Math 115, Summer 2012
Homework 2
Solution
NZM a.b.c refers to a problem in our text, 5th edition - these may dier slightly from the problems
appearing in other editions, so use the version printed her
MATH 115, SUMMER 2012
QUIZ 4 SOLUTION
JAMES MCIVOR
There are two problems - one is on the back of this page, 20 points total. Write
clearly and in complete sentences. If you need extra paper, ask me.
MATH 115, SUMMER 2012
QUIZ 4
JAMES MCIVOR
There are two problems - one is on the back of this page, 20 points total. Write
clearly and in complete sentences. If you need extra paper, ask me. You may n
MATH 115, SUMMER 2012
QUIZ 5 SOLUTION
JAMES MCIVOR
There are problems on both sides of this page, 20 points total. Write clearly and
in complete sentences. If you need extra paper, ask me.
(1) (2 poin
MATH 115, SUMMER 2012
QUIZ 5
JAMES MCIVOR
There are problems on both sides of this page, 20 points total. Write clearly and
in complete sentences. If you need extra paper, ask me.
(1) (2 points each)
MATH 115, SUMMER 2012
QUIZ 3
JAMES MCIVOR
There are problems on the back of this page, 20 points total. Write clearly and
in complete sentences. If you need extra paper, ask me.
(1) (8 points) Find al
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MATH 115, SUMMER 2012
' QUIZ 3 '
JAMES MCIVOR
There are problems on the back of this page, 20 points total. Write clearly and
in complete sentences. If'you need extra paper, ask me. '
MATH 115, SUMMER 2012
QUIZ 1 SOLUTION
THURSDAY, JUNE 21ST
JAMES MCIVOR
Please show your work carefully and write neatly. Make sure to double-check
your answers. There are 20 points total.
(1) (6 point
MATH 115, SUMMER 2012
MIDTERM EXAM
WEDNESDAY, JULY 18TH
JAMES MCIVOR
The exam is out of 180 points. You have the full class time (1 hour, fty minutes)
to complete it. No calculators or cheat sheets ar
MATH 115, SUMMER 2012
QUIZ 1
THURSDAY, JUNE 21ST
JAMES MCIVOR
Please show your work carefully and write neatly. Make sure to double-check
your answers. There are 20 points total.
(1) (6 points) Calcul
MATH 115, SUMMER 2012
QUIZ 2
JAMES MCIVOR
There are problems on the back of this page. Write clearly and in complete
sentences. If you need extra paper, ask me.
(1) (6 points) Solve the system of cong
MATH 115, SUMMER 2012
MIDTERM EXAM
WEDNESDAY, JULY 18TH
JAMES MCIVOR
The exam is out of 180 points. You have the full class time (1 hour, fty minutes)
to complete it. No calculators or cheat sheets ar
MATH 115, SUMMER 2012
WORKSHEET FOR LECTURE 14
JAMES MCIVOR
(1) (8 points) Find all solutions to the congruence x2 4x + 23 0 mod 125.
Solution: Working mod 5, we get the solutions x = 1, x = 3. These
Math 115, Summer 2012
Homework 4
Due Tuesday, July 16th
NZM a.b.c refers to a problem in our text, 5th edition - these may dier slightly from the problems
appearing in other editions, so use the versi
MATH 115, SUMMER 2012
HOMEWORK 5
SOLUTION
JAMES MCIVOR
(1) (NZM 3.5.1) Find a reduced form equivalent to 7x2 + 25xy + 23y 2 .
Solution: By applying step 2 with k = 2, and then step 1, we obtain
the re
Math 115, Summer 2012
Homework 3
Due Thursday, July 12th
NZM a.b.c refers to a problem in our text, 5th edition - these may dier slightly from the problems
appearing in other editions, so use the vers
Math 115, Summer 2012
Homework 1
Due Tuesday, June 26th
NZM a.b.c refers to a problem in our text, 5th edition - these may dier slightly from the problems
appearing in other editions, so use the versi
Math 115, Summer 2012
Homework 3
Solution
NZM a.b.c refers to a problem in our text, 5th edition - these may dier slightly from the problems
appearing in other editions, so use the version printed her
Math 115, Summer 2012
Homework 2
Due Tuesday, July 3rd
NZM a.b.c refers to a problem in our text, 5th edition - these may dier slightly from the problems
appearing in other editions, so use the versio
MATH 115, SUMMER 2012
HOMEWORK 6
DUE TUESDAY, AUGUST 7TH
JAMES MCIVOR
(1) Show that the equation 12x2 + 13y 2 = 227 has no solutions in integers.
(2) Show that the curve 17x2 + 24y 2 = 221z 2 contains
Math 115, Summer 2012
Homework 4
Solution
NZM a.b.c refers to a problem in our text, 5th edition - these may dier slightly from the problems
appearing in other editions, so use the version printed her
MATH 115, SUMMER 2012
HOMEWORK 5
DUE TUESDAY, JULY 31ST
JAMES MCIVOR
(1) (NZM 3.5.1) Find a reduced form equivalent to 7x2 + 25xy + 23y 2 .
(2) (NZM 3.5.4) Show that a binary quadratic form f properly
MATH 115, SUMMER 2012
MOCK QUIZ, LECTURE 9
JAMES MCIVOR
Pretend this is a reai quiz and take. It's not for a grade, though. First look for
the ones you already know how to do. Well go over it at the e
SAC/[gen
If
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MATH 115, SUMMER 2012
QUIZ 2
JAMES MCIVOR
There are problems on the back of this page.
Write clearly and in complete
sentences. If you need extra paper, ask me.
(1) (6 points) Solve the
Mathematics 115
Professor K. A. Ribet
First Midterm Exam
September 22, 2011
Please put away all cell phones, books, iPads, iPods, laptops, etc., etc. You may consult
a single two-sided sheet of notes.
MATH 115 MID-TERM 1
1. (4 pts) a) (3 pts) Given the factorisation 1728 = 26 33 , show that for any integer a which is relatively prime to 7, 13 and 19, we have a1728 a a1728 (hint: use Fermat's litt