College of Engineering and Science

Louisiana Tech UniversityCollege of Engineering and Science

Connecting Mathematics with

Engineering and the Sciences (Chautauqua workshop)

Bernd S. W. SchröderProgram 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 DoLong standing need for people (including

mathematicians/math majors) who can apply mathematics in context.

George reportCarnegie Initiative papersCUPM recommendationsCognitive 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 relevantThis can be achieved by providing context Content can be reordered (dependency chart)Technology, not “if?” but “how?”Time is limitedAsk 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

fall springwinter

math 240 3 math 241 3 math 242 3Precalc algebra & trig, singlevariable differential calculus

Single variable differential calculus

Integral calculus, intro differential equations

engr 120 2 engr 121 2 engr 122 2Problem solving, data analysis, team skills, statistics

Statics, strengths, reportwriting, sketching, design

Circuits, engr economics,MathCAD, design project

Freshman Year

chem 100 2 chem 101 2 Engineering chemistry Engineering chemistry

phys 201 3Mechanics

Plus 1 additional class -- History, English, Art, ...

Engineering Fundamentals

Teamwork

Communication Skills

Design

Computer Skills

Laboratory Experiences

2 classes/labs (2 hrs each) per weekEngineering

Class

Big Picture: Integrated Courses

fall springwinter

math 243 3 math 244 3 math 245 3Basic statistics, multivariableintegral calculus

Multivariable differential calculus, vector analysis

Sequences, series, differentialequations

engr 220 3 engr 221 3 engr 222 3Statics and strengths EE applications and circuits Thermodynamics

memt 201 2 physics 202 3 Engineering materials Electric 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 weekEngin

eeri

ng

C

lass

Statistics, Qualitative Evaluation and AnecdotesStatistics: 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

ChallengesFacilitiesTimeMaterialsDiversity of learning stylesInterface 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 ImplementationEvery 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 clienteleChallenges make people think. Self-esteem works best when it is earned.

College of Engineering and Science