College of Engineering and Science Louisiana Tech University College of Engineering and Science Connecting Mathematics with Engineering and the Sciences (Chautauqua workshop) Bernd S. W. Schröder Program of Mathematics and Statistics

Why connect mathematics with engineering and the sciences? §Who are you? §Why are you here? §(Find people with similar interests.) College of Engineering and Science

It’s the Right Thing to Do §Long standing need for people (including mathematicians/math majors) who can apply mathematics in context. §George report §Carnegie Initiative papers §CUPM recommendations §Cognitive research (BSVR) §It’s also a lot of fun. College of Engineering and Science

Most importantly, it’s why we do mathematics. College of Engineering and Science

Most importantly, it’s why we do mathematics. §(and back) §but do we start with full generality? College of Engineering and Science

Best resource: Your own interests and ideas, if they fit. §The density altitude of air gives the altitude at which dry air (0% humidity) at a temperature of 59F and a standard pressure of 29.92inch-Hg (the International Standard Atmosphere) has the same oxygen content as the air being evaluated. A one degree increase in temperature increases the density altitude of air by 100ft. A 10% change in humidity increases the density altitude of air by 100ft. A 0.01inch-Hg drop in pressure increases the density altitude of air by 100ft. §Determine your density altitude if the temperature is 80F with a pressure of 29.90inch Hg and 30\% humidity. §Determine your density altitude if the temperature is 100F with a pressure of 29.85inch Hg and 70% humidity. College of Engineering and Science

Does this problem work for someone §Who is not a drag racer? §Who is not a pilot? §Who was not “at the race that day”? §Who does not live in Louisiana? §Does it matter? (It’s virtually impossible to catch everyone.) §Would a story around the whole thing help? College of Engineering and Science

Homework §Think about similar problems/stories/connections that you might be able to easily weave into your class or which you have already used in class. §Do you have any right away? §We’ll talk about these kinds of examples tomorrow. College of Engineering and Science

What we “must do.” §Activity College of Engineering and Science

What do our students really need? §Content is most effective when considered relevant §This can be achieved by providing context §Content can be reordered (dependency chart) §Technology, not “if?” but “how?” §Time is limited §Ask hard questions: What is more important: Solid vector analysis or convergence tests for series? §Do not sacrifice your identity in the process. College of Engineering and Science

Big Picture: Integrated Courses fallspringwinter math 240 3math 241 3math Precalc algebra & trig, single variable differential calculus Single variable differential calculus Integral calculus, intro differential equations engr 120 2engr engr Problem solving, data analysis, team skills, statistics Statics, strengths, report writing, sketching, design Circuits, engr economics, MathCAD, design project Freshman Year chem chem Engineering chemistry phys Mechanics Plus 1 additional class -- History, English, Art,... Engineering Fundamentals Teamwork Communication Skills Design Computer Skills Laboratory Experiences 2 classes/labs (2 hrs each) per week Engineering Class

Big Picture: Integrated Courses fallspringwinter math 243 3math 244 3math Basic statistics, multivariable integral calculus Multivariable differential calculus, vector analysis Sequences, series, differential equations engr 220 3engr engr Statics and strengthsEE applications and circuitsThermodynamics memt physics Engineering materialsElectric and magnetic fields, optics Sophomore Year Plus 1 additional class -- History, English, Art,... Engineering Fundamentals Teamwork Communication Skills Design Statistics & Engr Economics Laboratory Experiences 3 hours lab & 2.5 hours lecture per week Engineering Class

Statistics, Qualitative Evaluation and Anecdotes §Statistics: Integrated students performed better than non-integrated peers. §Focus group: Female students’ performance was positively affected by the availability of peers. “Lagged” students still quite mature. §Private conversation: “I slept through the first half of my fields class and still made an A because you got me ready.” (B/C student) §Positive feedback from ENGR (FE, grade analysis) College of Engineering and Science

Challenges §Facilities §Time §Materials §Diversity of learning styles §Interface with other disciplines §“This is hard.” (Faculty and students.) §“This is not how we used to do things.” (“This is how I would have liked it to be done.”) §Plus all the other things we already complain about ;) College of Engineering and Science

“Guide” to Successful Implementation §Every institution is different. §“Change agents’ ” buy-in is necessary. §Admin. support is necessary (“small” is o.k.). §Money helps, attitude succeeds. §Systemic adjustments persist. §Side remarks can help (“When … it clicked.”) §Student apprehensions (greener grass on the other side), analyze your clientele §Challenges make people think. §Self-esteem works best when it is earned. College of Engineering and Science