty good shape...

I am an undergrad student studying chemistry and I was wondering from the pros what classes you thought were the most interesting or helpful after school.

I'm asking because I'm going to be a senior next year and I really, really don't want to take AP Literature. I loathe English with every fiber of my being. I'm also taking German IV which I've heard is mainly going to be a writing/literature class and I don't think I can handle two similar...

Passing the AP Physics C Tests usually gives credit at college for a similar class. However, I was wondering, if I'm majoring in Physics and did pass the AP Physics C Tests, should I skip the classes in college and move on? Or would it be better to take the classes at a college anyway in order...

When I was in high school I took 7 classes in a typical semester and each class met 50 minutes per day 5 days a week. We were punished rather harshly for tardiness and classes never dismissed early. Since college is supposedly the next step of the academic ladder, it would seem natural that...

Here are two very similar questions about polynomials that I feel may have deeper roots (excuse pun). a) Does anyone know of any interesting theory related to them that I could read up upon? b) How would one start solving them? Here are the problems: 1) Show that there are...

Need help with Summer/Fall classes :( WOW ... UH has the worst schedule system ever! Ok, so I'm transferring to a University this year. I would really love to get advice on what courses to take. Background: I started studying Mathematics around 2 years ago at the age of 21, so I didnt grow...