CME 305: Discrete Mathematics and Algorithms

Instructor: Reza Zadeh

Winter 2015
Time: Tuesdays and Thursdays 12:50 PM - 2:05 PM
Room: Building 60 Room 120

Topics Covered

  • Basic Algebraic Graph Theory
  • Minimum Spanning Trees and Matroids
  • Maximum Flow and Submodularity
  • NP-Hardness
  • Approximation Algorithms
  • Randomized Algorithms
  • The Probabilistic Method
  • Spectral Sparsification

Course Description

This course is targeting doctorate students with strong foundations in mathematics who wish to become more familiar with the design and analysis of discrete algorithms. An undergraduate course in algorithms is not a prerequisite, only familiarity with basic notions in linear algebra and discrete mathematics.

Required textbook:
Algorithm Design by Kleinberg and Tardos [KT]

Optional textbooks:
Graph Theory by Reinhard Diestel [D]
Approximation Algorithms by Vijay Vazirani [V]
Randomized Algorithms by Rajeev Motwani and Prabakhar Raghavan [MR]
The Probabilistic Method by Noga Alon and Joel Spencer [AS]

Grade breakdown: 50% final, 30% midterm, 20% assignments (4 of them). The midterm and final will be good practice for the ICME qualifying exam.

Midterm: Date TBA in class
Final: Date TBA

Assignments

  • Assignment 1
  • Assignment 2
  • Assignment 3
  • Assignment 4

References

Note that these references are neither required reading for the class nor intended to be any substitute for the material covered during lectures.

  • Tu 1/5: Introduction to The Probabilistic Method

Exams

Midterm Solutions pdf,

2011 Midterm pdf, Solutions pdf.

2010 Midterm pdf, Solutions pdf.

Practice Midterm 1 (In-Class) pdf, Solutions pdf.

Practice Midterm 2 (In-Class) pdf, Solutions pdf.

Spring 2012 Qual pdf.

Fall 2012 Qual pdf.

Spring 2013 Qual pdf.

Problem Sessions

Problem Session 2/10/14 and Solutions

Problem Session 2/20/14 and Solutions

Pre-Final Workshop

Previous years

Winter 2014: Class website

Contacts

Reza Zadeh (rezab at stanford)
Office hours: by appointment

Nolan Skochdopole (naskoch at stanford)
Office hours: TBA

Simon Anastasiadis (simonsa at stanford)
Office hours: TBA

TA office hours will be held in the Huang Engineering Center basement (in front of the ICME office)