# Engineering and Industrial Applied Mathematics Clinic

## Overview

Embracing the Mathematics Clinics at CGU and at the highly regarded undergraduate Claremont Colleges, the Claremont Mathematics Clinic has proven to be an effective "two-way street" between applied mathematicians at the colleges and scientists and mathematicians in industry or government laboratories in need of amplified mathematical experience.

In the 170-plus year-long projects that have been completed by Clinic teams over the last two decades, students and faculty have gained an opportunity to apply their mathematical skills to an impressive variety of real-world, current problems. Client scientists and engineers who propose projects benefit from useful, relevant solutions. Recent projects led to two patents and a computational model that outperforms the current industry standard.

## Mathematics Clinic goals are to:

- provide students with experience for a career in industry or government
- provide students with experience far beyond normal university training
- sustain a curriculum attuned to real-world applications foster an ongoing dialog between faculty and scientists, xbring industrial trends to campus, and alert industry to new techniques developed in academia
- allow business and industry to draw upon the intellectual and physical resources of
__The Claremont Colleges__
- develop specific projects to be addressed by joint teams of faculty members, students, and industry

## Description

Clinic teams address problems of sufficient magnitude and complexity that their analysis, solution and exposition require substantial effort over the course of an academic year or full-time involvement over a summer. If problems require expertise from disciplines other than mathematics--such as engineering, physics or economics--advanced undergraduate or graduate students from these disciplines may join the Clinic team. The CGU Mathematics Clinic works closely with its counterparts at the Claremont Colleges, with clinic teams often combining graduate students and advanced undergraduates.

The creative resources of the Mathematics Clinic often far exceed those normally available even to a fairly large organization.

The Claremont Colleges' mathematics programs stress creative thinking. This means that students and faculty members are exceptionally well equipped to address problems. Many faculty members have considerable background in industry.

The Clinic includes specialists actively engaged in research in nearly all phases of applied mathematics, with established reputations in areas such as mathematical modeling of physical and economic systems; differential and integral equations; numerical analysis; Monte Carlo methods; operations research; scheduling; mathematical programming and optimization; probability theory; applied statistics; and computer science.

Recognizing the value of the Mathematics Clinic, the __National Science Foundation__ has provided two major grants: one to develop the Clinic, and the other to bring new mathematicians to Claremont. To date, 52 post-doctoral mathematicians have participated in and benefited from the Clinic experience.

Students receive credit for their work in the Mathematics Clinic.

## Recent Projects

- Optimizing Transmission of Renewable Energy

Sponsor: Southern California Edison
- Hardware-Software Codesign

Sponsor: Los Alamos National Laboratory
- Data Cohort Analysis

Sponsor: Fair Isaac
- Optimizing Smart Power Grids

Sponsor: Los Alamos National Laboratory
- Credit Risk in a Network Economy

Sponsor: Fitch Rating
- Isogeometric Analysis

Sponsor: Boeing
- Gate to Base Capacitance Modeling for Nano-scale MOSFETs

Sponsor: USC Information Sciences Institute
- Practical Semi-Analytic Model for the Substrate Current of Short Channel MOSFETs with LDDs

Sponsor: USC Information Sciences Institute

Pipeline capacitance tomography

Sponsor: Instituto Mexicano del Petroleo
- Fast Optimization Algorithms for Mars Relay Network Planning and Scheduling

Sponsor: Jet Propulsion Laboratory

## Clinic Report

Gate to Base Capacitance Modeling for Nano-scale MOSFETs (pdf)

USC Information Sciences Institute -- 2007

## Sample Projects

There have been more than 250 projects conducted by the Mathematics Clinic over the last 30 years.

## Clinic Faculty

The areas of expertise of The Claremont Colleges faculty members who participate in the Mathematics Clinic cover an impressive range of mathematical applications. In addition to those faculty members listed below, more than 50 post-doctoral mathematicians from such institutions as Purdue University, Indiana University, The University of Guelph (Canada) and Trinity College (Ireland) have served as Mathematics Clinic advisors during year-long visits to Claremont

**John Angus:** Probability, statistics, neural networks, genetic algorithms, computer-intensive methods in statistics.
**Ellis Cumberbatch: **Fluids, solids, transistor modeling, asymptotics.
**Mario Martelli: **Non-linear analysis, chaos, applied mathematics.

** **
**Ali Nadim**: Applied mathematics, fluid dynamics, scientific computing.
**Allon Percus**: Discrete optimization, algorithms, network models.
**Ami Radunskaya: **Dynamical systems, stochastic processes, applications of dynamical systems to instrument modeling, sound generation, interactive composition.
**Adolfo Rumbos: **Partial differential equations, bifurcation techniques.
**Henry Schellhorn**: Mathematical finance, stochastic analysis, credit risk, Monte Carlo simulation.