The SCUBA-2 Ultra Deep Imaging EAO Survey (STUDIES) is a three-year JCMT Large Program aiming at reaching the 450 $mu$m confusion limit in the COSMOS-CANDELS region, to study a representative sample of the high-redshift far-infrared galaxy population that gives rise to the bulk of the far-infrared background. We present the first-year data from STUDIES. We have reached a 450 $mu$m noise level of 0.91~mJy for point sources at the map center, covered an area of 151 arcmin$^2$, and detected 98 and 141 sources at 4.0 and 3.5 $sigma$, respectively. Our derived counts are best constrained in the 3.5-25 mJy regime using directly detected sources. Below the detection limits, our fluctuation analysis further constrains the slope of the counts down to 1 mJy. The resulting counts at 1-25 mJy are consistent with a power law having a slope of $-2.59$ ($pm0.10$ for 3.5-25 mJy, and $^{+0.4}_{-0.7}$ for 1-3.5 mJy). There is no evidence of a faint-end termination or turn-over of the counts in this flux density range. Our counts are also consistent with previous SCUBA-2 blank-field and lensing cluster surveys. The integrated surface brightness from our counts down to 1 mJy is $90.0pm17.2$ Jy deg$^{-2}$, which can account for up to $83^{+15}_{-16}%$ of the COBE 450 $mu$m background. We show that Herschel counts at 350 and 500 $mu$m are significantly higher than our 450 $mu$m counts, likely caused by its large beam and source clustering. High-angular resolution instruments like SCUBA-2 at 450 $mu$m are therefore highly beneficial for measuring the luminosity and spatial density of high-redshift dusty galaxies.
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