What is Abstract: Definition and 532 Discussions

Abstract expressionism is a post–World War II art movement in American painting, developed in New York City in the 1940s. It was the first specifically American movement to achieve international influence and put New York at the center of the Western art world, a role formerly filled by Paris. Although the term "abstract expressionism" was first applied to American art in 1946 by the art critic Robert Coates, it had been first used in Germany in 1919 in the magazine Der Sturm, regarding German Expressionism. In the United States, Alfred Barr was the first to use this term in 1929 in relation to works by Wassily Kandinsky.

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  1. L

    Abstract Algebra Struggles: Navigating Levi and Malcev Theorems

    Hello! I've got big problems with understanding abstract algebra, the way we deal with it in the seminar on Lie algebras. In just four weeks we progressed up to Levi and Malcev theorems, which are actually the culmination, the say, of classical Lie algebras theory. I didn't think, that the...
  2. S

    Question- abstract index notation

    How does abstract index notation work? What do the the indices represent? I know the Lorentz transformation tensor in arbitrary direction, so if you want to use a specific tensor in an example, that would be a good one.
  3. H

    Possible Rings with Product of Nonzero Elements Equal to 0?

    for which of the following rings is it possible for the product of two nonzero elements to be 0? 1. ring of complex numbers 2. ring of integers modulo 11 3. the ring of continuous real-valued functions on [0,1] 4. the ring {a+b(sqrt(2)) : a & b are rational numbers} 5...
  4. T

    Abstract Math: Beyond Category Theory

    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?
  5. Simfish

    Hey, I'm helping a HS student write a research abstract

    So after some corrections, this is her abstract. Can anyone suggest any further corrections? Thanks! (btw she went to a high school research program) I'm thinking of changing from "is created from" to something else, like "comes from". I'm also thinking of adding some conclusive statement at...
  6. A

    Question about a Theorem in Gallian's Contemporary Abstract Algebra

    Question about a Theorem in Gallian's "Contemporary Abstract Algebra" I'm using this book as a reference for my Algebra course, and there's a lemma in the book that is really confusing me. It is on Page 102 of the Sixth Edition, for those who have the book. The lemma states: If...
  7. N

    Groups, Normalizer, Abstract Algebra, Dihedral Groups help?

    [b]1. Let G be a Group, and let H be a subgroup of G. Define the normalizer of H in G to be the set NG(H)= the set of g in G such that gHg-1=H. a) Prove Ng(H) is a subgroup of G b) In each of the part (i) to (ii) show that the specified group G and subgroup H of G, CG(H)=H, and NG(H)=G...
  8. S

    Abstract AlgebraDesperately in need for help?

    Homework Statement Prove that the octic group D_4 has no subgroups of order, 3, 5, 6 and 7. I would appreciate any help on this one. Thanx in advance! Homework Equations The Attempt at a Solution I usually have at least an idea on how to start about proving things, but...
  9. S

    Proving Concurrent Segments in a Triangle-Circle Configuration

    Homework Statement Given a triangle ABC and a circle intersecting each side of ABC at two points( intersects AB at E and E', BC at D and D', and AC at F and F') Prove that if the segments AD, BF, and CE are concurrent, then the segments AD', BF', and CE' are concurrent. I am just looking...
  10. S

    Abstract Algebra Test: Can I Still Make an A?

    Hi guys, I was just wondering, i had a test in Abstract Algebra, and i got a 85, which roughly means a B, and i am really pissed off at myself, because if i only had been less stressful during the test i could have easily gotten a score above 90...because not more than 1 hour or sth after the...
  11. T

    Show G(p) of Order p^t when G is an Abelian Group of Order (p^t)m

    If G is an abelian group of order (p^t)m, and (p,m)=1, show that G(p) has order p^t and G(p) = {a e G| |a|=p^m where m is a natural number} any suggestions?
  12. P

    Introductory abstract algebra question (computing permutations)

    Homework Statement Let A, B be permutations and A = (1 3 5 10)(3 15 8)(4 14 11 7 12 9) and B = (1 14)(2 9 15 13 4)(3 10)(5 12 7)(8 11) Find AB. Homework Equations The Attempt at a Solution I am struggling with finding the product of this permutations and can't quite get the...
  13. T

