1. Department of Mathematical Sciences The University of Texas at El Paso 1 Getting Ready To Study Mathematics, Science and Engineering at UTEP Helmut Knaust Chair, Department of Mathematical Sciences February 28, 2007 Parkland High School

2. Department of Mathematical Sciences The University of Texas at El Paso 2 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

3. Department of Mathematical Sciences The University of Texas at El Paso 3 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

4. Department of Mathematical Sciences The University of Texas at El Paso 4 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

5. Department of Mathematical Sciences The University of Texas at El Paso 5 Transfer student Got M.S. in Mathematics University of Bonn, Germany

6. Department of Mathematical Sciences The University of Texas at El Paso 6 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

7. Department of Mathematical Sciences The University of Texas at El Paso 7 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

8. Department of Mathematical Sciences The University of Texas at El Paso 8 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

9. Department of Mathematical Sciences The University of Texas at El Paso 9 Undergraduate Students –Engineering: 2,151 –Science: 1,624 –Total: 3,775 –Total at UTEP:17,060 Source: CIERP, Fall 2006

10. Department of Mathematical Sciences The University of Texas at El Paso 10 Undergraduate Enrollment Trends In Math, Science and Engineering

11. Department of Mathematical Sciences The University of Texas at El Paso 11 Enrollment Trends at UTEP

12. Department of Mathematical Sciences The University of Texas at El Paso 12 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

13. Department of Mathematical Sciences The University of Texas at El Paso 13 UTEP’s Math Department –27 Tenure/tenure track faculty –14 Lecturers The department is offering about 160 courses per semester* * not including developmental mathematics

14. Department of Mathematical Sciences The University of Texas at El Paso 14 140 Undergraduate Majors BS in Mathematics BS in Applied Mathematics BA in Mathematics (College of Liberal Arts) 65 Graduate Students MS in Mathematics MS in Statistics MAT in Mathematics MS in Bioinformatics (interdisciplinary) Starting Fall 2008: Ph.D. in Computational Science (interdisciplinary)

15. Department of Mathematical Sciences The University of Texas at El Paso 15 “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!

16. Department of Mathematical Sciences The University of Texas at El Paso 16

17. Department of Mathematical Sciences The University of Texas at El Paso 17 Departmental Research Concentrations –Algebra and Combinatorics –Analysis and Topology –Applied Mathematics –Mathematics Education –Statistics

18. Department of Mathematical Sciences The University of Texas at El Paso 18 Mathematics is an ART and a SCIENCE = Mathematics is BEAUTIFUL and USEFUL

19. Department of Mathematical Sciences The University of Texas at El Paso 19 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)

20. Department of Mathematical Sciences The University of Texas at El Paso 20 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

21. Department of Mathematical Sciences The University of Texas at El Paso 21 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)

22. Department of Mathematical Sciences The University of Texas at El Paso 22 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 2 nd ed 2006. 2. G. Orsak, S. Wood, et al. The Infinity Project, Pearson 2004.

23. Department of Mathematical Sciences The University of Texas at El Paso 23 “Hot Areas” for Applying Mathematics Computational Science Mathematical Biology Bioinformatics Biostatistics Modeling of Environmental Systems Modeling of Geophysics Systems Mathematics Education

24. Department of Mathematical Sciences The University of Texas at El Paso 24 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

25. Department of Mathematical Sciences The University of Texas at El Paso 25 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

26. Department of Mathematical Sciences The University of Texas at El Paso 26 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 Durham Bachelor’s in Mathematics 1966

27. Department of Mathematical Sciences The University of Texas at El Paso 27 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

28. Department of Mathematical Sciences The University of Texas at El Paso 28

29. Department of Mathematical Sciences The University of Texas at El Paso 29

30. Department of Mathematical Sciences The University of Texas at El Paso 30 Math 0310Algebra I Math 0311Algebra II Math 1319Math in the Modern World (Liberal Arts majors) Math 1320Math for Social Sciences (Business majors) Math 1508Pre-Calculus (All STEM majors) Math 1411Calculus I [Prerequisite: Math 1508]

31. Department of Mathematical Sciences The University of Texas at El Paso 31 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, 2 nd ed. 2005.

32. Department of Mathematical Sciences The University of Texas at El Paso 32 UTEP’s Model for STEM* Student Success * STEM = Science, Technology, Engineering and Math

33. Department of Mathematical Sciences The University of Texas at El Paso 33 Circles of Learning for Entering Students UTEP’s entering student program for STEM students CircLES provides: summer orientation placement exams peer mentoring expert advising course clustering

34. Department of Mathematical Sciences The University of Texas at El Paso 34 Timeline

35. Department of Mathematical Sciences The University of Texas at El Paso 35 CONNECTIONS TO UNIVERSITY SERVICES STUDY SKILLS DEVELOPMENTAL MATH REVIEW AND PLACEMENT RESEARCH MODULES (Science and Engineering) CircLES - One Week-Long Orientation

36. Department of Mathematical Sciences The University of Texas at El Paso 36 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

37. Department of Mathematical Sciences The University of Texas at El Paso 37 Placement Before and After Math Review 2001-03 - STEM Students -

38. Department of Mathematical Sciences The University of Texas at El Paso 38 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%

39. Department of Mathematical Sciences The University of Texas at El Paso 39 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%

40. Department of Mathematical Sciences The University of Texas at El Paso 40 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%

41. Department of Mathematical Sciences The University of Texas at El Paso 41 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%)

42. Department of Mathematical Sciences The University of Texas at El Paso 42 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.

43. Department of Mathematical Sciences The University of Texas at El Paso 43 “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)

44. Department of Mathematical Sciences The University of Texas at El Paso 44 Factoring I Factor x 2 +5x+6 (x+2)(x+3)

45. Department of Mathematical Sciences The University of Texas at El Paso 45 Factoring II Factor x 2 +5x+5 Use the Quadratic Equation (Connection between Factoring and Solving)

46. Department of Mathematical Sciences The University of Texas at El Paso 46 Factoring III Factor x 2 +2x+3 Cannot be factored over the Reals (Difference between factoring over the Real and the Complex Numbers)

47. Department of Mathematical Sciences The University of Texas at El Paso 47 Factoring IV How can you tell whether a quadratic polynomial can be factored over the Reals? Role of the Discriminant

48. Department of Mathematical Sciences The University of Texas at El Paso 48 Factoring V Does x 3 +5x 2 +13x+9 have a linear factor? Which polynomials can be factored? (Three Strategies: Fundamental Theorem of Algebra; odd degree; rational zeros)

49. Department of Mathematical Sciences The University of Texas at El Paso 49 How can you tell from the graph how to factor this 4 th degree polynomial? Factoring VI No formula, “Seeing” the roots, Connection between Roots and Factoring

50. Department of Mathematical Sciences The University of Texas at El Paso 50 Factoring VII “Multiplicity” of roots How can you tell from the graph how to factor this 4 th degree polynomial?

51. Department of Mathematical Sciences The University of Texas at El Paso 51 Factoring VIII For which values of b does x 4 +2bx 2 -4 =0 have no (or 2, or 4) complex roots? Conceptual and computational mastery

52. Department of Mathematical Sciences The University of Texas at El Paso 52 All Questions Answered, All Answers Questioned Email: hknaust@utep.edu This Presentation: www.math.utep.edu/Faculty/helmut/pedagogy.html