MATH 3020 A: Homework 10
SOLUTION IDEAS
To submit, use the assignment box for the course which is across from the North 5th oor Ross
elevators. Late homework will not be accepted.
Solve the following.
MATH 3020 A: Homework 1
Solution Ideas
Solve the following. Carefully justify any statements you make.
1. Let S be a set and let 2S be the set whose elements are the various subsets of S . In 2S dene
MATH 3020 A: Homework 6
Solution Ideas
1. Give a careful and detailed proof of
Theorem 6.5: For every positive integer n, Aut(Zn ) is isomorphic to U (n).
You may use the proof sketch in the text as a
MATH 3020 A: Homework 5
Solution Ideas
1. (Herstein) Prove that the smallest subgroup of Sn containing (1, 2) and (1, 2, . . . , n) is Sn .
Suggestion: To obtain some insight, study the case n = 4.
SO
MATH 3020 A: Homework 4
Soution Ideas
Herstein, in Topics in Algebra poses the following exercise.
Let G be a nite abelian group in which the number of solutions in G of the equation
xk = e is at most
MATH 3020 A: Homework 2
Solution Ideas
Solve the following. Carefully justify any statements you make.
1. (a) Prove that if a is a divisor of bc and gcd(a, b) = 1, then a is a divisor of c.
(b) If a i
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MAT H 3020 A: H omework 3
Du e F r iday Oct ober 12 a t No on
To s ub m it , use the assign me nt box for t h e course which is across from the Nort h 5 t h floor Ross
elevators. Late
MATH 3020 A: Homework 7
Solution Ideas
1. Give a careful and detailed proof of the rst part of
Theorem 8.3: Suppose s and t are relatively prime. Then U(st) is isomorphic to the external
direct produc
MATH 3020 A: Homework 8
SOLUTION IDEAS
To submit, use the assignment box for the course which is across from the North 5th oor Ross
elevators. Late homework will not be accepted.
1. Up to isomorphism,
York University
Faculty of Science and Engineering
Math 3020 A
Class Test 3
SOLUTIONS
Instructions:
1. Time allowed: 50 minutes.
2. Calculators are not permitted.
NO INTERNET CONNECTED DEVICES OR OTHE
York University
Faculty of Science and Engineering
Math 3020 A
Class Test 4
SOLUTIONS
Instructions:
1. Time allowed: 80 minutes.
2. Calculators are not permitted.
NO INTERNET CONNECTED DEVICES OR OTHE
York University
Faculty of Science and Engineering
Math 3020 A
Class Test 2
SOLUTIONS
Instructions:
1. Time allowed: 50 minutes.
2. Calculators are not permitted.
NO INTERNET CONNECTED DEVICES OR OTHE
York University
Faculty of Science and Engineering
Math 3020 A
Class Test 1
SOLUTION IDEAS
Instructions:
1. Time allowed: 50 minutes.
2. Calculators are not permitted.
NO INTERNET CONNECTED DEVICES OR
MATH 3020 A: Homework 9
SOLUTION IDEAS
To submit, use the assignment box for the course which is across from the North 5th oor Ross
elevators. Late homework will not be accepted.
Solve the following.