26 Mar 2014

Group Theory for Mathematicians

Five Slides About

Submitted by Anne Bentley, Lewis & Clark College
Categories
Description: 

While informally chatting with friends in our math department, I realized that I could put together a presentation about how chemists use group theory.  I was invited to give the presentation as part of our math department's weekly colloquium series.  The talk was to be one hour in length, and my math colleague described their typical format as:

15 minutes should be understandable to a precalc level student
15 minutes understandable to a math major
15 minutes understandable to those who already have seen groups
15 minutes as high a level as you want
 
I really enjoyed putting together the presentation, which did end up being 1 hour in length.  (It could have been longer - I rushed through the molecular orbital material at the end.)  I did not assume audience members had had any previous chemistry, but at the same time, I assumed they would be comfortable with the concepts of atoms and molecules presented visually.  (I brought models and other hands on activities.)  The presentation condensed about nine 1-hour lectures from my inorganic course, covering symmetry elements and operations, point groups, matrix representation of groups, character tables, and then applications in IR spectroscopy and molecular orbital theory.  I primarily focused on the water molecule in the first half of the talk, then used carbon dioxide and methane (both greenhouse gases) to show the importance of vibrational spectroscopy.  The last few slides cover the topic of molecular orbital theory.
 
Others who love group theory may be interested in giving their own presentations to math colleagues.  Or, this talk could serve as a very general introduction to group theory concepts and applications for those who aren't currently teaching group theory.   
Learning Goals: 

After attending and participating in the talk, it was my goal that the math majors be able to:

- describe how symmetry operations can be used as a quantitative way to classify objects into point groups

- apply matrix multiplication to symmetry operations

- understand that mathematical concepts can be applied more broadly to chemistry, specifically in the areas of IR spectroscopy and molecular bonding theories

Implementation Notes: 

I gave the presentation as part of the math department's weekly colloquium series in mid-February.  I scheduled it to arrive near the end of my group theory unit in my spring inorganic course.  The audience was diverse - approximately 5-8 math majors, 4-5 math professors, one physics professor, one physics major, and about five chemistry majors.  Three of the students from my inorganic course came, as I told them it would be a good review before our first midterm exam. 

I have uploaded the "stretching videos" I obtained from Spartan separately from the powerpoint file due to restrictions on file size.  If you plan to use the powerpoint, you'll need to insert the stretching videos individually.  I have included some notes at the bottom of each powerpoint slide to describe any models or websites that I used during the talk.  The slides may seem very spare, as I tried to keep them simple and do most of the explaining myself.  The talk was much more of a tutorial than a formal presentation.

Time Required: 
one hour
Evaluation
Evaluation Methods: 

From my perspective, the talk was a success.  The audience seemed engaged throughout and I heard positive feedback from attendees after the talk.  When I handed around sets of character tables for everyone to look at, two of my math colleagues were so excited that I had to "shush" them to regain everyone's attention.  It was great to be able to draw connections between our departments.

Creative Commons License: 
Creative Commons Licence

The VIPEr community supports respectful and voluntary sharing. Click here for a description of our default Creative Commons license.