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

SUPER-CHARGING MARKET-DRIVEN COMMUNITIES Sidharth Jaggi School of Mathematics Dept. of Information Engineering University of Bristol Chinese University of Hong Kong

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Week 0: Week 1 Week 2 Week 3 * wxmaxima: Free software for 1. Vectors and matrices 8. Elementary row opns Ex01 17. Determinants Ex01 matrix calculations 2. Definitions Ex01 9. Row equiv systems Ex02 18. Properties-I Ex02 * Structure of class 3. Addition/scalar mult Ex02 10. Row-echelon form Ex03 19. Properties-II (Rank) Ex03 4. Properties Ex03 11. Lin (in)dependence Ex04 20. Leibniz formula Ex04 5. Matrix multiplication Ex04 12. Row/col rank Ex05 21. Cramer's rule Ex05 6.Definitions/properties Ex05 13. Vector spaces: Ex06 22. Matrix inverses Ex06 7. Gaussian elimination Ex06 14. More definitions Ex07, 08 23. Properties Ex07 15. Matrix vector spaces Ex9 25. Inverses via dets Ex08 16 Vec spaces & lin eqn Ex10 26. Properties-II Ex09 27. Inner prod spaces Ex 10 28. Function spacesEx11 29. Linear transforms-I 30. Linear Transforms-II Ex12 Week 4 Week 6 Week 7 Week 5 31. Eigenvalues Ex01 51. Vectors in R2 & R3 60. Arc-length paramet Ex01-03 42. Unitary matrices Ex01 32. Eigenvals/eigenvecs Ex02 61. Acceler/Curvature/Torsion Ex01 43. Orthog complement 33. Repeated eigenvalues Ex04-06 52. Dot-products Ex02 34. Some theorems about 62. Coriolis acceleration Ex07 53. Properties of dot- eigenvecs/eigenvals Ex03 63. Chain-rule/Mean-val Thm 44. Spectral theorem-I 35. Algebraic/geometric Ex08 products 45. Spectral theorem-II multiplicity of eigenvalues 64_Gradient/Direc deriv-1 Ex09 54. More projections Ex02 46. Schur decomposition 36. Eigenvalue/eigenvector 64_Gradient/Direc deriv-2 55. Vector cross product application examples Ex04 47. Jordan canon form 65. Gradient descent Ex10 37. Eigenvals/eigenvecs of Ex03 66. Multivar opt via gradients Ex03 symm/skew-symm matrices Ex11 67. Divergence/Laplacian 56. Scalar triple product: 48. SVD Ex04 38. Orthogonal matrices-I: 39. 68. Curl Ex12 57. 49. SVDs-II Orthogonal mats-II Ex05 Curves/Surfaces/Vector 40. Orthogonal mats-III 50. One application of 3 41. Diagonalization-I Ex06 fields Ex04-Ex09 SVD: matrix 58. Scalar/vector "compression"

Week 8 Week 9 Week 10 Week 11 78. What is a "field"? 69. (Scalar) Line 86. Green's Theorem- 97. Sets of numbers Ex01, Ex02 Ex01 integrals 1Ex01 98. Limit of a sequence Ex03 79. Euclid’s algorithm 70. Line integrals 87. Green's theorem-2 99. Cauchy's convergence criterion Ex02 Ex01 88. Green's thm: Ex04 80. Prime fields Ex03 71. Path Applications Ex02 100. Bolzano-Weierstrass Theorem 81. Similarities/ in/dependence 89. Ex05 differences between Ex02 Surfaces/parametrizati 101. Limits of functions Ex06 finite fields and 72. Path ons/surface 102. Continuity of functions Ex07 real/complex fields in/dependence normals/tangent 103. Continuity of functions in two Ex04 Ex03 planes Ex03 variables 82. Applications of 73. Closed 90. Surface vector Ex08 finite fields: Reed- curves/Curl test integrals Ex04 104. Derivatives Ex09 Solomon Codes Ex05, Ex04 91. Surface scalar 105. Mean-value theorems Ex10 Ex06 74. Simple- integrals Ex05 106. Taylor's theorem Ex11 83. Polynomials over connectedness 92. Divergence thm of 107. Riemann integral Ex12 finite fields/Schwartz- Ex05 Gauss Ex06 108. Numerical integration Ex13 Zippel 75. Double 93. Divergence lemma/applications integrals-1 theorem of Gauss-2 Ex07 76. Double 94. Gauss Diverg thm: 84. Extension fields integrals-2 Ex04 applications 85. Finite field 77. Change of 95. Stokes' Theorem-1 calculations on variables/Jacobian: Ex07 4 wxmaxima Ex08 Ex05 96. Stokes' Theorem-2

 Cayley-Hamilton theorem  Capacity of the Binary erasure channel  Fixed point theorem  Gershgorin Disc theorem  Kepler’s 3 rd law  Spectral theorem for normal matrices  Geodesics  Rank-metric codes  Multi-dimensional scaling  Césaro convergence  Positive-definite matrix properties  Pursuit problems  Compositions of rotations  No-cloning theorem  Reimann series theorem  Deriving Error-term in trapezoidal rule  Sylvester’s inequality  Rayleigh coefficients  Properties of nilpotent matrices  Projection matrices  Rates of convergence of Markov chains  Primitive elements of finite fields  Eigenvectors from eigenvalues  Gilbert-Varshamov codes  Sherman-Morrison formula  Non-analytic smooth functions 5

6 … 19 projects…

• Cryptography • Quantum algorithms • Planimeter • Tomography • Talking Piano • Game theory • 3D-projection • Wavelet image compression • Civil Engineering • Community detection • Deep Learning • Fractals • Ranking algorithms • Linear programming • Image processing • Game of Life • PCA face recognition • Fast Matrix Multiplication • Denoising audio signals 7

Is that all? 8

MARKET-DRIVEN COMMUNITIES Market Incentives Community Norms Prof. Michael J. Sandel (Harvard) What money can't buy: the moral limits of markets . Macmillan , 2012. 9

MARKET-DRIVEN COMMUNITIES 10

MARKET-DRIVEN FRAMEWORK COMMUNITIES 11

MARKET-DRIVEN COMMUNITIES • Interactive exercises • Social engineering incentives  Is that all? One-way content delivery: Lectures/ Videos Bloom Taxonomy 12

SUPER-CHARGING FLIPPED CLASSROOMS: MARKET-DRIVEN FRAMEWORK COMMUNITIES • HAROLD Essays Capstone Collaborative Projects creative designs • Market-Aided Peer-to-peer Summative Review Teaching Exchange teaching Synthesized Synergistic • Fruits/coins Presentations learning • “Social Network” Challenging Collaborative problem-solving Worksheets Problem-solving • DICE grading Deepening Interleaved Interactive Exercises • Threshold grading Videos: Basic content delivery Seeding knowledge 13

 ~9 videos /week, ~10 mins/video = ~90 mins video/week 14

 ~10 automated interactive online exercises /week  Interleaved between videos  Points deducted for not doing 15

 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+ 16

“Social - network” Problem-solving • • 17

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 MATE ( M arket- A ided T eaching E xchange)  Peer-to-peer review • Students seek help from someone who understands. • Helpers get points for helping 19

 3x week feedback loop  Paper feedback slips end of each class  Respond to each comment  Can track longitudinally/anonymous student Co-ownership in the Community of Learning • Rapid iteration • Pressure-release valve Some colleagues use this system 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 20

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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 others 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. ’’ 22

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