Ape,
The old "Staff Data Handbook" had casualty rate tables and such based on historical data. I've never met the Lanchester Equation before as such in formal training (I went into Political Science to avoid having to squaring things). The US Army had a combat ratio table that gave each type of unit a value and was used to predict outcomes but that may have fallen out of favour (it wasn't terribly useful IMHO). Math is one thing that I do not want to do in the field.
Our doctrine and schools emphasize "manoeuvre" and place the emphasis on shattering the will of the enemy as opposed to achieving his physical destruction. That being said, in my opinion we are a methodical army and not truly manoueverist. Our roots are in the deliberate attack and defence. We now seem to try to turn every attack into a deliberate attack and are shunning "advancing to contact." We talk manoeuvre, but in my opinion we practice methodically. Perhaps this will change over time.
Going back to attrition, perhaps there is an element of attritional exchange equations in the rule of thumb that the attacker should have at least three to one odds. Defenders normally get the first shot (or shots), so sending three tanks over the crest for every defending tank should mean that when the exchange of fire is done one or two attacking tanks are destroyed, the defending tank is destroyed but at least one attacking tank is left to breakthrough...I've seen this in JANUS, JCATS and SIMNET (CCTT) which are simulations/simulators. In these scenarios the side that brings the most guns to the fight (and masses them at the right time and place) seems to win the exchange most of the time (fastest with the mostest). We tried some one to one attacks against prepared defences in JANUS two years ago and my "virtual" combat team was vaporized in about ten seconds (darn full-defilade mode for the defence).
What can allow us break out of the "exchange ratio attack" are superior training, tactics or equipment. The rapid advances of coalition forces in '91 and '03 were, in my opinion, due to the armour of the M1 and Challenger. They could take a hit and not be destroyed. This threw any "exchange" calculations out the window. Superior training gave the Israelis and edge while combined arms doctrine was the German ace in the hole.
Sorry, I've rambled and haven't answered your question :blotto:. The short answer is that you will meet principles of war and ideas such as battlespace and manoeuvre warfare that you will recognize from your studies (I'm making some assumptions here) in future training. You will meed the tactical, operational and strategic levels of war as well as the spectrum of conflict. Just remember, high level war-fighting theory is one thing, crew commanding a vehicle or leading a section attack in Gagetown is another.
Cheers,
2B