Lecture Notes

Students in this class were required to scribe lecture notes in order to gain experience writing mathematics. The lecture notes files are included courtesy the students listed below.

LEC # TOPICS LECTURE NOTES SCRIBES / LECTURERS
1 Introduction    
2 The Condition Number (PDF) (Courtesy of Steve Weis. Used with permission.)

Scribe: Steve Weis

Lecturer: Daniel Spielman

3 The Largest Singular Value of a Matrix (PDF) (Courtesy of Arvind Sankar. Used with permission.)

Scribe: Arvind Sankar

Lecturer: Daniel Spielman

4 Gaussian Elimination Without Pivoting (PDF) (Courtesy of Matthew Lepinski. Used with permission.)

Scribe: Matthew Lepinski

Lecturer: Daniel Spielman

5 Smoothed Analysis of Gaussian Elimination Without Pivoting (PDF) (Courtesy of Nitin Thaper. Used with permission.)

Scribe: Nitin Thaper

Lecturer: Daniel Spielman

6 Growth Factors of Partial and Complete Pivoting

Speeding up GE of Graphs with Low Bandwidth or Small Separators

(PDF) (Courtesy of Brian Sutton. Used with permission.)

Scribe: Brian Sutton

Lecturer: Daniel Spielman

7 Spectral Partitioning Introduced (PDF) (Courtesy of Michael Korn. Used with permission.)

Scribe: Michael Korn

Lecturer: Shang-Hua Teng

8 Spectral Partitioning of Planar Graphs (PDF) (Courtesy of Jan Vondrák. Used with permission.)

Scribe: Jan Vondrák

Lecturer: Daniel Spielman

9

Spectral Parititioning of Well-Shaped Meshes and Nearest Neighbor Graphs

Turner’s Theorem for Bandwidth of Semi-Random Graphs

(PDF)

Scribe: Stephan Kalhamer

Lecturer: Daniel Spielman

10

Smoothed Analysis and Monotone Adversaries for Bandwidth and Graph Bisection

McSherry’s Spectral Bisection Algorithm

(PDF) Lecturer: Daniel Spielman
11

Introduction to Linear Programming

von Neumann’s Algorithm, Primal and Dual Simplex Methods

Duality

(PDF) (Courtesy of José Correa. Used with permission.) Scribe: José Correa

Lecturer: Daniel Spielman

12

Strong Duality Theorem of Linear Programming

Renegar’s Condition Numbers

(PDF) (Courtesy of Arvind Sankar. Used with permission.)

Scribe: Arvind Sankar

Lecturer: Daniel Spielman

13 Analysis of von Neumann’s Algorithm (PDF) (Courtesy of Nitin Thaper. Used with permission.)

Scribe: Nitin Thaper

Lecturer: Daniel Spielman

14 Worst-Case Complexity of the Simplex Method (PDF ) (Courtesy of Brian Sutton. Used with permission.) Scribe: Brian Sutton

Lecturer: Daniel Spielman

15 The Expected Number of Facets of the Convex Hull of Gaussian Random Points in the Plane (PDF)

Scribe: Mikhail Alekhnovitch

Lecturer: Daniel Spielman

16 The Expected Number of Facets of the Convex Hull of Gaussian Random Points in the Plane (cont.) (PDF) (Courtesy of Mikhail Alekhnovitch. Used with permission.)

Scribe: Mikhail Alekhnovitch

Lecturer: Daniel Spielman

17 The Expected Number of Facets of the Shadow of a Polytope Given by Gaussian Random Constraints (PDF) (Courtesy of Steve Weis. Used with permission.)

Scribe: Steve Weis

Lecturer: Daniel Spielman

18 The Expected Number of Facets of the Shadow of a Polytope Given by Gaussian Random Constraints: Distance Bound  

Scribe: Stephan Kalhamer

Lecturer: Daniel Spielman

19 The Expected Number of Facets of the Shadow of a Polytope Given by Gaussian Random Constraints: Angle Bound and Overview of Phase 1 (PDF) (Courtesy of Matthew Lepinski. Used with permission.)

Scribe: Matthew Lepinski

Lecturer: Daniel Spielman

Course Info

Learning Resource Types

notes Lecture Notes