Helmut Knaust, Chair

Department of Mathematical Sciences

July 12 and 13, 20051/14

Helmut Knaust, Chair

Studying Mathematics

At UTEP


July 12 and 13, 20052/14

1. Our Department and its Students2. What is Mathematics?3. Mathematics as a Career

Overview


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24 Tenure/tenure track faculty16 Lecturers

The department is offering about 150 courses per semester*

* not including developmental mathematics

Faculty and Course Offerings


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126 Undergraduate Majors BS in MathematicsBS in Applied MathematicsBA in Mathematics (College of Liberal Arts)

63 Graduate StudentsMS in MathematicsMS in StatisticsMAT in MathematicsMS in Bioinformatics (interdisciplinary)

Planned: Ph.D. in Computational Science (interdisciplinary)

Our Students


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Mathematical Subject Areas


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How to Pack Oranges as Tightly as Possible….

• Kepler Conjecture – Johannes Kepler conjectured in 1611 that the

“hexagonal packing” (see picture) is the best possible

– This packing fills slightly more than 74% of space– Finally Proved by Thomas Hales in 2002

• Making extensive use of computer calculations – Applications of sphere packing to “packing”

telephone calls on glass fiber cables

“The packing will be the tightest possible, so that in no other arrangement could more pellets be stuffed into the same container.”

Johannes Kepler (1571-1630)


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• In 1807, Fourier invented Fourier series to solve the Steady-State Heat Equation, one of the most important equations in Physics.

• Starting in 1965, Cooley, Tuckey and others used a Fast Fourier Transform – based on Fourier’s results – to solve partial differential equations numerically.

• Today the Fast Fourier Transform is the major ingredient for the compression algorithms used in JPEG (images), MP3 (sound) and MPEG (video) files.

Compression Algorithms

“Heat, like gravity, penetrates every substance of the universe, its rays occupy all parts of space. The object of our work is to set forth the mathematical laws which this element obeys. The theory of heat will hereafter form one of the most important branches of general physics.”

Joseph Fourier (1769-1830)


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• Science and Engineering

• Economics and Business

• Philosophy (Logic), Cognitive Science and Psychology

• Pedagogy

Mathematics is by its nature interdisciplinary…


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• Computational Science• Mathematical Biology• Bioinformatics• Biostatistics• Modeling of Environmental Systems• Modeling of Geophysics Systems• Mathematics Education

“Hot” Areas for Mathematics Applications


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Quiz Question: Who is our Math Department’s

most famous Alumnus?

Larry DurhamBachelor’s in

Mathematics 1966


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• Broad range of positions in – Business,– Industry, – Government, – and Education

• Employers include– Federal, state and local government,– Companies in the computer and

communications industries,– Oil and energy companies, – Banks and insurance companies, – Consulting firms

Mathematics as a Career

“Most working mathematicians use mathematics on a daily basis, but many others are hired because of the general problem-solving skills acquired in their mathematics courses.”


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• Federal Agencies hiring Mathematicians include: – National Security Agency – Dept. of Health and Human Services– Dept. of Energy– Dept. of Defense– Dept. of Labor

• A Mathematics major is also an excellent preparation for graduate studies in:– Economics– Law School

Mathematics as a Career II


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Becoming a Mathematics Teachers

• Middle School (Grades 4-8)• BSIS in the College of Education

• Math specialist• Math/Science specialist

• High School (Grades 8-12)• BS in the College of Science

• Mathematics concentration• Mathematics/Physics concentration

• College and University • Minimal requirement is a Master’s degree

in the Mathematical Sciences


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• Careers in Mathematics– American Mathematical Society

• www.ams.org/careers-du/undergrad.html– Mathematical Association of America

• www.maa.org/careers/index.html– American Statistical Society

• www.amstat.org/careers/index.html– Society of Actuaries and Casual Actuarial

Society• www.BeAnActuary.org

– “101 Careers in Mathematics”, Andrew Sterrett (ed.), 2nd ed. 2003, Mathematical Association of America.

Resources Best Jobs*:#2 Actuary#8 Statistician

*CareerJournal.com (Wall Street Journal)http://www.careerjournal.com/salaryhiring/hotissues/20050614-intro1.html

http://www.ams.org/careers-du/undergrad.html

http://www.maa.org/careers/index.html

http://www.amstat.org/careers/index.html

http://www.beanactuary.org/

Documents

Helmut Knaust, Chair