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Dept. of Mathematics, Dept. of Mathematics, Computer Science & PhysicsComputer Science & Physics

College at FlorhamCollege at Florham

WELCOMEWELCOME

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Strengthening American Competitiveness for the 21st

CenturyMicrosoft Chairman Bill Gates warned in a testimony before the US Senate Committee on Health, Education, Labor and Pensions on March 7, 2007 ““A lack of technology skills is causing the US to fall behind in the global knowledge economy.We face a critical shortage of scientific talent.”

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College at FlorhamCollege at FlorhamBecton College of Arts and Becton College of Arts and

SciencesSciences

Becton College

Small

liberal

arts college

Committed

to a

liberal arts education

Practical,

career-oriented

approach

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Programs in Computer Science

• BS in Computer Science• BS in Computer Science, concentration in

Bioinformatics • Combined MS/BS in Computer Science – 5 year

program.• In the planning stage: Math/CS with concentration in

Bioinformatics:

- Emphasis on biology, statistics, data analysis and data management

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Programs in Mathematics

• BA in Mathematics• BA in Mathematics with concentration in Computer

Science• BA in Mathematics with concentration in Actuarial

Science• BA in Mathematics and Quest concentration in

Secondary Education• 5 year program towards elementary/secondary

school teaching

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Department of Department of Math/CSci/PhysicsMath/CSci/Physics

Ten highly qualified, full-time faculty membersTen highly qualified, full-time faculty members About 60-70 students each year About 60-70 students each year Small class size: average less than 15 studentsSmall class size: average less than 15 students Computer lab courses limited to 20 studentsComputer lab courses limited to 20 students Constantly updating computer equipment and softwareConstantly updating computer equipment and software Web-enhanced coursesWeb-enhanced courses HP tablet Mobile lab (A grant from HP)HP tablet Mobile lab (A grant from HP) Institute for the Enhancement of Teaching Science and Institute for the Enhancement of Teaching Science and

Math (IETSM)Math (IETSM) $500K Grant Grant from the John Martinson Foundation for

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InternshipsInternships

Work experience that leads to job opportunitiesWork experience that leads to job opportunities Part time work, 10 to 14 weeksPart time work, 10 to 14 weeks Arranged through the department, or through Arranged through the department, or through

the Career Center, through faculty contacts, or the Career Center, through faculty contacts, or by the studentby the student

Each student has a faculty mentor.Each student has a faculty mentor. Evaluated jointly by the mentor and the Evaluated jointly by the mentor and the

employer at mid-semester and end-of-semester.employer at mid-semester and end-of-semester. Student maintains a work journal.Student maintains a work journal.

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InternshipsInternships Some recent internships:Some recent internships:

Alcatel LucentAlcatel Lucent IntelIntel Knowledge SoftKnowledge Soft NovartisNovartis HoneywellHoneywell PfizerPfizer US Defense AcademyUS Defense Academy Several smaller companiesSeveral smaller companies

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Independent StudyIndependent Study

Independent research and reportIndependent research and report One_on_one experience with a faculty One_on_one experience with a faculty

mentormentor Senior Honors ProjectSenior Honors Project

Honors presentationsHonors presentations Honors work in any courseHonors work in any course Available for either CS majors or math Available for either CS majors or math

majorsmajors

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Faculty ResearchFaculty Research

Our Faculty are involved in a wide Our Faculty are involved in a wide range of interesting research projects.range of interesting research projects. Mathematics hypertext on the Web Mathematics hypertext on the Web Data Mining Data Mining Artificial Intelligence and Expert Systems Artificial Intelligence and Expert Systems Digital Rights Management Digital Rights Management Distributed SystemsDistributed Systems Computational Complexity Computational Complexity Numerical mathematicsNumerical mathematics

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Faculty GrantsFaculty Grants

HP grantHP grant The department received an HP grant worth The department received an HP grant worth

$68,000$68,000 HP tablet mobile lab, which is currently being HP tablet mobile lab, which is currently being

usedused

for teaching and research.for teaching and research. Grant Grant from the John Martinson Foundation

for $500K as seed money to develop:Institute for the Enhancement of Teaching

Science and Math (IETSM)

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CareersCareers Medical ImagingMedical Imaging

Doctors today can clean the arteries of a Doctors today can clean the arteries of a patient’s heart, preventing a future heart patient’s heart, preventing a future heart attack. attack.

Modern medical imaging can reveal a detailed Modern medical imaging can reveal a detailed view of clogged problem areas – without any view of clogged problem areas – without any surgery. surgery.

CAT scans, MRIs, and ultrasounds are all the CAT scans, MRIs, and ultrasounds are all the products of computing professionals.products of computing professionals.

Computer scientists devise the algorithms to Computer scientists devise the algorithms to process images from electrical impulses.process images from electrical impulses.

