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1. Is the group of permutations on the set {123} Cyclic? Justification required

Homework Statement Consider the group of permutation on the set {123}. Is this group cyclic? Justify your answer Homework Equations The Attempt at a Solution I wrote out the cayley table for this group, and noticed that if we take (123)^3 = e . Seeing as we can get back to the...
2. Squeeze Theorem - Multivarible question

Hi, I'm having a lot of difficulty with finding limits of multivariable functions. A question like this comes up every year in the final exam and it will always ask for use of the squeezing theorem. Homework Statement (a) Suppose that f(x, y) = 1 +(5x2y3)/x2 + y2 for (x, y) =/=...
3. Group Theory (Abstract algebra manipulations)

Homework Statement Let a,b,c,d be elements of a group G and let ab = c, bc = d, cd = a, da = b. Examine the expression da^2b and first derive an expression for b in powers of a. Then express c and d in powers of a. Show that a^5 = e (identity element) Homework Equations The Attempt...
4. Resits exams in the summer.

Hi, By leaving everything to the last minute I managed to flunk all my math courses this year. As such I now have 4 resit exams in August to prepare for. The courses are Introduction to Analysis Sets and Algebraic structures Linear Algebra Advanced Calc (goes up to about Calc II level...
5. Second Order Partial Derivatives + Chain Rule

Homework Statement Let z = z (x,y) be a function with x = x(s), y = y(t) satisfying the partial differential equation (Ill write ddz/ddt for the partial derivative of z wrt t and dz/dt for the total derivative of z wrt t, as I have no idea how to use Latex.) ddz/ddt +...
6. Convergent Sequences problem

Homework Statement Let f: N -> N be a bijective map. for n Є N a sub n = 1 / f(n) Show that the sequence (a sub n) converges to zero. Homework Equations The Attempt at a Solution Basically I have been stuck on this problem for hours now and have read through my notes and...
7. Equivalence relations and classes problem.

Homework Statement Let X = {a,b,c,d}. How many different equivalence relations are there on X? What subset of XxX corresponds to the relation whose equivalence classes are {a,c},{b,d} Homework Equations N/A The Attempt at a Solution So I wrote out all the possible "blocks"...