getting ready to study mathematics, science and engineering at utep
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Getting Ready To Study Mathematics, Science and Engineering at UTEP. Helmut Knaust Chair, Department of Mathematical Sciences. February 28, 2007 Parkland High School. Overview Introducing Myself Studying STEM Disciplines at UTEP The UTEP Math Department Studying Mathematics - PowerPoint PPT PresentationTRANSCRIPT
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
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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• Transfer student• Got M.S. in
Mathematics
University of Bonn, Germany
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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Undergraduate Students
– Engineering: 2,151 – Science: 1,624– Total: 3,775
– Total at UTEP: 17,060
Source: CIERP, Fall 2006
Department of Mathematical SciencesThe University of Texas at El Paso
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Undergraduate Enrollment Trends In Math, Science and Engineering
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe 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
Department of Mathematical SciencesThe University of Texas at El Paso
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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)
Department of Mathematical SciencesThe University of Texas at El Paso
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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!
Department of Mathematical SciencesThe University of Texas at El Paso
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Department of Mathematical SciencesThe University of Texas at El Paso
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• Departmental Research Concentrations– Algebra and Combinatorics– Analysis and Topology– Applied Mathematics– Mathematics Education– Statistics
Department of Mathematical SciencesThe University of Texas at El Paso
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Mathematics is an ART and a SCIENCE=
Mathematics is BEAUTIFUL and USEFUL
Department of Mathematical SciencesThe University of Texas at El Paso
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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)
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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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)
Department of Mathematical SciencesThe University of Texas at El Paso
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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.
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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Math Accuplacer Placement 2006 (n=3081)
17%
13%
44%
20%
6%
Below Algebra I Algebra I Algebra II Precalculus Calculus
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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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]
Department of Mathematical SciencesThe University of Texas at El Paso
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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.
Department of Mathematical SciencesThe University of Texas at El Paso
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UTEP’s Model for STEM* Student SuccessUTEP’s Model for STEM* Student Success
* STEM = Science, Technology, Engineering and Math
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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Timeline
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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Placement Before and After Math Review 2001-03- STEM Students -
Department of Mathematical SciencesThe University of Texas at El Paso
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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%
Department of Mathematical SciencesThe University of Texas at El Paso
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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%
Department of Mathematical SciencesThe University of Texas at El Paso
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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%
Department of Mathematical SciencesThe University of Texas at El Paso
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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%)
Department of Mathematical SciencesThe University of Texas at El Paso
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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.
Department of Mathematical SciencesThe University of Texas at El Paso
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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)
Department of Mathematical SciencesThe University of Texas at El Paso
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• Factoring I
Factor
x2+5x+6
(x+2)(x+3)
Department of Mathematical SciencesThe University of Texas at El Paso
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• Factoring II
Factor
x2+5x+5
Use the Quadratic Equation(Connection between Factoring and Solving)
Department of Mathematical SciencesThe University of Texas at El Paso
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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)
Department of Mathematical SciencesThe University of Texas at El Paso
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• Factoring IV
How can you tell whether a quadratic polynomial can be factored over the Reals?
Role of the Discriminant
Department of Mathematical SciencesThe University of Texas at El Paso
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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)
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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• Factoring VII
“Multiplicity” of roots
-4 -3 -2 -1 1 2 3
-10
10
20How can you tell from the graph how to factor this 4th degree polynomial?
Department of Mathematical SciencesThe University of Texas at El Paso
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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
Department of Mathematical SciencesThe University of Texas at El Paso
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All Questions Answered,All Answers Questioned
Email:[email protected]
This Presentation: www.math.utep.edu/Faculty/helmut/pedagogy.html