RYERSON UNIVERSITY
DEPARTMENT OF MATHEMATICS
MTH314 - DISCRETE MATHEMATICS FOR ENGINEERS - MIDTERM TEST
March 2, 2007
INSTRUCTIONS
1. Duration: 2 hours item You are allowed one 8.5" 11" formula sheet (two-sided). The information on the sheet must
RYERSON UNIVERSITY DEPARTMENT OF MATHEMATICS MTH 314 Total marks: 80 NAME (Print): Instructions:
1 You are allowed an 8 2 11 formula sheet written on both sides.
Final Exam
April 25, 2007 Time allowed: 3 Hours
STUDENT #:
No other aids allowed.
RYERSON UNIVERSITY
DEPARTMENT
OF
MATHEMATICS
MTH 314
Final Exam
Total marks: 80
NAME (Print):
April 17, 2009
Time allowed: 3 Hours
STUDENT #:
Instructions:
1
You are allowed an 8 2 11 formula sheet written on both sides.
No other aids allowed. Electroni
MTH 314 Course Outline
This outline may be updated during the term so pleasecheck regular&
Last updated: Dec 19,2010
(You may need to cl~ck ReloadRefiesh to get the page to update.)
on
The topics will not necessarily be covcred in the exact prder below.
S
Predicate Calculus
681'~&:4
set notation
Quantifiers and lnanipulation of English st&ments and their equivalent symbolic form.
Generalised De Morgan laws, multiple quantifiers.
Countcr-examples, necessary and sufficient conditions.
d.
a-
Practice Exercise
Graphs and ~ r e e s *
Introduction to graphs, trees, paths and circuits
Adjacency matricies
Kruskal and Prims algorithlns
Practice Exercises
Section
10.1
10.2
10.3
10.5
10.6
Exercises
1,5,8, 10a, 12, 15, 18,24,36.
1,8,9, 12, 19,23,25,28.
2a, 3a, 4a, 6a,
Predicate Calculus
.
~
d set n 0 t a t i o n ( 4 ; ~ ~ ~ ~ ~
Quantifiers and manipulation of English st&e~nel~ts their equivalent symbolic form.
and
Generalised De Morgan laws, multiple quantifiers.
Counter-examples. necessary and sufficient conditions.
P
Graphs and ~ r e e s *
Introduction to graphs, trees, paths and circuits
Adjacency matricies
Kruskal and Prims algoritlms
Practice Exercises
Section
10.1
10.2
10.3
10.5
10.6
Exercises
1,5, 8, 10a, 12, 15, 18,24,36.
1,8,9, 12, 19,23,25,28.
2a, 3a, 4a, 6a,
Predicate Calculus
Introduction to set theory and set notation (part of section 6.1).
Quantifiers and manipulation of English statements and their equivalent symbolic form.
Generalised De Morgan laws, multiple quantifiers.
Counter-examples, nccessaly and
2-3
V G U D ~ -J
TP~VALIDc t c u 6 4 J 7 s ~G
p
p
Definition.
A n argument is a sequence of statements, and an argument f o m , zs a sequence of statement
jorms.
All statements ill an argument and all statement form. in an argz~mentfor, except for the
fin
Graphs and ~ r e e s *
Introduction to graphs, trees, paths and circuits
Adjacency matricies
Kruskal and Prims algorithms
Practice Exercises
Section
10.1
10.2
10.3
10.5
10.6
Exercises
1, 5,8, 10a, 12, 15, 18,24,36.
1,8,9, 12, 19,23,25,28.
2a, 3a, 4a, 6a,
.
Binary relations and directed graphs.
Reflexivity, symmetry, transitivity, equivalence relations.
liqt~ivalence
relations, equivalence classes, and partitions o f a set.
A~itisyrnmetry,partial and total orders. (Not Hasse diagrams or I'ER'f & CI'M)
Prac
Binary relations and directed graphs.
Reflexivity, symmetry, transitivity, equivalence relations.
Equivalence relations, equivalence classes, and partitions of a set.
Antisymmetry, partial and total orders. (Not Hasse diagrams or PERT & CPM)
Practice Exer
Set Theory
Set inclusion and set identities. (Not including element method proofs).
