Foundations of Advanced Mathematics
Complex Numbers Practice Problems
For problems 1 5, state all of the sets of
numbers to which the given number belongs:
natural, integer, rational, irrational, real,
imaginary, and complex.
1. 0
2. 1
3.
4. e
5. i
6. 2

Foundations of Advanced Mathematics
Chapter 1 Preliminaries
Section 2 Sequences and Series Concepts Questions and Study Guide
Concept Questions
1. What is a sequence?
2. Is order important in a sequence?
3. What happens if the order of a sequence is chang

Foundations of Advanced Mathematics
Chapter 1 Preliminaries
Section 1 Sets of Numbers Concepts Questions and Study Guide
Concepts Questions
1. What is the set of natural numbers?
2. What symbol is used to denote the set of natural numbers?
3. What is the

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Foundations of Advanced
Mathematics
Chapter 1
Preliminaries
Section 3
Basic Definitions and
Introduction to Formal Proof
Section Overview
Give precise definitions of
divides
divisible by 3
divisible by 4
divisible by 5
even
odd
parity
perfect square
perf

Foundations of Advanced
Mathematics
Chapter 1
Preliminaries
Section 2
Sequence and Series
Section Overview
Review sequences.
Review series and sigma notation.
Review important properties of sigma notation.
Review important formulas for sigma notation.
Dis

Foundations of Advanced
Mathematics
Chapter 1
Preliminaries
Section 1
Sets of Numbers
Section Overview
Briefly touch on the question What is
mathematics?
Review important sets of numbers and their
notation.
Define imaginary numbers.
Define complex num

Foundations of Advanced Mathematics
Basic Definitions and Introduction to Formal Proof Practice
Problems
In problems 1 14, give a formal proof of
each the following statements by using
precise definitions.
1. 26 is even.
2. 25 is odd.
3. 0 is even.
4. 35

Foundations of Advanced Mathematics
Basic Definitions and Introduction to Formal Proof Answers
to Practice Problems
In problems 1 14, give a formal proof of
each of the following by using precise
definitions.
1. 26 is even.
PROOF: 26 = 2 13 and 13 is an i

Foundations of Advanced Mathematics
Complex Numbers Answers to Practice Problems
For problems 1 10, state all of the sets of
numbers to which the given number belongs:
natural, integer, rational, irrational, real,
imaginary, and complex.
1. 0; natural, in

Foundations of Advanced Mathematics
Chapter 1 Preliminaries
Section 3 Basic Definitions and Introduction to Formal Proof Concepts Questions
and Study Guide
Concepts Questions
1. What is meant by an undefined terms in mathematics?
2. What is meant by a def