MA-305 Transparencies for Lecture 13

Tuesday, February 24, 1998


Slide 1

Lect 13, slide 1
Russell's Set Theory Paradox
(Audio Part 1, 3:33)


Slide 2

Lect 13, slide 2
The Zenon Paradox
(Audio Part 1, 10:37)


Slide 3

Lect 13, slide 3
Computing the Determinant of a Matrix by Minor Expansion
and Operation Counts
(Audio Part 1, 15:33)


Slide 4

Lect 13, slide 4
Number of Calls to non-Memoized Fibonacci Function
(Audio Part 1, 26:45)


Slide 5

Lect 13, slide 5
Number of Calls for Fibonacci Function (cont.)
(Audio Part 1, 29:55)


Slide 6

Lect 13, slide 6
Determining Which Minors get Recomputed with our
Formula from Slide 3 above, and Computing with Memoization
(Audio Part 1, 36:51)


Slide 7

Lect 13, slide 7
Cramer's Rule Reviewed
(Audio Part 1, 46:26)
Quickly Determining a Determinant Given a Quick
Algorithm for Solving a Linear System
(Audio Part 1, 48:00)


Slide 8

Lect 13, slide 8
Introducing Vector Spaces:
Vector Space Definition
(Audio Part 1, 49:59)


Slide 9

Lect 13, slide 9
Notation for a Vector Space and
Formal Vector Space Definition
(Audio Part 1, 53:45)


Slide 10

Lect 13, slide 10
Continuing Definition of a Vector Space:
Associative and Identity Laws (Audio Part 1, 55:50)


Slide 11

Lect 13, slide 11
A Simple Example of a Vector Space
(Audio Part 2, 0:23)


Slide 12

Lect 13, slide 12
Geometric Illustration of Vector Space Axioms
(Audio Part 2, 4:02)


Slide 13

Lect 13, slide 13
Testing Commutativity of Vector Addition
(Audio Part 2, 10:46) Testing Laws of Distributivity for Vectors
(Audio Part 2, 11:35)