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CareersCareersGamingGaming

Microsoft Xbox 360, Sony Playstation 3, Microsoft Xbox 360, Sony Playstation 3, Nintendo Wii. Nintendo Wii.

Are great gaming machines, but the technology Are great gaming machines, but the technology behind them isn’t a game at all – it’s seriously behind them isn’t a game at all – it’s seriously powerful stuff. powerful stuff.

Games aren’t just for kids anymore. Adults not Games aren’t just for kids anymore. Adults not only play today’s video games, they create only play today’s video games, they create them, too, using cutting edge computing.them, too, using cutting edge computing.

CS experts create the artificial intelligence that CS experts create the artificial intelligence that makes each game challenging, keeping players makes each game challenging, keeping players coming back for more.coming back for more.

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CareersCareersOnline Music and Online Music and Movie DistributionMovie Distribution

The future of music, movies, and all media The future of music, movies, and all media is on the Internet. is on the Internet.

From iTunes to YouTube, commercial From iTunes to YouTube, commercial entertainment is moving to the Web – fast. entertainment is moving to the Web – fast.

You are witnessing a revolution that is You are witnessing a revolution that is powered by technology and computing powered by technology and computing professionals.professionals.

Computer scientists design the huge Computer scientists design the huge databasesdatabases

that store music, TV shows, and movies.that store music, TV shows, and movies.

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CareersCareersFinding Information on the Finding Information on the

WebWeb Search engines such as Google and Yahoo Search engines such as Google and Yahoo

are used by people every day to search for are used by people every day to search for information on the Web.information on the Web.

In the future you should be able to search In the future you should be able to search for objects in pictures? Or sounds? Or for objects in pictures? Or sounds? Or Scenes in movies? Scenes in movies?

Computer scientists devise the Computer scientists devise the revolutionary approaches that makes revolutionary approaches that makes search possible.search possible.

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CareersCareersMobile DevicesMobile Devices

Soon, the idea of using your cell phone only Soon, the idea of using your cell phone only for voice will seem old fashioned.for voice will seem old fashioned.

Cell phones can access the Web, Play games, Cell phones can access the Web, Play games, and and

Even tell you where you are right now. Even tell you where you are right now. Soon you’ll be able to press a key and Soon you’ll be able to press a key and

instantly buy tickets to see your favorite band instantly buy tickets to see your favorite band at a club you’re just walking by, at a club you’re just walking by,

Or pay bus fare just by hopping onto the bus.Or pay bus fare just by hopping onto the bus.Computer scientists create compression Computer scientists create compression algorithms to transmit information more algorithms to transmit information more efficiently.efficiently.

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CareersCareersOur AlumniOur Alumni

Our alumni have gone on to become...Our alumni have gone on to become... Computer ProgrammersComputer Programmers TeachersTeachers Accomplished industrial researchersAccomplished industrial researchers Actuaries Actuaries

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CareersCareersOur AlumniOur Alumni

Employment at:Employment at: Picatinny ArsenalPicatinny Arsenal Genware Computer Genware Computer

SystemsSystems Novartis Novartis

PharmaceuticalsPharmaceuticals Cendant Cendant

CorporationCorporation DialogicDialogic Department of Department of

DefenseDefense

Dell IncDell Inc Hi-tech HealthHi-tech Health The Realm National The Realm National

Insurance CompanyInsurance Company MGM StudiosMGM Studios East Hanover East Hanover

Public School, and Public School, and Washington Washington Township Public Township Public Schools.Schools.

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Computer ScienceComputer Science

Strong theoretical base with a practical Strong theoretical base with a practical approachapproach

Fundamental concepts in core computer Fundamental concepts in core computer science topicsscience topics Data StructuresData Structures Operating SystemsOperating Systems Software Design and EngineeringSoftware Design and Engineering Computer OrganizationComputer Organization

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Computer ScienceComputer Science

Broad Range Of Elective Courses

Computer data security

Computer graphics

Expert systems and logic programming

Computer networks

Numerical analysis

Computer algorithms

Artificial Intelligence

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Options with Computer Options with Computer ScienceScience

Combined MS/BS in Computer ScienceCombined MS/BS in Computer Science Accelerated program, 5 years ( you save a whole Accelerated program, 5 years ( you save a whole

year!)year!) Requires a GPA of 2.8 or higherRequires a GPA of 2.8 or higher Many students from industryMany students from industry

BS in Computer Science- Concentration in BS in Computer Science- Concentration in BioinformaticsBioinformatics

Prepares students for a career in the fast-paced Prepares students for a career in the fast-paced pharmaceutical or biotechnology industriespharmaceutical or biotechnology industries

Combines mathematics, statistics, computer Combines mathematics, statistics, computer science, and biology to explore and understand science, and biology to explore and understand biological databiological data

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Computer ScienceComputer Science

OutlookOutlook Government economists expect jobs for computer scientists to Government economists expect jobs for computer scientists to

grow much faster than the average for all professions through grow much faster than the average for all professions through 2014. 2014.