    Exploring Subgroups of the Additive Group Q/Z in Abstract Algebra

    Homework Statement If G is the additive group Q/Z, what are the elements of the subgroup G(2)? Of G(P) for any positive prime P? Where G(n)={a e G| |a| = n^(k) for some k is greater than or equal to 0}...That is the set of all a in G, s.t. the order of a is some power of n. (But since...
  14. T

    Elements of Subgroups in Additive Group Q/Z: G(2) and G(P)

    The question: If G is the additive group Q/Z, what are the elements of the subgroup G(2)? Of G(P) for any positive prime P? Where G(n)={a e G| |a| = n^(k) for some k is greater than or equal to 0}...That is the set of all a in G, s.t. the order of a is some power of n. (But since it is the...
  15. S

    Abstract Algebra Homework: Proving H is a Subgroup of G

    Homework Statement Let a be in a group G, and let H=\{ a^n: n\in Z\}. Show the following: (i) if h and h' are in H, so is hh'. (ii) The identity e of G is in H. (iii) if h is in H, so is h^{-1}. The Attempt at a Solution Here is what i tried. First of all i am not sure...
  16. rocomath

    Can the Rule of Simplification be Applied to Not (P and Q)?

    Abstract Algebra, first Proof :( I really want to do well in this class! :) http://img329.imageshack.us/img329/2636/abstract001sq3.jpg http://img329.imageshack.us/img329/7108/abstract002ym3.jpg Def U = Definition of Universe UQ = Universal Quantification
  17. T

    Abstract Algebra or Real Analysis

    Which one should I take first? Does it help to take one before the other?
  18. T

    Concrete way of doing abstract maths?

    Much of the physics in 'Beyond the Standard Model' use a lot of abstract mathematics. So I was just wondering is doing this type of physics a unique way of doing concrete abstract maths, if that makes any sense? In other words being able to do abstract maths in a very concrete manner. Have a...
  19. T

    What Are the Best Advanced Textbooks for Studying Abstract Algebra?

    My current algebra class is using Fraleigh's "First Course in Abstract Algebra", and it doesn't feel very challenging (and is extremely verbose!). I'd like to study the subject deeper, since I really enjoy it. I picked up Lang's "Undergraduate Algebra", which seems to be much better, but if...
  20. F

    Proving 1 + 1 = 3: Abstract Math & Visualization

    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...
  21. I

    Linear algebra and abstract algebra simultaneously?

    Is this a good idea (provided the university will allow it)? I'll be going into my sophomore year at my university. But I'm unfamiliar with exactly how much linear algebra an intro course in abstract algebra would require. In hindsight I probably should have taken linear last semester, but...
  22. L

    Abstract Schrödinger's equation in QFT

    Hi folks! A QFT question: you start from the lagrangian, compute the hamiltonian via Legendre transform and promote the the fields to operators with canonical equal-time commutation relations. Now you can compute the relation [H,F(x)]=-\mathrm{i}\partial_0 F(x) \ , where H is the hamiltonian...
  23. W

    What Should I Include in my Congress Abstract?

    There is this congress for which I would like to submit an abstract. Authors of accepted abstracts will be invited to write a full paper which will be published in a preceeding series and will be indexed in isi. Now I was wondering what exactly is expected from such an abstract? Is it...
  24. Z

    Abstract algebra: irreducible polynomials

    Homework Statement Prove that f(x)=x^3-7x+11 is irreducible over Q Homework Equations The Attempt at a Solution I've tried using the eisenstein criterion for the polynomial. It doesn't work as it is written so I created a new polynomial...
  25. W

    Integration/Differentiation on abstract spaces

    Hi, everyone: I was wondering if it makes sense to define a theory of integration in abstract spaces (i.e., spaces other than IR^n, or homeomorphs), and, if so, how to do it (and wether we can then define a theory of differentiation). If so, do we need to define a measure...
  26. P

