Dartmouth College
Mathematics 17
Assignment 6
due Wednesday, February 15
1. Using the fundamental theorem for nite abelian groups, list a complete set of nonisomorphic abelian groups of order 73 114 .
2. For n 1, Un is a nite abelian group, For 5 n 15, us
Dartmouth College
Mathematics 17
Assignment 5
due Wednesday, February 8
1. We investigate some general classes of groups. The symmetric group is dened as the
set of permutations of the set cfw_1, 2, . . . , n, that is, as a set
Sn = cfw_f : cfw_1, 2, . .
Dartmouth College
Mathematics 17
Assignment 4
due Wednesday, February 1
1. Lets consider a special case of the Chinese Remainder Theorem (CRT). Let m, n > 1
be coprime integers, and let a, b be arbitrary integers. Then the system of congruences:
x a (mod
Dartmouth College
Mathematics 17
Assignment 3
due Wednesday, January 25
In the rst two problems, we consider two equivalence relations in addition to the one
given in class by congruence modulo n. The rst is the notion of fractions or rational numbers
whi
Dartmouth College
Mathematics 17
Assignment 2
due Wednesday, January 18
1. Another use for calculus. In our discussion of the Bachet problem, we assumed that
a tangent to the cubic intersected in one other point. Solving simultaneously gave a
cubic whose
Dartmouth College
Mathematics 17
Assignment 1
due Wednesday, January 11
1. Describe all the rational points on xn + y n = 1 for n > 2, and justify your answer.
2. Consider the following set S of dierentiable real-valued functions:
S = cfw_f | f = f ,
that