Download Mathematics and Computer Science

Dept. of Mathematics, Computer
Science & Physics
College at Florham
WELCOME
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Strengthening American
Competitiveness for the 21st Century
Microsoft 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 Florham
Becton College of Arts and Sciences
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
Math/CSci/Physics
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Ten highly qualified, full-time faculty members
About 60-70 students each year
Small class size: average less than 15 students
Computer lab courses limited to 20 students
Constantly updating computer equipment and software
Web-enhanced courses
HP tablet Mobile lab (A grant from HP)
Institute for the Enhancement of Teaching Science and Math
(IETSM) $500K Grant from the John Martinson Foundation for
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Internships
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Work experience that leads to job opportunities
Part time work, 10 to 14 weeks
Arranged through the department, or through the Career
Center, through faculty contacts, or by the student
Each student has a faculty mentor.
Evaluated jointly by the mentor and the employer at midsemester and end-of-semester.
Student maintains a work journal.
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Internships
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Some recent internships:
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Alcatel Lucent
Intel
Knowledge Soft
Novartis
Honeywell
Pfizer
US Defense Academy
Several smaller companies
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Independent Study
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Independent research and report
One_on_one experience with a faculty mentor
Senior Honors Project
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Honors presentations
Honors work in any course
Available for either CS majors or math majors
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Faculty Research
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Our Faculty are involved in a wide range of
interesting research projects.
Mathematics hypertext on the Web
 Data Mining
 Artificial Intelligence and Expert Systems
 Digital Rights Management
 Distributed Systems
 Computational Complexity
 Numerical mathematics
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Faculty Grants
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HP grant
The department received an HP grant worth $68,000
 HP tablet mobile lab, which is currently being used
for teaching and research.
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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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Careers
Medical Imaging
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Doctors today can clean the arteries of a patient’s heart,
preventing a future heart attack.
Modern medical imaging can reveal a detailed view of
clogged problem areas – without any surgery.
CAT scans, MRIs, and ultrasounds are all the products
of computing professionals.
Computer scientists devise the algorithms to process
images from electrical impulses.
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Careers
Gaming
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Microsoft Xbox 360, Sony Playstation 3, Nintendo Wii.
Are great gaming machines, but the technology behind
them isn’t a game at all – it’s seriously powerful stuff.
Games aren’t just for kids anymore. Adults not only
play today’s video games, they create them, too, using
cutting edge computing.
CS experts create the artificial intelligence that makes
each game challenging, keeping players coming back for
more.
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Careers
Online Music and
Movie Distribution
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The future of music, movies, and all media is on the
Internet.
From iTunes to YouTube, commercial entertainment is
moving to the Web – fast.
You are witnessing a revolution that is powered by
technology and computing professionals.
Computer scientists design the huge databases
that store music, TV shows, and movies.
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Careers
Finding Information on the Web
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Search engines such as Google and Yahoo are used by
people every day to search for information on the Web.
In the future you should be able to search for objects in
pictures? Or sounds? Or Scenes in movies?
Computer scientists devise the revolutionary
approaches that makes search possible.
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Careers
Mobile Devices
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Soon, the idea of using your cell phone only for
voice will seem old fashioned.
Cell phones can access the Web, Play games, and
Even tell you where you are right now.
Soon you’ll be able to press a key and instantly buy
tickets to see your favorite band at a club you’re just
walking by,
Or pay bus fare just by hopping onto the bus.
Computer scientists create compression algorithms
to transmit information more efficiently.
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Careers
Our Alumni
Our alumni have gone on to become...
 Computer Programmers
 Teachers
 Accomplished industrial researchers
 Actuaries
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Careers
Our Alumni
Employment at:
 Picatinny Arsenal
 Genware Computer
Systems
 Novartis
Pharmaceuticals
 Cendant Corporation
 Dialogic
 Department of Defense
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Dell Inc
Hi-tech Health
The Realm National
Insurance Company
MGM Studios
East Hanover Public
School, and Washington
Township Public
Schools.
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Computer Science
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Strong theoretical base with a practical approach
Fundamental concepts in core computer science topics
 Data Structures
 Operating Systems
 Software Design and Engineering
 Computer Organization
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Computer 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 Science
Combined MS/BS in Computer Science
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Accelerated program, 5 years ( you save a whole year!)
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Requires a GPA of 2.8 or higher
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Many students from industry
BS in Computer Science- Concentration in
Bioinformatics
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Prepares students for a career in the fast-paced
pharmaceutical or biotechnology industries
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Combines mathematics, statistics, computer science, and
biology to explore and understand biological data
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Computer Science
Outlook
 Government economists expect jobs for computer scientists to grow much
faster than the average for all professions through 2014.
Compensation
 According to the United States Bureau of Labor Statistics, the average yearly
salary of research computer and information scientists was $96,440 in 2006.
 According to the National Association of Colleges and Employers, starting
salary offers in 2005 averaged
 $50,820 for graduates with a bachelor’s degree in computer science;
 $46,189 for those with a degree in computer systems analysis;
 $44,417 for those with a degree in management information systems; and