    Derivative in an abstract polynomial ring

    "Derivative" in an abstract polynomial ring Homework Statement Let R be any ring and define D:R[X]-->R[X] by setting D[\sum a_nX^n]=\sum na_nX^{n-1}. a) Check that, if f(X)=\sum a_nX^n and g(X)=\sum b_nX^n, then D[f+g]=D[f]+D[g] b) Check that...
  27. G

    Abstract Algebra Questions - Need help for exam

    Abstract Algebra Questions - Need help for exam! Homework Statement I am studying Abstract Algebra in college and my exams are approaching fast.I need somebody to help me out to do a few exam papers. I am going to post the questions below from the exam papers and if you can advise me how...
  28. S

    Abstract Algebra (Was: Book recommendation)

    Hi, Next fall i will be taking Intro to Abstract Algebra so i was planning to give it a shot on my own during the summer break, but i don't know what would be a good book to buy online, that is not too expensive. I would like the book to be quite rigorous, like very proof based one, but that...
  29. M

    Proving Isomorphism and Galois Group Existence in Abstract Algebra Homework

    Homework Statement Show that G is isomorphic to the Galois group of an irreducible polynomial of degree d iff is has a subgroup H of index d such that \bigcap_{\sigma \in G} \sigma H \sigma^{-1} = {1} .Homework Equations The Attempt at a Solution I know that if G acts transitively as a...
  30. M

    What are the properties of quartic polynomials with different cubic resolvents?

    Homework Statement I'm trying to come up with an example of a quartic polynomial over a field F which has a root in F, but whose splitting field isn't the same as its resolvent cubic. Homework Equations The Attempt at a Solution Well, I know the splitting field of the cubic...
  31. B

    Groups of Order 144: Abelian Groups Up to Isomorphism

    I'm going insane. The question is: List all abelian groups (up to isomorphism) of order 144. There are 10 non-isomorphic groups of order 144 and I only have 9. Here they are: Z2 X Z2 X Z2 X Z2 X Z3 X Z3 Z2 X Z2 X Z2 X Z2 X Z9 Z4 X Z2 X Z2 X Z3 X Z3 Z4 X Z2 X Z2 X Z9 Z8 X Z2 X Z3 X Z3 Z8 X Z2...
  32. J

    Number Theory & Abstract Algebra

    I'm currently taking a course, "Abstract Algebra I & Number Theory" and I'm wondering: what is the difference between abstract algebra and number theory? the two topics seem meshed together. i tried googling both of them and it doesn't really help. it's hard to tell the differences between...
  33. E

    Biology Lab Abstract: Photosynthesis

    [SOLVED] Biology Lab Abstract: Photosynthesis Homework Statement I am having trouble understanding how increased transmission is an indication to photosynthesis occurring. My teacher gave us the prediction for this lab: if photosynthesis is happening then transmittance goes up. I know...
  34. L

    Abstract Algebra any help is appreciated

    [b]1. On the set of real numbers, R the following operation is defined: *RxR implies (arrow) R, (x,y) implies (arrow) x*y=2(x+y)-xy-2 Find the neutral element of this operation. [b]3. since we know x*e=x, e*x=x, so i attempted: using e as y, because it would just mean y...
  35. A

    Any suggestions for a book on abstract algebra?

    Hello folks! Do you have any suggestions for a book on abstract algebra? Someone gave me this suggestion Algebra - Michael Artin https://www.amazon.com/dp/0130047635/?tag=pfamazon01-20 however there are some bad (and convincing) reviews on amazon.com about this book (although the...
  36. B

    Courses MIT course number for abstract algebra

    Anybody know the name of the MIT course number for Abstract Algebra . Is it even listed as a course on the MIT opencourseware website?
  37. M

    Understanding Voltage with Abstract Confusion

    I just bought the book Art of Electronics that berkman recommended and I just started reading it. I already know what voltage is but if I didn't I would have made no sense of their explanation. They say "The voltage between two points is the cost in energy (work done) required to move a unit...
  38. P

    Can abstract math be understood through concrete examples?