Empty set, disjointness, partitions, power sets and cartesian products.
Russell's Paradox.
The Halting Problem.
Cardinality and computability.
The pigeonhole principle.
Pr
Set Theory
Set inclusion and set identities. (Not including element niethod proofs).
Empty set, disjointness, partitions, power sets and cartesian products.
Russell's Paradox.
The Halting Problem.
Cardinality and computability.
The pigeonhole principle.
P
Set inclusion and set identities. (Not including element method proofs).
Empty set, disjointness, partitions, power sets and cartesian products.
Russell's Paradox.
The Halting Problem.
Cardinality and computability.
The pigeonhole principle.
Practice Exer
RYERSON UNIVERSITY
DEPARTMENT OF MATHEMATICS
MTH314 - DISCRETE MATHEMATICS FOR ENGINEERS - MIDTERM
TEST
March 3, 2006
INSTRUCTIONS
1. Duration: 2 hours item You are allowed one 8.5 11 formula sheet (two-sided). The information
on the sheet must be hand-wr
RYERSON POLYTECHNIC UNIVERSITY
DEPARTMENT
OF
MATHEMATICS, PHYSICS AND COMPUTER SCIENCE
MTH 314
Final Exam
December 10, 2002
Total marks: 70
Time allowed: 3 Hours
NAME (Print):
STUDENT #:
Circle your Instructor:
Danziger
Grandison
Instructions:
You are al
RYERSON UNIVERSITY
DEPARTMENT OF MATHEMATICS
MTH 314
SAMPLE EXAM
Winter, 2010
Total marks: 60
Time allowed: 3 hours.
Instructions:
Verify that your paper contains 15 questions on 10
pages, the last of which is a table of set identities.
An aid sheet, co
RYERSON UNIVERSITY
DEPARTMENT OF MATHEMATICS
MTH314 - DISCRETE MATHEMATICS FOR ENGINEERS - MIDTERM
TEST
March 2, 2007
INSTRUCTIONS
1. Duration: 2 hours
2. You are allowed one 8.5 11 formula sheet (two-sided). The information on the sheet must be
hand-writ
RYERSON UNIVERSITY
DEPARTMENT OF MATHEMATICS
MTH314 DISCRETE MATHEMATICS FOR ENGINEERS
MIDTERM TEST
March 5, 2013
INSTRUCTIONS
1. Duration: 1.5 hours item You are allowed one 8.511 formula sheet (two-sided). The information
on the sheet must be hand-writt
RYERSON UNIVERSITY
DEPARTMENT
OF
MATHEMATICS
MTH 314
Final Exam
Total marks: 80
NAME (Print):
April 23, 2012
Time allowed: 3 Hours
STUDENT #:
Instructions:
1
You are allowed an 8 2 11 formula sheet written on both sides.
No other aids allowed. Electroni
MTH 314 - Midterm (Practice) Solutions - Winter 2015
(1) (a) Let p, q, and r be three statements. Show that
(p q r) (p q) (p r) p (q r)
using standard logical equivalences (associativity, commutativity, etc).
You do not need to provide the names, but I wi
RYERSON UNIVERSITY
DEPARTMENT OF MATHEMATICS
MTH314 ~— DISCRETE MATHEMATICS FOR ENGINEERS
MIDTERM TEST
March 2013
INSTRUCTIONS
1. Duration: 1.5 hours item You allowed one 8.5” X 11" formula sheet (twosided). The information
on the sheet must be hand-writt
MTH 314
RYERSON UNIVERSITY
MIDTERM (Practice) - Winter 2015
Family Name (print):
Given Name (print):
Student ID #:
Signature:
Prof. Jonah Horowitz
Date: Feb. 23, 2015
(Time allowed: 90 minutes)
INSTRUCTIONS:
Read all instructions before starting.
Calcula
RYERSON UNIVERSITY
DEPARTMENT OF MATHEMATICS
MTH314 - DISCRETE MATHEMATICS FOR ENGINEERS - MIDTERM
TEST
March 2, 2012
INSTRUCTIONS
1. Duration: 1.5 hours item You are allowed one 8.511 formula sheet (two-sided). The information
on the sheet must be hand-w