# CME 305: Discrete Mathematics and Algorithms

Winter 2017
Time: Tue, Thu 10:30 AM - 11:50 AM
Room: Bishop Auditorium

## 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: Thursday, Feb 16th
Final: 03/22/2017, 12:15 - 3:15 P.M. at STLC 114 (science teaching & learning center)

## Assignments

• Assignment 1 [pdf] [tex], Due at the beginning of class Thursday 01/26. [Solutions]
• Assignment 2 [pdf] [tex], Due at the beginning of class Thursday 02/09. [Solutions]
• Assignment 3 [pdf] [tex], Due at the beginning of class Thursday 03/02 [Solutions]
• Assignment 4 [pdf] [tex], Due at the beginning of class Thursday 03/16 [Solutions]

## References

Note that these references are not intended to be any substitute for the material covered during lectures.

## Practice Exams

Spring 2012 Qual pdf.

Fall 2012 Qual pdf.

Spring 2013 Qual pdf.

2016 Midterm pdf, Solutions pdf

2015 Midterm pdf, Solutions pdf

2014 Midterm and 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.

## Problem Sessions

Problem Session 3/20/17, 2 Solutions

Problem Session 2/15/17 Solutions

## Previous years

Winter 2016: Class website

Winter 2015: Class website

Winter 2014: Class website

### Contacts

Office hours: by appointment

Andreas Santucci (santucci at stanford)
Office hours: Tuesday, 12 - 2.