department of mathematical sciences the university of texas at el paso 1 getting ready to study...

Department of Mathematical SciencesThe University of Texas at El Paso

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Getting Ready To Study Mathematics, Science

and Engineering at UTEP

Helmut KnaustChair, Department of Mathematical Sciences

February 28, 2007Parkland High School


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• Overview– Introducing Myself– Studying STEM Disciplines at UTEP– The UTEP Math Department– Studying Mathematics– Math Placement: Accuplacer– Entering Students Program for STEM Majors:

CircLES– ACT Research on College Readiness– An Example: Factoring Polynomials


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• Why did I study Math?

– Encouragement from • My Dad• My Mathematics High School Teacher

– I was good at Math

– Promise of a secure job as a Math Teacher


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• First one in my family to attend a university

• Started out as a commuter student at the local university

• Goal: Become a HS Math Teacher

University of Bielefeld, Germany


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• Transfer student• Got M.S. in

Mathematics

University of Bonn, Germany


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• Ph.D. from UT Austin in 1989

• At UTEP since 1991• 2001-2003 Director of the Entering Students Program in Science and Engineering• Department Chair since 2003


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UTEP Undergraduate Science & Engineering Programs

• SCIENCE– Biology– Chemistry– Environmental Science– Geology– Geophysics– Mathematics– Microbiology– Physics– Psychology

• ENGINEERING– Civil Engineering– Computer Science– Electrical and Computer

Engineering– Industrial Engineering– Materials and

Metallurgical Engineering

– Mechanical Engineering


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Math Requirements – Three examples

Physics (22 hours)

• Calculus I• Calculus II• Calculus III• Differential

Equations• Applied

Analysis I• 2 more upper

division math courses

Electrical Engineering (19 hours)

• Calculus I• Calculus II• Calculus III• Differential

Equations• Matrix Algebra• Probability and

Statistics (EE)

Biology (11 hours)

• Calculus I• Statistical Methods I• Statistical Methods II


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Undergraduate Students

– Engineering: 2,151 – Science: 1,624– Total: 3,775

– Total at UTEP: 17,060

Source: CIERP, Fall 2006


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Undergraduate Enrollment Trends In Math, Science and Engineering


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14,695

15,224

16,220

17,232

18,54218,918

19,268

19,842

12,000

14,000

16,000

18,000

20,000

22,000

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

Year

Stu

den

ts

Enrollment Trends at UTEP


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UTEP Student Population Profile

• 24 years of age (undergraduate average)• 69% Hispanic• 55% female• 81% from El Paso County and commute

daily• 84% employed• 50% first generation university students

• 2001-2002 Facts, The University of Texas at El Paso


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• UTEP’s Math Department

– 27 Tenure/tenure track faculty

– 14 Lecturers

• The department is offering about 160 courses per semester*

*not including developmental mathematics


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

• 65 Graduate StudentsMS in MathematicsMS in StatisticsMAT in MathematicsMS in Bioinformatics (interdisciplinary)

• Starting Fall 2008: Ph.D. in Computational Science (interdisciplinary)


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• “MAT Cohort” Program– MAT = Master of Arts in Teaching Mathematics– Geared towards high school and middle school

teachers– 36 credit hours of math content and math

pedagogy courses– Courses conveniently scheduled two evenings

per week; takes two years (and two summers)– Cohort V will start this summer!


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• Departmental Research Concentrations– Algebra and Combinatorics– Analysis and Topology– Applied Mathematics– Mathematics Education– Statistics


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Mathematics is an ART and a SCIENCE=

Mathematics is BEAUTIFUL and USEFUL


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• Kepler Conjecture, or How to Pack Oranges as Tightly as Possible– Johannes Kepler conjectured in 1611

that the “hexagonal packing” (see picture on next slide) is the best possible

“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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• This packing fills slightly more than 74% of space

Resource: George G. Szpiro. Kepler’s Conjecture, J. Wiley 2003.

• 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


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• Fourier Series– In 1807, Fourier invented

Fourier Series to solve the Steady-State Heat Equation, one of the most important equations in Physics.

“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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• 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), MP3/4 (sound) and MPEG (video) files.

Resources: 1. D. Bressoud. A Radical Approach to Real Analysis, MAA 2nd ed 2006.2. G. Orsak, S. Wood, et al. The Infinity Project, Pearson 2004.


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• “Hot Areas” for Applying Mathematics

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


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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


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• Mathematics as a Career– 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


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• Resource for Math Careers:– Andrew Sterrett (ed.).“101

Careers in Mathematics”, Mathematical Association of America, 2nd ed. 2003.

Quiz:Who Is UTEP’s Most

Famous Math Alumnus?

