Mathematics 124
MIDTERM
Collaboration: On the midterm no collaboration is allowed. Show all your working, and
write up your solutions as neatly as possible. The points on the Exam total 105, although
Mathematics 124
HOMEWORK ASSIGNMENT # 3
DUE, Friday, October 17
Collaboration: On the homework sets, collaboration is not only allowed but encouraged.
However, you must write up and understand your ow
Mathematics 124
HOMEWORK ASSIGNMENT # 1
DUE, Friday, October 3
Collaboration: On the homework sets, collaboration is not only allowed but encouraged.
However, you must write up and understand your own
Mathematics 124
HOMEWORK ASSIGNMENT # 4
DUE, Friday, October 24
Collaboration: On the homework sets, collaboration is not only allowed but encouraged.
However, you must write up and understand your ow
Mathematics 124
HOMEWORK ASSIGNMENT # 5
DUE, Friday, October 31
Collaboration: On the homework sets, collaboration is not only allowed but encouraged.
However, you must write up and understand your ow
Math 124 Homework 4 Solutions
1. Consider the coecient of xp in the expansion of (1 + x)2p = (1 + x)p (1 +
2p
x)p . On the left side, the coecient of xp is
. On the right side, it is
p
given by
p
p
2
Math 124 Homework 2 Solutions
1. First, cancel out the factors of p so that we avoid division by zero:
2p
p
2p(2p 1)(2p 2) (1)
p2 (p 1)2 (p 2)2 (1)2
=
=
2p(2p 1)(2p 2) (p + 1)
p(p 1)(p 2) (1)
=
2(2p 1
1
Lecture 1
Number theory is generally split into two elds: Algebraic number theory: Sol.
to poly. eqs over Q, Z, /n (Book for this part: Davenport) Analytic number
theory: Asymptotic estimates on dis
Math 124 Homework 5 Solutions
1. 163 12 (mod 2) gives p = 2 the smallest prime.
2a. First, consider q = 2. We know 2 is not a quadratic residue if and only
if p 3, 5 (mod 8). By Dirichlets theorem, th
Mathematics 124
HOMEWORK ASSIGNMENT # 2
DUE, Friday, October 10
Collaboration: On the homework sets, collaboration is not only allowed but encouraged.
However, you must write up and understand your ow