Getting Ready To Study Mathematics, Science and Engineering at UTEP

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. 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. 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. 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. Transfer student • Got M.S. in Mathematics University of Bonn, Germany

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. SCIENCE Biology Chemistry Environmental Science Geology Geophysics Mathematics Microbiology Physics Psychology UTEP Undergraduate Science & Engineering Programs • ENGINEERING • Civil Engineering • Computer Science • Electrical and Computer Engineering • Industrial Engineering • Materials and Metallurgical Engineering • Mechanical Engineering

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. Undergraduate Students • Engineering: 2,151 • Science: 1,624 • Total: 3,775 • Total at UTEP: 17,060 Source: CIERP, Fall 2006

10. Undergraduate Enrollment Trends In Math, Science and Engineering

11. Enrollment Trends at UTEP

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. 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. 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. “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!

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

18. Mathematics is an ART and a SCIENCE = Mathematics is BEAUTIFUL and USEFUL

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

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. 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.

23. “Hot Areas” for Applying Mathematics • Computational Science • Mathematical Biology • Bioinformatics • Biostatistics • Modeling of Environmental Systems • Modeling of Geophysics Systems • Mathematics Education

24. Mathematics as a Career • 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

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. 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. Students and Teachers in El Paso: A “Closed Loop” UTEP Local School Districts 65% of all math teachers in El Paso County get their college education at UTEP Close to 90% of all students come from El Paso County

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, 2nd ed. 2005.

32. UTEP’s Model for STEM* Student Success * STEM = Science, Technology, Engineering and Math

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. Timeline

35. CircLES - One Week-Long Orientation CONNECTIONS TO UNIVERSITY SERVICES DEVELOPMENTAL MATH REVIEW AND PLACEMENT RESEARCH MODULES (Science and Engineering) STUDY SKILLS

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

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. 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. 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. 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. 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. “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. Factoring I Factor x2+5x+6 (x+2)(x+3)

45. Factoring II Factor x2+5x+5 Use the Quadratic Equation (Connection between Factoring and Solving)

46. Factoring III Factor x2+2x+3 Cannot be factored over the Reals (Difference between factoring over the Real and the Complex Numbers)

47. Factoring IV How can you tell whether a quadratic polynomial can be factored over the Reals? Role of the Discriminant

48. 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)

49. Factoring VI How can you tell from the graph how to factor this 4th degree polynomial? No formula, “Seeing” the roots, Connection between Roots and Factoring

50. Factoring VII How can you tell from the graph how to factor this 4th degree polynomial? “Multiplicity” of roots