Experience Teaching Industrial Mathematics at a Liberal Arts College

My PIC Math Experience Teaching An Industrial Mathematics Course At A Small Liberal Arts College Ron Buckmire Occidental College ron@oxy.edu 2016 Joint Mathematics Meetings Seattle, WA

Outline Goals of this Talk Overview of PIC Math Program My PIC Math Experience Institutional Context Lessons Learned Questions 2

Goals of this Talk Provide an example of one person s experience teaching an industrial mathematics course Present details of the PIC Math program 3

PIC Math (Preparation for Industrial Careers in Math) Supported by NSF (DMS-1345499), SIAM & MAA Directors (Dorff, Weekes, Braddy & Malek-Madani) Multiple Components Summer Faculty Workshops (@BYU) Spring Semester Industrial Math course (S16,S17) Student Competition (by 12-minute Video) Student Recognition Conference (SIAM AN16) 4

PIC Math (Preparation for Industrial Careers in Math) PIC Math program provides (A few) BIG Math problems with Industrial Liaisons for PIC Math faculty and their students to access Stipend to the faculty member Online resources for Spring PIC Math course Network of new and experienced PIC Math faculty Funds to support travel (faculty to summer workshop; student to attend math conference) 5

My PIC Math Experience Institutional Context Occidental College Small (2150 students), Private, Highly-Selective, Liberal Arts College in Los Angeles ~12 graduating Mathematics majors per year No specific Advanced Math courses required for graduation No Computer Science or Statistics degree offered Other Applied Math Courses: ODEs, PDEs, Probability, Numerical Analysis, Complex Analysis, Operations Research, Mathematical Statistics, Math Models in Bio 6

My PIC Math Experience Institutional Context Details of the class Math 396 : Mathematical Modeling (Industrial Mathematics) o 2-units (Tuesdays 1:30-2:55pm for 14 weeks) o Limited class size (No more than 12) o Pre-requisites: (multivariable calculus AND linear algebra) OR permission of instructor 300-level math class (suitable for math majors or minors) Advertised during Differential Equations class in Fall 2014 ( clinical capstone experience & hands-on seminar ) 7

My PIC Math Experience Institutional Context Details of the class: course goals provide students with the experience of using mathematics to solve an actual real world problem of their choice by o developing, testing and implementing a mathematical model of their own devising o performing calculations and evaluating their results for accuracy and appropriateness assist in the preparation of students for a potential career in industrial or applied mathematics by o exposure to non-academic stakeholders in business, industry or government; o developing collaboration skills by working in small teams towards a common goal o improving communication skills (especially of mathematical/technical content) 8

My PIC Math Experience Institutional Context Actual class composition 10 students (three teams: 4, 3 and 3) o 7 male, 3 female o Majors: 7 Math, 1 Cognitive Science, 2 physics, 1 Biochemistry, 1 French(!) 2 double majors (math/physics and math/french) o 7 seniors, 2 juniors, 1 advanced sophomore o 2 Latino, 1 Asian, 1 International, 2 first-generation 9

My PIC Math Experience Institutional Context Finding Industrial Math Problems Five B.I.G. Industrial Math problems from PIC Math Contacted (by phone and by e-mail with attached PDF letters) six companies (found from list of recent internships) Initiated conversations with four (Kaiser Permanente, Southern California Edison, Occidental College Facilities Department and Payden & Riegel) Resulted in one local problem (another fell in my lap!) 10

My PIC Math Experience Institutional Context 2015 Local Problem 1 Industrial Liaison: Michelle Hill, Assistant Director of Energy Services, Facilities Management, Occidental College The original question What is the total amount of carbon sequestered by all the trees on the campus of Occidental College, what is its monetary value as a carbon offset and how do these quantities change with time? 11

My PIC Math Experience Institutional Specifics 2015 Local Problem 1 Expected Deliverable: Occidental College would like to know the annual amount of carbon sequestered by the trees located on its campus. Additionally, calculating the monetary value of this carbon for offset purposes and how it compares to the value of the trees themselves and how these quantities vary relative to each other with time. 12

My PIC Math Experience Institutional Specifics 2015 Local Problem 2 Industrial Liaison: Jason Heidecker, Founder, (redacted).com The original question Can one create a scoring system that can be used to predict how people will perform in an athletic competition given a large data set of individual performance metrics for various athletic events? 13

My PIC Math Experience Institutional Context 2015 Local Problem 2 Expected deliverable The client would like a 100x100 table of BScores where B(i,j) represents the location in the ith row and jth column of the table of the probability that a competitor with BScore i will be ranked higher in the national athletic competition (NAC) than a competitor with BScore j with the condition that B(i,j)+B(j,i)=1. 14

My PIC Math Experience Lessons Learned No group size larger than three o Group with four had widest variation in assessment of individual participation & increased logistical difficulties o Groups with three people seemed more well-balanced Discuss video presentation and written paper early in semester o The logistics of taping student presentations can be daunting (especially if you have not done this before) 15

My PIC Math Experience Lessons Learned Have fewer one-on-team oral progress reports There were written progress reports due at the beginning of class every other week but these became repetitive towards the end of the semester: (suggestion) each member of the group should have specific responsibility for (atleast) one written and one oral progress report 16

My PIC Math Experience Lessons Learned Have fewer classes end with no explicit progress goals for next time At the end of every class, each group should have to put in writing what they want have accomplished by the next class, with each student member committing to what they want to get done (this can be maintained in the cloud) 17

My PIC Math Experience Lessons Learned Be more explicit and intentional about assessing individual student contributions Require draft of final paper before end of semester Provide an example/model of a well-done solution Have teams pick name and set up online file drive immediately to facilitate collaboration and accountability Have firm date by which problem selection is final Have some kind of individual student journal/log 18

Questions? Ron Buckmire Occidental College ron@oxy.edu http://sites.oxy.edu/ron/math/396/16 OR http://bit.ly/oxypicmath 20