[PPT] - SUPER-CHARGING MARKET-DRIVEN COMMUNITIES Sidharth Jaggi School of PowerPoint Presentation

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SUPER-CHARGING

MARKET-DRIVEN COMMUNITIES

Dept. of Information Engineering

Chinese University of Hong Kong School of Mathematics University of Bristol Sidharth Jaggi

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Week 0: * wxmaxima: Free software for matrix calculations * Structure of class Week 1

1. Vectors and matrices
2. Definitions Ex01
3. Addition/scalar mult Ex02
4. Properties Ex03
5. Matrix multiplication Ex04

6.Definitions/properties Ex05

7. Gaussian elimination Ex06

Week 2

8. Elementary row opns Ex01
9. Row equiv systems Ex02
10. Row-echelon form Ex03
11. Lin (in)dependence Ex04
12. Row/col rank Ex05
13. Vector spaces: Ex06
14. More definitions Ex07, 08
15. Matrix vector spaces Ex9

16 Vec spaces & lin eqn Ex10 Week 3

17. Determinants Ex01
18. Properties-I Ex02
19. Properties-II (Rank) Ex03
20. Leibniz formula Ex04
21. Cramer's rule Ex05
22. Matrix inverses Ex06
23. Properties Ex07
25. Inverses via dets Ex08
26. Properties-II Ex09
27. Inner prod spaces Ex 10
28. Function spacesEx11
29. Linear transforms-I
30. Linear Transforms-II Ex12

Week 4

31. Eigenvalues Ex01
32. Eigenvals/eigenvecs Ex02
33. Repeated eigenvalues
34. Some theorems about

eigenvecs/eigenvals Ex03

35. Algebraic/geometric

multiplicity of eigenvalues

36. Eigenvalue/eigenvector

application examples Ex04

37. Eigenvals/eigenvecs of

symm/skew-symm matrices

38. Orthogonal matrices-I: 39.

Orthogonal mats-II Ex05

40. Orthogonal mats-III
41. Diagonalization-I Ex06

Week 5

42. Unitary matrices Ex01
43. Orthog complement

Ex02

44. Spectral theorem-I
45. Spectral theorem-II
46. Schur decomposition
47. Jordan canon form

Ex03

48. SVD Ex04
49. SVDs-II
50. One application of

SVD: matrix "compression"

Week 6

51. Vectors in R2 & R3

Ex01

52. Dot-products
53. Properties of dot-

products

54. More projections Ex02
55. Vector cross product

Ex03

56. Scalar triple product:

57. Curves/Surfaces/Vector fields Ex04-Ex09

58. Scalar/vector

Week 7

60. Arc-length paramet Ex01-03
61. Acceler/Curvature/Torsion

Ex04-06

62. Coriolis acceleration Ex07
63. Chain-rule/Mean-val Thm

Ex08 64_Gradient/Direc deriv-1 Ex09 64_Gradient/Direc deriv-2

65. Gradient descent Ex10
66. Multivar opt via gradients

Ex11 67. Divergence/Laplacian

68. Curl Ex12

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Week 8

78. What is a "field"?

Ex01

79. Euclid’s algorithm

Ex02

80. Prime fields Ex03
81. Similarities/

differences between finite fields and real/complex fields Ex04

82. Applications of

finite fields: Reed- Solomon Codes Ex05, Ex06

83. Polynomials over

finite fields/Schwartz- Zippel lemma/applications Ex07

84. Extension fields
85. Finite field

calculations on wxmaxima Ex08

Week 9

69. (Scalar) Line

integrals

70. Line integrals

Ex01

71. Path

in/dependence Ex02

72. Path

in/dependence Ex03

73. Closed

curves/Curl test Ex04

74. Simple-

connectedness Ex05

75. Double

integrals-1

76. Double

integrals-2 Ex04

77. Change of

variables/Jacobian: Ex05

Week 10

86. Green's Theorem-

1Ex01

87. Green's theorem-2
88. Green's thm:

Applications Ex02 89. Surfaces/parametrizati

ns/surface

normals/tangent planes Ex03

90. Surface vector

integrals Ex04

91. Surface scalar

integrals Ex05

92. Divergence thm of

Gauss Ex06

93. Divergence

theorem of Gauss-2

94. Gauss Diverg thm:

applications

95. Stokes' Theorem-1

Ex07

96. Stokes' Theorem-2

Week 11

97. Sets of numbers Ex01, Ex02
98. Limit of a sequence Ex03
99. Cauchy's convergence criterion

Ex04

100. Bolzano-Weierstrass Theorem

Ex05

101. Limits of functions Ex06
102. Continuity of functions Ex07
103. Continuity of functions in two

variables Ex08

104. Derivatives Ex09
105. Mean-value theorems Ex10
106. Taylor's theorem Ex11
107. Riemann integral Ex12
108. Numerical integration Ex13

