University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT C158 W'inter 2015
Problem Set #5
Due: Thursday, March 26, 2015, in class at the start of lecture
All problems are f
University of Toronto Scarborough
Department of Computer 85 Mathematical Sciences
MAT 0158 Winter 2015
Problem Set #4
Due: Monday, March 9, 2015, in class at the start of lecture
All problems are from
Department of Computer & Mathematical Sciences
University of Toronto Scarborough
Term Test
MATClSH Introduction to Number Theory
Examiner: J. Friedlander Date: Mar. 4, 2016
Time: 3:00PM5:00PM
FAMILY N
Department of Computer 85 Mathematical Sciences
University of Toronto at Scarborough
Final Examination
MATC15H Introduction to Number Theory
Examiner: J. Friedlander Date: Dec. 13, 2011
1 Time: 7:00PM
Department of Computer & Mathematical Sciences
University of Toronto Scarborough
Term Test
MATC15H Introduction to Number Theory
Examiner: J. Friedlander Date: Mar. 8, 2014
Time: 1:00PM3200PM
FAMILY N
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT C15S
Winter 2015
Problem Set #1
Due: Monday, January 19, 2015 at the start of lecture
All problems are from text (V
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT C15S
Winter 2015
Problem Set #2
Due: Monday, February 2, 2015 at the start of lecture
All problems are from text (V
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT C15S
Winter 2015
Problem Set #5
Due: Thursday, March 26, 2015, in class at the start of lecture
All problems are fr
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT C15S
Winter 2015
Problem Set #3
Due: Monday, February 23, 2015, in class at the start of lecture
All problems are f
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT C15S
Winter 2015
Problem Set #4
Due: Monday, March 9, 2015, in class at the start of lecture
All problems are from
Department of Computer & Mathematical Sciences
University of Toronto Scarborough
Term Test
MATC15H — Introduction to Number Theory
Examiner: J. Friedlander Date: Mar. 7, 2015
Time: 5:00PM—7200PM
FAMIL
U NIVERSITY OF T ORONTO S CARBOROUGH
MATC15 : Introduction to Number Theory
FINAL EXAMINATION
April 23, 2013
Duration 3 hours
Aids: none
KEY
NAME (PRINT):
Last/Surname
First/Given Name (and nickname)
Midterm Solutions
by Pinar Colak
(1) By Chebyshevs Theorem, we know that there exists two positive real numbers
and such that
x
x
< (x) <
.
log x
log x
Let x = pn , that is, the nth prime number, the
Instructor: Leo Goldmakher
Name:
University of Toronto Scarborough
Department of Computer and Mathematical Sciences
MATC15: NUMBER THEORY
Midterm exam (due Tuesday, March 12th, during the rst ve minut
University of Toronto Scarborough
Department of Computer 85 Mathematical Sciences
MAT 0158 Winter 2016
Problem Set #1
Due: Thursday, January 21, 2016 at the start of lecture
All problems are from text
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT 0153 Winter 2016
Problem Set #2
Due: Thursday, February 11, 2016 at the start of lecture
All problems are from te
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT C158 Winter 2016
Problem Set #3
Due: Thursday, March 3, 2016 at the start. of lecture
All problems are from text (V
COMPLEX VARIABLES MATC34 SOLUTIONS 5.
1. Find the Laurent series for f (z) =
log(1z 2 )
z4
around z = 0.
Solution. One has
w2
w3
w4
+
.,
2
3
4
z6
z8
z4
.,
log(1 z 2 ) = z 2
2
3
4
log(1 z 2 )
1
1 z2
z
COMPLEX VARIABLES MATC34 ASSIGNMENT 6 . DUE BY OCTOBER 30.
1. Find all singular point, the principal part of the Laurent series and the residue at each of these points
z
2
for (a) f = 1+e z , (b) f =
COMPLEX VARIABLES MATC34. ASSIGNMENT 4 . DUE BY OCTOBER 2.
1. Using Cauchy inequalities for derivatives of analytic function verify the following statement. Let f (z)
be entire function. Assume that |
COMPLEX VARIABLES MATC34 ASSIGNMENT 1 . DUE BY SEPTEMBER 20.
1. Calculate (1 + i 3)3 straightforward and also with help of polar form.
1
1
2. Find all roots 1 5 , (4 + 3i) 5
3. Explain why the inequal