Larry DurhamBachelor’s in Mathematics 1966


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Students and Teachers in El Paso: A “Closed Loop”

UTEP

Local School Districts

Close to 90% of all students

come from El Paso County

65% of all math teachers in El Paso

County get their college education

at UTEP


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Math Accuplacer Placement 2006 (n=3081)

17%

13%

44%

20%

6%

Below Algebra I Algebra I Algebra II Precalculus Calculus


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Math Placement via Accuplacer 2006 (n=3081)

6%12%

13%

25%

18%

20%

6%

EPCC 0300 EPCC 0301 MATH 0310

MATH 0311 or 1319 MATH 0311 or 1319 or 1320+0120 MATH 1319 or 1320 or 1508

MATH 1411 or 2301


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Math 0310 Algebra I

Math 0311 Algebra II

Math 1319 Math in the Modern World (Liberal Arts majors)

Math 1320 Math for Social Sciences (Business majors)

Math 1508 Pre-Calculus (All STEM majors)

Math 1411 Calculus I [Prerequisite: Math 1508]


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• Math 1319 - Mathematics in the Modern World

An introduction to some of the great ideas of mathematics, including current applications of logic, algebra, geometry, statistics, and other topics.

Edward B. Burger and Michael Starbird: “The Heart of Mathematics: An Introduction to Effective Thinking”, Key College Publishing, 2nd ed. 2005.


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UTEP’s Model for STEM* Student SuccessUTEP’s Model for STEM* Student Success

* STEM = Science, Technology, Engineering and Math


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Circles of Learning for Entering Students

UTEP’s entering student program for STEM students

CircLES provides: summer orientationplacement examspeer mentoringexpert advisingcourse clustering


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Timeline


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CONNECTIONS TO UNIVERSITY SERVICES

STUDY SKILLS

DEVELOPMENTAL MATH REVIEW AND PLACEMENT

RESEARCH MODULES (Science and Engineering)

CircLES - One Week-Long Orientation


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Mathematics Review

• Duration: 3 days, 2 hours each day• Students solve math problems in small groups of 4 or 5

students• Math review is led by peer facilitators• The accompanying text focuses on short explanations

and practice problems• After the math review is complete, students retake

UTEP’s math placement exam


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Placement Before and After Math Review 2001-03- STEM Students -


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• ACT and College Readiness in Math

– Based on 1.2 million high school graduates who took the ACT

– College ready:• All students 42%• Females 37%, Males 47%• Whites 48%, Hispanics 25%, African

Americans 11%


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• College Readiness in Math by Course Taken– Algebra I, Geometry, Algebra II 14%– Algebra I, Geometry, Algebra II,

Advanced Math 37%– Algebra I, Geometry, Algebra II,

Trigonometry, Advanced Math 56%– Algebra I, Geometry, Algebra II,

Trigonometry, Calculus 74%


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• College Readiness in Math by Grades in Last Course Taken– Grades A,B

• College ready 43%• NOT College ready 57%

– Grades C,D,F• College ready 18%• NOT College ready 82%


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• College Readiness and Student Success– Students who are college ready in Math

are more likely to• Enroll in college (77% vs. 60%)• Earn grades of B or better in their first

college level math course (53% vs. 31%)• Earn college GPAs of 3.0 or higher (61% vs.

35%)• Return for their second year (81% vs. 67%)


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• What Matters?– High-level course content– Well-qualified teachers– Flexible pedagogical styles– Tutorial support

• What Can Be Done?– Alignment between schools and colleges

at the state and local level– End-of-course exams

Source: C. Schmeiser, State of College Readiness in Mathematics.


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“The greatest danger for most of us is not that our aim is too high and we miss it, but that it is too low and we reach it.”

Michelangelo (1475-1564)


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• Factoring I

Factor

x2+5x+6

(x+2)(x+3)


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• Factoring II

Factor

x2+5x+5

Use the Quadratic Equation(Connection between Factoring and Solving)


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• Factoring III

Factor

x2+2x+3

Cannot be factored over the Reals(Difference between factoring over the Real

and the Complex Numbers)


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• Factoring IV

How can you tell whether a quadratic polynomial can be factored over the Reals?

Role of the Discriminant


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• Factoring V

Does

x3+5x2+13x+9

have a linear factor?

Which polynomials can be factored?(Three Strategies: Fundamental Theorem of Algebra;

odd degree; rational zeros)


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-3 -2 -1 1 2 3

-5

5

10How can you tell from the graph how to factor this 4th degree polynomial?

• Factoring VI

No formula, “Seeing” the roots, Connection between Roots and Factoring


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• Factoring VII

“Multiplicity” of roots

-4 -3 -2 -1 1 2 3

-10

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20How can you tell from the graph how to factor this 4th degree polynomial?


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• Factoring VIII

For which values of b does

x4+2bx2-4 =0

have no (or 2, or 4) complex roots?

Conceptual and computational mastery


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All Questions Answered,All Answers Questioned

Email:[email protected]

This Presentation: www.math.utep.edu/Faculty/helmut/pedagogy.html

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