Trying to help out a gentleman who made an inquiry to me via email - I have begun searching, but am posting this here too -
Hi Marion,
I've just found your great website on the subject of the Combat Engineers.
Very interesting reading.
I was wondering if you could supply any info on a U.S WWII Captains Uniform I own.
Name inside: Captain Robert Mathieson
3RD INFANTRY / 3RD ARMORED DIVISION / CORPS OF ENGINEERS
I would really like to know if you could supply any more info on the unit etc?
Kind Regards,
Jamie
I am trying to find personal info on Robert. Found several instances at NARA, which could be his, but am trying to narrow it down. Just beginning my search today, so...
Yes, we have quite a bit of info on the units, so that is not a problem, in and of itself. 
Including the uniform pics
Another post from my new friend:
Hi Marion,
Managed to get a photo of the tag inside which may help some more.
Captain Robert G. Mathieson
No. 36438
Date. 9 - 9 - 44
Regards,
Jamie
He also stated that he is going to contact the gentleman he bought the coat from and see if he can glean any other info.
During 1944 and 1945, the units comprising the Third Armored Division included:
Combat Units:
32nd Armored Regiment
33rd Armored Regiment
36th Armored Infantry Regiment
54th Field Artillery Battalion
67th Field Artillery Battalion
391st Field Artillery Battalion
143rd Signal Company
23rd Armored Engineer Battalion
83rd Armored Reconnaissance Battalion
Headquarters Units:
While I'm looking for him specifically, let's post some other information about the 23rd Armored Eng Bn. Here's a great amateur COLOR film from training exercises in the states.
http://www.36air-ad.com/3ad.php
Just sent an email to them to, for I read this on their page:
We have a copy of the 36th Armored Infantry Regiment "Personnel Directory" which was privately published in November 1945. This booklet lists the name and address of all known members of the 36th Armored Infantry Regiment, including those that died in the line of service. That is all the information it contains, and was intended mainly as a means to facilitate other unit members trying to contact their buddies.
We will gladly look up the name of any veteran believed to have served in the 36th Armored Infantry Regiment in World War II. In order to do so, we need to know the veteran's rank, full name, hometown (if known) and the company to which he was assigned (if known).
Conducted research on NARA's site within their enlistment category. It turned up several by that name, but none from the Detroit area.
