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▾
Bridge course
•
Countable and uncountable sets
▸
Proof techniques
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Example of a nonconstructive proof
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Direct proof
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Disproof by counterexample
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Proof by cases
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Proving properties of absolute value
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Proof by contrapositive
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Proof by contradiction
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Proof by induction
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Proof by strong induction
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Proving de Moivre's theorem
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Visual proof
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Challenge
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Relations
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Equivalence relations
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Intersection of equivalence relations
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Representing relations using matrices
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Combining relations
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Composition of relations
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Inverse of composite relation
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Representing relations using digraphs
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Properties of relations
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Proving equivalence relations
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What is a relation?
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Finding the inverse of a relation on a finite set
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Functions (bridge course)
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Injective, surjective, and bijective
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Intro
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Is it bijective? (infinite domain)
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Is it injective?
▸
Is it surjective?
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Proof: Composite of surjections is surjection
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Proving properties of injective, surjective, and bijective functions
›
Bridge course
Other resources
YouTube videos
3433
The Traveler and the Strange Staircase (Screencast 4.1.1)
GVSUmath
3434
Affine ciphers (Screencast 7.4.4)
GVSUmath
3435
Extended Principle of Mathematical Induction: Example from computational geometry (Screencast 4.2.2)
GVSUmath
3436
Function example: Counting primes (Screencast 6.1.4)
GVSUmath
3437
Equivalence relations (Screencast 7.2.2)
GVSUmath
3440
Functions: Terminology (Screencast 6.1.2)
GVSUmath
3455
The Division Algorithm and Integer Congruence (Screencast 3.5.3)
GVSUmath
3457
Negating quantified statements (Screencast 2.4.2)
GVSUmath
3458
Application to Cryptography (Screencast 3.5.4)
GVSUmath
3461
Conditional statements (Screencast 1.1.3)
GVSUmath
More YouTube videos...
Webpages
128
How To Write Proofs