Introduction
Overview
Needs
Fundamentals of Mathematics
Bernd Schroder
Bernd Schroder
Fundamentals of Mathematics
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Louisiana Tech University, College of Engineering and Science
Introduction
Overview
Needs
What are the Fundamentals of Mathematics?
1.
Fundamental Concepts of
Mathematics
Lecture 2 :
AM-GM Inequality,
Recurrence Relations
Chin CheeWhye
Department of Mathematics
National University of Singapore
17 August 2015
Announcements
Homework 1:
Due 27 August 2015 at 12pm
Write your Name and Student
Fundamental Concepts of
Mathematics
Lecture 3 :
Strong Induction,
Well-Ordering Property,
Fallacies of induction proof
Chin CheeWhye
Department of Mathematics
National University of Singapore
20 August 2015
Announcements
Homework 1:
Due 27 August 2015 at
Fundamental Concepts of
Mathematics
Lecture 4 :
Propositions,
Connectives, Conditionals,
Quantiers
Chin CheeWhye
Department of Mathematics
National University of Singapore
24 August 2015
Announcements
Homework 1:
Due 27 August 2015 at 12pm
Write your Name
Fundamental Concepts of
Mathematics
Lecture 5 :
Set Theory (part 1 of 2):
equality, membership, subset relations,
constructing subsets, empty set, Russells paradox,
unordered pairs, singleton, uniqueness, ordered pairs
Chin CheeWhye
Department of Mathemat
Fundamental Concepts of
Mathematics
Lecture 6 :
Set Theory (part 2 of 2):
ordered pairs,
unions and intersections,
dierences and complements
power sets, direct products,
the other axioms
Chin CheeWhye
Department of Mathematics
National University of Singa
Fundamental Concepts of
Mathematics
Lecture 7 :
Maps:
equality of maps,
identity map, composite map, invertible map,
injective, surjective, bijective maps,
image, preimage
universal properties
Chin CheeWhye
Department of Mathematics
National University of
Fundamental Concepts of
Mathematics
Lecture 8 :
Maps:
image, preimage,
restrictions and prolongations,
universal properties
Chin CheeWhye
Department of Mathematics
National University of Singapore
7 September 2015
Announcements
Homework 2:
Due 10 Septembe
Fundamental Concepts of
Mathematics
Lecture 9 :
Cardinality, Finite and Innite sets,
Cardinality of a Finite set
Principles of Counting:
bijection principle, injection principle
Chin CheeWhye
Department of Mathematics
National University of Singapore
10 S
Fundamental Concepts of
Mathematics
Lecture 1 :
Natural Numbers, Summation,
Mathematical Induction
Chin CheeWhye
Department of Mathematics
National University of Singapore
13 August 2015
References / Suggested Readings
P. R. Halmos, Naive set theory , Spr
Fundamental Concepts of
Mathematics
Lecture 02
Natural Numbers
Recurrence Relations,
Strong Induction, Well-Ordering Property,
Fallacies of induction proof
Chin CheeWhye
Department of Mathematics
National University of Singapore
AY 2016/2017 Semester 1
Re
Unions
Distributivity
DeMorgans Laws
Boolean Algebra
The Axiom of Unions
Bernd Schroder
Bernd Schroder
The Axiom of Unions
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Louisiana Tech University, College of Engineering and Science
Unions
Distributivity
DeMorgans Laws
Boolean Algebra
The Axiom o
Fundamental Concepts of
Mathematics
Lecture 01
Natural Numbers
Summation and Product Notation,
Mathematical Induction,
AM-GM Inequality
Chin CheeWhye
Department of Mathematics
National University of Singapore
AY 2016/2017 Semester 1
Natural Numbers N
N
Properties Sets Should Have
The Problem
The Remedy
Russells Paradox
Bernd Schroder
Bernd Schroder
Russells Paradox
logo1
Louisiana Tech University, College of Engineering and Science
Properties Sets Should Have
The Problem
The Remedy
If We Could Define Se
Definition
Examples
Truth Values
Statements
Bernd Schroder
Bernd Schroder
Statements
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Louisiana Tech University, College of Engineering and Science
Definition
Examples
Truth Values
A statement or proposition is a sentence that is
either true or false
Fundamental Concepts of
Mathematics
Lecture 10 :
Principles of Counting, Permutations
Chin CheeWhye
Department of Mathematics
National University of Singapore
14 September 2015
Announcements
Midterm test 1:
17 September 2015 (this coming Thursday) startin