 $44,775 for those with a degree in information sciences and systems.
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Mathematics
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Interdisciplinary approach
Joint courses with computer science
 Lab science requirements
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A good learning environment for mathematics
Small classes, individual attention
 Honors and independent work
 Exploration with technology tools
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Mathematics
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Broad range of mathematics in the major
requirements
Probability and Statistics
 Discrete Structures
 Linear Algebra
 Calculus Sequence
 Advanced Calculus
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Mathematics
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Elective courses in advanced mathematics
Abstract Algebra
 Analysis
 Combinatorics
 Complex Variables
 Differential Equations
 Number Theory
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Mathematics
Strong Program in Applied Mathematics
Game Theory
Modeling and Simulation
Partial Differential Equations
Numerical Analysis
Operations Research
Probability and Statistics II
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Mathematics
Concentrations
Computer
Science
Quest
(Secondary Education)
Actuarial Science
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Math / QUEST Program
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Five year secondary education program
Two degrees:
 BA in Mathematics
 MA in Education
Preparation for secondary school/mathematics, and for
middle-school and elementary certification.
The mathematics program emphasizes K-12
certification.
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Math / QUEST Program
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Field experience
Shadow teaching for a semester
Placed into the high school by the School of Education
 BA in Mathematics
 MA in education
Virtually all students start teaching after graduation.
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Mathematics with Actuarial
Science Concentration
An Actuary is a person who:
 Analyzes, manages and measures the financial
implications of future risk.
 Works to maximize profit while managing volatility.
 Develops and validates financial models to guide
decision making.
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Mathematics with Actuarial
Science Concentration
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BA in mathematics with a set of elective courses
Courses in the School of Business in economics, accounting,
and finance
Help students prepare for the first two actuarial exams
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Administered by the Society of Actuaries and the Casualty
Actuarial Society
Opportunities for independent study with highly qualified
and experienced advisors
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Where do Actuaries Work?
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Consulting firms
Insurance companies
Government insurance departments
Banks and investment firms
Large corporations
Public accounting firms
Colleges and universities
Anywhere else
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Typical Actuarial Projects
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Designing and pricing life insurance products.
Estimating the amount of money to be set aside
for insurance claims.
Setting HMO premium rates.
Pricing the cost of increasing retirement
benefits.
Portfolio diversification studies.
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Some Student Projects
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Teaching Mathematics
and its Applications:
An Approach for the
Middle School
Presented by
Jessica Alfano
Mentored by Dr. Robert Mayans
Fairleigh Dickinson University
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Joe’s Game
This game can be played using any graph. Player 1 and
Player 2 alternate picking vertices in the graph, subject
to the following rules:
1.
2.
Neither player can pick a vertex that has been picked
earlier in the game.
Every vertex must be adjacent to the vertex picked just
before.
The winner is the last player who can choose a vertex.
A.
1
B.
Player 1
is the
WINNER!
1
2
1
2
2
1
1
Player 2
is the
WINNER!
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The Secret of Joe’s
Game
Find a maximum matching in the graph.
If the maximum matching is perfect, pick to be Player 2.
Perfect
Maximum
Matching
Matching
If the maximum matching is not perfect (if the number of vertices
are odd), pick to be Player 1.
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Fibonacci Sequence
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1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,
144, …
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Many plants produce new branches in
quantities that are based on
Fibonacci numbers.
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Plants illustrate the Fibonacci series
in the numbers and arrangements of
petals, leaves, sections and seeds.
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Online Content
Management System
Using Microsoft IIS, SQL Server, Visual Studio, and
ASP.NET to create an interactive website
By Paul Gamble
Senior Project, 2005.
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Client
Client
Client
Internet
Microsoft
IIS
Windows Server
2003 Enteprise
Web
Server
.NET
Framework
Visual Studio
.NET
SQL Query Analyzer
Development
PC
Core runtime
libraries
Microsoft .NET
ASP.NET
Compiled Web
Site
.ASPX
and .DLL
files
MS
SQL
Server
Databas
e
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Robustness Studies
For a Multi-Mode Information Embedding Scheme
for Digital Images
Daniel Eliades
Mentor: Dr. Neelu Sinha
Department of Math and Computer Science, Fairleigh Dickinson University
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1024 x 1024 Imperceptibility Test
Original Image
Watermarked Image
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256 x 256 Images
Total Number of Packets
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Clock.tiff
Series2
Airplane.tiff
Series4
Chemical.tiff
Series6
Walter02.tiff
Series8
Walter04.tiff
Series10
Walter06.tiff
Series12
Walter08.tiff
Series14
Walter10.tiff
Series16
Walter12.tiff
Series18
Walter14.tiff
Series20
20
15
10
5
0
29.23%
38.46%
44.62%
56.92%
Jpeg Compression
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Gosper’s Algorithm
By Zachary Vogel
Presented at the GS Undergraduate
Mathematics Conference, 2004
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Hypergeometric Terms
• General Form of a hypergeometric term
k
 a1 , a2 ...am

a1k a2k ...am
zk
F
| z 
k
k
k
b
,
b
...
b
b
b
...
b
n
 1 2
k
1
2
n k!
1,1

1k1k z k
k !zk
k
F
| z 


z
k
1
k!
1
k!

k
 n  k  1,1 
 n
(n  k  1) k
F
| 1 
 
1
k!

k
k 
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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  n
k
T (k )  k        (1)
 n  k 
 k  n
T (k )       (1) k 1
 n  k 
 n  1
k 1
T (k )  
 (1)
 k  1
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Department Activities
• Student Faculty Dinner 2007
• Student Presentations
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Play a Game of Chess
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Chess Files
A Cellular Model of a Forest Fire
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Forest Fire Files
Lattice Gas Automata
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Lattice Gas Files
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