CompensationCompensation According to the United States Bureau of Labor Statistics, the According to the United States Bureau of Labor Statistics, the

average yearly salary of research computer and information average yearly salary of research computer and information scientists was $96,440 in 2006. scientists was $96,440 in 2006.

According to the National Association of Colleges and Employers, According to the National Association of Colleges and Employers, starting salary offers in 2005 averaged starting salary offers in 2005 averaged $50,820 for graduates with a bachelor’s degree in computer $50,820 for graduates with a bachelor’s degree in computer

science; science; $46,189 for those with a degree in computer systems analysis; $46,189 for those with a degree in computer systems analysis; $44,417 for those with a degree in management information $44,417 for those with a degree in management information

systems; and systems; and $44,775 for those with a degree in information sciences and $44,775 for those with a degree in information sciences and

systems.systems.

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MathematicsMathematics

Interdisciplinary approachInterdisciplinary approach Joint courses with computer scienceJoint courses with computer science Lab science requirementsLab science requirements

A good learning environment for A good learning environment for mathematicsmathematics Small classes, individual attentionSmall classes, individual attention Honors and independent workHonors and independent work Exploration with technology toolsExploration with technology tools

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MathematicsMathematics

Broad range of mathematics in the Broad range of mathematics in the major requirementsmajor requirements Probability and StatisticsProbability and Statistics Discrete StructuresDiscrete Structures Linear AlgebraLinear Algebra Calculus SequenceCalculus Sequence Advanced CalculusAdvanced Calculus

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MathematicsMathematics

Elective courses in advanced Elective courses in advanced mathematicsmathematics Abstract AlgebraAbstract Algebra AnalysisAnalysis CombinatoricsCombinatorics Complex VariablesComplex Variables Differential EquationsDifferential Equations Number TheoryNumber Theory

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MathematicsMathematicsStrong Program in Applied Mathematics

Game Theory

Modeling and Simulation

Partial Differential Equations

Numerical Analysis

Operations Research

Probability and Statistics II

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MathematicsMathematics

Concentrations

Computer

ScienceQuest

(Secondary Education)

Actuarial Science

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Math / QUEST ProgramMath / QUEST Program

Five year secondary education programFive year secondary education program Two degrees: Two degrees:

BA in MathematicsBA in Mathematics MA in EducationMA in Education

Preparation for secondary Preparation for secondary school/mathematics, and for middle-school/mathematics, and for middle-school and elementary certification.school and elementary certification.

The mathematics program emphasizes K-The mathematics program emphasizes K-12 certification.12 certification.

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Math / QUEST ProgramMath / QUEST Program

Field experienceField experience Shadow teaching for a semesterShadow teaching for a semester Placed into the high school by the School Placed into the high school by the School

of Education of Education BA in MathematicsBA in Mathematics MA in educationMA in education

Virtually all students start teaching after Virtually all students start teaching after graduationgraduation..

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Mathematics with Mathematics with Actuarial Science Actuarial Science

ConcentrationConcentrationAn Actuary is a person who:An Actuary is a person who: Analyzes, manages and measures the financial Analyzes, manages and measures the financial

implications of future risk.implications of future risk. Works to maximize profit while managing Works to maximize profit while managing

volatility.volatility. Develops and validates financial models to Develops and validates financial models to

guide decision making.guide decision making.

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Mathematics with Mathematics with Actuarial Science Actuarial Science

ConcentrationConcentration BA in mathematics with a set of elective coursesBA in mathematics with a set of elective courses Courses in the School of Business in economics, Courses in the School of Business in economics,

accounting, and financeaccounting, and finance Help students prepare for the first two actuarial Help students prepare for the first two actuarial

examsexams Administered by the Society of Actuaries and the Administered by the Society of Actuaries and the

Casualty Actuarial SocietyCasualty Actuarial Society Opportunities for independent study with highly Opportunities for independent study with highly

qualified and experienced advisorsqualified and experienced advisors

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Where do Actuaries Where do Actuaries Work?Work?

Consulting firmsConsulting firms Insurance companiesInsurance companies Government insurance Government insurance

departmentsdepartments Banks and investment firmsBanks and investment firms Large corporationsLarge corporations Public accounting firmsPublic accounting firms Colleges and universitiesColleges and universities Anywhere elseAnywhere else

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Typical Actuarial Typical Actuarial ProjectsProjects

Designing and pricing life insurance Designing and pricing life insurance products.products.

Estimating the amount of money to Estimating the amount of money to be set aside for insurance claims.be set aside for insurance claims.

Setting HMO premium rates.Setting HMO premium rates. Pricing the cost of increasing Pricing the cost of increasing

retirement benefits.retirement benefits. Portfolio diversification studies.Portfolio diversification studies.

