Rapid Progress?

I think that at the beginning of most fitness programs, after a couple days of extra soreness, most people experience some rapid progress. I see this in myself especially since I'm not really working towards a new level of fitness, but simply recapturing old ground.

I ran 3 miles on the treadmill today, the same as yesterday. I did time my miles today, and I'm sure I was at least a minute faster than yesterday. I started faster (6.8 MPH), held yesterday's fastest pace (8.8 MPH) for almost a mile, and then bumped it up to 9.0 MPH for a quarter mile.

Mile 1 - 8:23
Mile 2 - 7:15 (15:38 cumulative)
Mile 3 - 6:54 (22:34 cumulative)

I checked my pulse again and it was about the same, 174. I'm not sure how accurate that is as I am checking it for 10 seconds and multiplying by 6, and it feels to me as if my pulse is rapidly decreasing during those 10 seconds.

For comparison, my pulse right now (about 20 minutes after my run) is about 78.

I then walked another two tenths of a mile as a cool-down. I have now run 6 consecutive days.

Weight is also the same as earlier in the week at 193 lbs.