MATH1050: Foundation of Modern Mathematics
Logic, proof, number systems, sets and their applications.
1. Statements, logic and quantifier order
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Chapter 1
1. Statements, logic and quantifier order
1. Statements, logic and quantifier order
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1. Statements, logic and quantifier order
1. Statements, logic and quantifier order
Chapter 2
2. Direct proof, contradiction and induction
2. Direct proof, contradiction and induction
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2. Direct proof, contradiction and induction
2. Direct proof, contradiction and induction
Chapter 3
3. Sets, images and inverse images
3. Sets, images and inverse images
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3. Sets, images and inverse images
3. Sets, images and inverse images
Chapter 4
4. Relations, equivalence classes and order
4. Relations, equivalence classes and order
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4. Relations, equivalence classes and order
4. Relations, equivalence classes and order
Chapter 5
5. Countability and diagonal arguments
5. Countability and diagonal arguments
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5. Countability and diagonal arguments
5. Countability and diagonal arguments
Chapter 6
6. Integers, divisibility and rational constructions
6. Integers, divisibility and rational constructions
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6. Integers, divisibility and rational constructions
6. Integers, divisibility and rational constructions
Chapter 7
7. Polynomial identities, roots and rational-root arguments
7. Polynomial identities, roots and rational-root arguments
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7. Polynomial identities, roots and rational-root arguments
7. Polynomial identities, roots and rational-root arguments
Chapter 8
Optional: 8. Affine and orthogonal geometry in higher dimensions
Optional: 8. Affine and orthogonal geometry in higher dimensions
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Optional: 8. Affine and orthogonal geometry in higher dimensions
Optional: 8. Affine and orthogonal geometry in higher dimensions
Chapter 9
Optional: 9. Conics and quadrics through equations and sections
Optional: 9. Conics and quadrics through equations and sections
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Optional: 9. Conics and quadrics through equations and sections
Optional: 9. Conics and quadrics through equations and sections
Chapter 10
Number-system depth: constructing integers without hidden subtraction
Number-system depth: constructing integers without hidden subtraction
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Number-system depth: constructing integers without hidden subtraction
Number-system depth: constructing integers without hidden subtraction
Chapter 11
Proof depth: auditing arguments, dependence and uniqueness
Proof depth: auditing arguments, dependence and uniqueness
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Proof depth: auditing arguments, dependence and uniqueness
Proof depth: auditing arguments, dependence and uniqueness
Chapter 12
Quotient depth: descending maps and checking representatives
Quotient depth: descending maps and checking representatives
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Quotient depth: descending maps and checking representatives
Quotient depth: descending maps and checking representatives
Chapter 13
Real and complex number systems: axioms and proof consequences
Real and complex number systems: axioms and proof consequences
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Real and complex number systems: axioms and proof consequences
Real and complex number systems: axioms and proof consequences
Chapter 14
Elementary inequalities: identities, domains and equality cases
Elementary inequalities: identities, domains and equality cases
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Elementary inequalities: identities, domains and equality cases
Elementary inequalities: identities, domains and equality cases
Chapter 15
Countability depth: listings, trees and mistaken enumerations
Countability depth: listings, trees and mistaken enumerations
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Countability depth: listings, trees and mistaken enumerations
Countability depth: listings, trees and mistaken enumerations