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Some Student ProjectsSome Student Projects

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Teaching Teaching Mathematics and its Mathematics and its

Applications: An Applications: An Approach for the Approach for the

Middle SchoolMiddle SchoolPresented byPresented byJessica AlfanoJessica Alfano

Mentored by Dr. Robert MayansMentored by Dr. Robert MayansFairleigh Dickinson UniversityFairleigh Dickinson University

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Joe’s GameJoe’s Game

This game can be played using any graph. Player 1 and Player 2 This game can be played using any graph. Player 1 and Player 2 alternate picking vertices in the graph, subject to the alternate picking vertices in the graph, subject to the following rules:following rules:

1.1. Neither player can pick a vertex that has been picked Neither player can pick a vertex that has been picked earlier in the game.earlier in the game.

2.2. Every vertex must be adjacent to the vertex picked just Every vertex must be adjacent to the vertex picked just before.before.

The winner is the last player who can choose a vertex.The winner is the last player who can choose a vertex.

B.1

2

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Player 1 is the

WINNER!

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1 1

Player 2 is the

WINNER!

A.

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The Secret of Joe’s The Secret of Joe’s GameGame

Find a maximum matching in the graph.Find a maximum matching in the graph.

If the maximum matching is perfect, pick to be Player 2.If the maximum matching is perfect, pick to be Player 2.

If the maximum matching is not perfect (if the number of If the maximum matching is not perfect (if the number of vertices are odd), pick to be Player 1.vertices are odd), pick to be Player 1.

Perfect Maximum Matching

Matching

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Fibonacci SequenceFibonacci Sequence

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …144, …

Many plants produce new branches Many plants produce new branches in quantities that are based on in quantities that are based on Fibonacci numbers.Fibonacci numbers.

Plants illustrate the Fibonacci series Plants illustrate the Fibonacci series in the numbers and arrangements of in the numbers and arrangements of petals, leaves, sections and seeds.petals, leaves, sections and seeds.

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Online Content Online Content Management Management

SystemSystem

By Paul GambleBy Paul Gamble

Senior Project, 2005.Senior Project, 2005.

Using Microsoft IIS, SQL Server, Visual Studio, and ASP.NET to create an interactive website

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Internet

Microsoft IIS

Windows Server 2003 Enteprise

Client Client Client

WebServer

Database

.NET Framework

Compiled Web Site

Visual Studio .NET

SQL Query Analyzer

Core runtime libraries

Microsoft .NETASP.NET

DevelopmentPC

MS SQL Server

.ASPX and .DLL files

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Robustness Robustness StudiesStudies For a Multi-Mode Information Embedding For a Multi-Mode Information Embedding

SchemeScheme for Digital Images for Digital Images

Daniel EliadesDaniel EliadesMentor: Dr. Neelu SinhaMentor: Dr. Neelu Sinha

Department of Math and Computer Science, Fairleigh Department of Math and Computer Science, Fairleigh Dickinson UniversityDickinson University

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1024 x 1024 1024 x 1024 Imperceptibility TestImperceptibility Test

Original Image Watermarked Image

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256 x 256 Images

0

5

10

15

20

25

29.23% 38.46% 44.62% 56.92%

Jpeg Compression

To

tal N

um

ber

of

Pac

kets

Clock.tiffSeries2Airplane.tiffSeries4Chemical.tiffSeries6Walter02.tiffSeries8Walter04.tiffSeries10Walter06.tiffSeries12Walter08.tiffSeries14Walter10.tiffSeries16Walter12.tiffSeries18Walter14.tiffSeries20

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Gosper’s Gosper’s AlgorithmAlgorithm

By Zachary VogelBy Zachary Vogel

Presented at the GS Presented at the GS Undergraduate Mathematics Undergraduate Mathematics

Conference, 2004Conference, 2004

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Hypergeometric Terms

• General Form of a hypergeometric term

1 2 1 2

1 2 1 2

, ... ...|

, ... ... !

k k k km m

k k kn nk

a a a a a a zF zb b b b b b k

1,1 1 1 !|

1 !1 !

k k k kk

kk

z k zF z z

kk

1,1 ( 1)|1

1 !

k

k

n k nn kF

kk

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Solution to negation identity

• Now we know our s(k) = -1/n, so we plug in to get T(k):

1( ) ( 1)k

nT k k

kn

1( ) ( 1)knk

T kkn

11( ) ( 1)

1kn

T kk

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Department Activities

• Student Faculty Dinner 2007

• Student Presentations

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Play a Game of ChessPlay a Game of Chess

Chess FilesChess Files

A Cellular Model of a A Cellular Model of a Forest FireForest Fire

Lattice Gas AutomataLattice Gas Automata

Forest Fire FilesForest Fire Files

Lattice Gas FilesLattice Gas Files