# Fall 2015 Course Notes

## Stat 051 Probability

### Prof. Kelly McConville

### Tues-Thurs 9:55-11:10 Science Center L32

An introduction to the mathematical theory of probability. Topics include sample spaces and events, conditional probability and Bayes' theorem, univariate probability and density functions, expectation and variance, moment generating functions, Binomial, Negative Binomial, Poisson, Normal, t, Gamma and Beta distributions, joint, marginal and conditional distributions, independence, transformations, the multivariate Normal distribution, the law of large numbers and the central limit theorem.

Prerequisites: MATH 033, 034, 035 or permission of the instructor.

1 credit.

## Stat 061S Probability & Mathematical Statistics

### Prof. Phil Everson

### MWF 10:30-11:20 Science Center 181

A final offering of the old Stat 61, open to seniors (class of 2016) only. Stat 51 and the new Stat 61 (offered Spring 2016, with Stat 51 as a prerequisite) will cover and expand on the material covered in the old Stat 61.

Prerequisites: MATH 033, 034, 035 or permission of the instructor.

1 credit.

## Math 056 Modeling

### Prof. Victor Barranca

### MWF 11:30 Science Center 158

An introduction to the formulation and analysis of mathematical models. This course will present a general framework for the development of discrete, continuous, and graphical models of diverse phenomena. Principles of modeling will be drawn from kinetics, population dynamics, traffic flow, diffusion, continuum mechanics, cellular automata, and network science. Mathematical techniques for understanding models will be emphasized, including dimensional analysis, phase plane diagrams, stability analysis, bifurcation theory, conservation laws, steady-state solutions, and computer simulation. Specific applications from chemistry, biology, physics, engineering, and neuroscience will be discussed. A primary goal of this course is to give insights into the connections between mathematics and real-world problems, allowing students to apply the course concepts to applications that excite them.

Prerequisites: Linear algebra and basic differential equations, or permission of the instructor.

## Math 075 Advanced Topics in Geometry

### Prof. Michael Biro

Discrete geometry studies the structural and combinatorial properties of discrete sets of geometric objects (points, lines, polygons, circles, etc). In particular, we will consider how these objects can intersect each other,

how they can be combined to cover or fill each other, and which patterns and relationships must occur in their arrangements. These topics have particularly important applications in computer science, combinatorics,

optimization, and graph theory.

Prerequisites: At least one of MATH 055, MATH 059, MATH 063, MATH 067, or MATH 069 is recommended.

## CPSC 049/Math 059 The Probabilistic Method (Topics in Discrete Mathematics)

### Prof. Josua Brody

### MWF 10:30-11:20 Science Center 264

### Lab W 1:15-2:45 Science Center 105

In mathematics and theoretical computer science, we often consider classes of objects (say graphs, circuits or matrices) and we'd like to know if there are objects that have certain nice properties. One way to show these nice objects exist is to look at a random object, and show it has the nice property with nonzero probability. If this is true, there must be some object with this nice property.

This is the Probabilistic Method in a nutshell. It has become an essential tool for understanding structure of lots and lots of things in theoretical computer science and combinatorics, even in problems and applications which involve no randomness at all.

This class will start from the ground up. I'll introduce first discrete probability theory, giving you most of what you need to understand randomness in computer science. Most of the course will cover the probabilistic method in detail: how it works, extensions, and most of all lots of applications. We'll also spend a few weeks discussing NP-Completeness and randomized algorithms.

Prerequisites are CS35 and Math 029, although either can be skipped with permission from the instructor.