    How to go about it? I had abstract algebra in mind. Is the main thing to do as many solid examples as possible? So the only way to understand the abstract it is to think concrete then generalise?
  39. W

    Solving Abstract Algebra Problem: Proving Isomorphism & Listing Generators

    Can some one help me, how to solve this problem?. Please explain me how is done, been having problem with the subject Let H be the subgroup of GL(2, R) under Matrix multiplication defined by H = {[ 1 n ]}| n E Z } 0 1 Let 0...
  40. E

    Abstract Algebra: Prove Unit question

    Homework Statement Let R be an Integral Domain. Prove that if a,b are elements of R and both a and b are units in R, then prove a*b is a unit of R. Homework Equations a is a unit in R if and only if there exists an element u in R such that au=1=ua where 1 is the identity element of R...
  41. L

    Abstract Algebra: Proving Normal Subgroup and Isomorphisms

    Homework Statement If G1, G2 are two groups and G = G1 times G2 = {(a,b) such that a is an element of G1, b is and element of G2}, where we define (a,b)(c,d) = (ac, bd), (a) Show that N = {(a, e2) such that a is an element of G1}, where e2 is the unit element of G2, is a normal subgroup...
  42. L

    Proving Normality of Homomorphic Image and Subgroup - Abstract Algebra Homework

    Homework Statement If f is a homomorphism of G onto G' and N is a normal subgroup of G, show that f(N) is a normal subgroup of G'. Homework Equations The Attempt at a Solution Once again, I'm completely lost.
  43. R

    Abstract algebra: f(x) is reducible so is f(x+c)

    Homework Statement Let F be a field and f(x) in F[x]. If c in F and f(x+c) is irreducible, prove f(x) is irreducible in F[x]. (Hint: prove the contrapositive) Homework Equations So, I am going to prove if f(x) is reducible then f(x+c) is reducible. The Attempt at a Solution f(x)...
  44. N

    Abstract Algebra - lifting up a factor group

    Abstract Algebra -- lifting up a factor group After spending an extended period with my Professor during office hours I must admit I am mystified. He kept on talking about "lifting up" factor groups. I think this has something to do with using a factor group, say G/N, to show that there...
  45. N

    Abstract Algebra - no Sylow allowed

    Abstract Algebra -- no Sylow allowed Please note Sylow's theorem(s) may not be used. Using Theorem 1 as a tool, prove that if o(G)=p^{n}, p a prime number, then G has a subgroup of order p^m for all 0\leq m\leq n. Theorem 1: If o(G)=p^{n}, p a prime number, then Z(G)\neq (e). Theorem 1 uses...
  46. N

    Abstract Algebra - group

    Abstract Algebra -- group Show that in a group G of order p^2 any normal subgroup of order p must lie in the center of G. I am pretty sure here that p is supposed to be a prime number, as that is the stipulation in preceding and later problems. However, the problem statement does not...
  47. quasar987

    Falling back on the Lebesgue measure from the abstract theory?

    I am studying the abstract theory of measure and I was wondering how the Lebesgue case for real functions of a real variable arises. But I did not find it. In the original theory of Lebesgue, a function f:E-->R was said to be measurable if for every real constant b, the preimage of ]-\infty, b]...
  48. N

    Abstract Algebra - automorphism

    I have two problems I would like to discuss. 1.For any group G prove that the set of inner automorphisms J(G) is a normal subgroup of the set of automorphisms A(G). Let A be an automorphism of G. Let T_{g} be an inner automorphism, i.e. xT_{g}=g^{-1}xg The problem can be reduced to the...
  49. S

    What Group Contains Elements a and b in Abstract Algebra?

    1) find a group that contains elements a and b such that ︱a︱=︱b︱= 2 and a) ︱ab︱ = 3 b) ︱ab︱=4 c) ︱ab︱=5 2) suppose that H is a proper subgroup of Z under addition and H contains 18, 30 and 40. determine H? does anyone can help me out? and ...i am really in...
  50. N

    Abstract Algebra - isomorphism question

    Abstract Algebra -- isomorphism question If N, M are normal subgroups of G, prove that NM/M is isomorphic to N/N intersect M. That's how the problem reads, although I am not sure how to make the proper upside-down cup intersection symbol appear on this forum. Or how to make the curly "="...
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