BEE3054 Advanced Mathematics for Economicsts
Numbers, Topology
Dieter Balkenborg
University of Exeter
01/02/2014
Dieter Balkenborg (University of Exeter) BEE3054 Advanced Mathematics for Economicsts
01/02/2014
1 / 55
Partitions and equivalence relations
D

BEE3054 Advanced Mathematics for Economicsts
Proofs, Sets, Numbers
Dieter Balkenborg
University of Exeter
20721/01/2014
Dieter Balkenborg (University of Exeter) BEE3054 Advanced Mathematics for Economicsts
20721/01/2014
1 / 28
Proofs: Direct Proofs
A dire

BEE3054
UNIVERSITY OF EXETER
BUSINESS SCHOOL
February 2014
ADVANCED MATHEMATICS
FOR ECONOMISTS
Mock Exam
Module convenors:
Dieter Balkenborg
Vladislav Damjanovic
Problem 1 (10 marks) What is the value of the following non-negative integers written
as bina

BEE3054 Advanced mathematics for Economists
Dieter Balkenborg
Departments of Economics
University of Exeter
Homework Week 4 solutions
Exercise 1 Let R2 = R R be the set of all pairs of numbers (a; b). Dene an addition
and multiplication on R2 via
(a; b) +

BEE3054 Advanced mathematics for Economists
Dieter Balkenborg
Departments of Economics
University of Exeter
Homework Week 1 Solutions
Exercise 1 What is the intersection of the set of all even numbers and the set of all
numbers divisible by 3?
Solution 1

BEE3054 Advanced mathematics for Economists
Dieter Balkenborg
Departments of Economics
Homework Week 3 Solutions
University of Exeter
Exercise 1 For any objects a; b; c; d show that
ff?; ag ; ff?g ; bgg = ff?; cg ; ff?g ; dgg () (a = c and b = d)
if not a

BEE3054 Advanced mathematics for Economists
Dieter Balkenborg
Departments of Economics
University of Exeter
Homework Week 1 Solutions
Exercise 1 What is the intersection of the set of all even numbers and the set of all
numbers divisible by 3?
Denition 1

BEE3054 Advanced mathematics for Economists
Dieter Balkenborg
Departments of Economics
University of Exeter
Homework Week 2
Exercise 1 For any objects a; b; c; d show that
ff?; ag ; ff?g ; bgg = ff?; cg ; ff?g ; dgg () (a = c and b = d)
You can assume ? 6

BEE3054 Advanced mathematics for Economists
Dieter Balkenborg
Departments of Economics
University of Exeter
Homework Week 2
Exercise 1 Which of the following strings are sentences (well-dened formulas) in the
logic system we dened.
(A ^ B)
(A ! A0 ) ! (A

BEE3054 Advanced mathematics for Economists
Dieter Balkenborg
Departments of Economics
University of Exeter
Homework Week 2
Exercise 1 Which of the following strings are sentences (well-dened formulas) in the
logic system we dened.
(A ^ B)
(A ! A0 ) ! (A