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Capacity of the Binary erasure channel
Gershgorin Disc theorem
Kepler’s 3rd law
Rank-metric codes
Césaro convergence
Pursuit problems
No-cloning theorem
Deriving Error-term in trapezoidal rule
Rayleigh coefficients
Projection matrices
Primitive elements of finite fields
Gilbert-Varshamov codes
Non-analytic smooth functions

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Cayley-Hamilton theorem
Fixed point theorem
Spectral theorem for normal matrices
Geodesics
Multi-dimensional scaling
Positive-definite matrix properties
Compositions of rotations
Reimann series theorem
Sylvester’s inequality
Properties of nilpotent matrices
Rates of convergence of Markov chains
Eigenvectors from eigenvalues
Sherman-Morrison formula

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… 19 projects…

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Quantum algorithms
Tomography
Game theory
Wavelet image compression
Community detection
Fractals
Linear programming
Game of Life
Fast Matrix Multiplication
Cryptography
Planimeter
Talking Piano
3D-projection
Civil Engineering
Deep Learning
Ranking algorithms
Image processing
PCA face recognition
Denoising audio signals

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Is that all?

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MARKET-DRIVEN COMMUNITIES

Prof. Michael J. Sandel (Harvard)

Community Norms Market Incentives

What money can't buy: the moral limits of markets. Macmillan, 2012.

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MARKET-DRIVEN COMMUNITIES

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MARKET-DRIVEN FRAMEWORK COMMUNITIES

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Is that all?

Bloom Taxonomy

One-way content delivery: Lectures/ Videos

Interactive exercises
Social engineering

incentives

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MARKET-DRIVEN COMMUNITIES

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Videos: Basic content delivery Interleaved Interactive Exercises Challenging Worksheets Capstone Projects Peer-to-peer teaching Synergistic learning

SUPER-CHARGING FLIPPED CLASSROOMS:

MARKET-DRIVEN FRAMEWORK COMMUNITIES

DICE grading
Market-Aided

Teaching Exchange

“Social Network”

problem-solving

Fruits/coins
HAROLD Essays
Threshold grading

Summative Review Collaborative creative designs Collaborative Problem-solving Synthesized Presentations Seeding knowledge Deepening

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~9 videos/week, ~10 mins/video = ~90 mins video/week

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~10 automated interactive online exercises/week
Interleaved between videos
Points deducted for not doing

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In-class challenging exercises
3 person groups
DICE Grading
Each student in each group submits solution
TA randomly selects one to grade
Entire group gets equal points for that solution
Incentive to discuss/peer-learn

A+

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“Social-network” Problem-solving

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MATE (Market-Aided Teaching Exchange)
Peer-to-peer review
Students seek help from someone who understands.
Helpers get points for helping

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3x week feedback loop
Paper feedback slips end of each class
Respond to each comment
Can track longitudinally/anonymous

student On a scale of 0 to 10 (0=hell, 10=best class ever), today’s class was…. (Comments on reverse side) SECRET ID: 0 1 2 3 4 5 6 7 8 9 10

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Co-ownership in the Community of Learning

Rapid iteration
Pressure-release valve

Some colleagues use this system

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“ dear professor, you change my life I have to admit that I hated 1004 before. I struggled and felt disappointed

everyday. To be honest, I did not work hard at first. I thought this course

should be as easy as the courses in my last semester. And even after I realized that this course was difficult, I didn’t know what to do. I did not know how to study at university. I did a very bad job at my midterm and I almost dropped this course. But, I held on and tried my best to catch up with the

thers after midterm. Today I got my grade of my final exam, even though I

am not the best, I can see that I made progress. Last semester, I did not go to library at all. But this semester, I went there everyday. You change my habit and make be feel excited when facing challenges. Besides, I learned how to manage my time. Anyway, I feel so lucky to meet you and choose your class. I really appreciate you. Without you, I may continue wasting my time at dorm. haha. Thank you professor, I would like to choose your other course next time. See you.’’

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