Abstract: We show a simple perceptron-like algorithm to learn origin-centered halfspaces in $\mathbb{R}^n$ with accuracy $1-\epsilon$ and confidence $1-\delta$ in time \n \[\n \mathcal{O}\left(\frac{n^2}{\epsilon}\left(\log \frac{1}{\epsilon}+\log \frac{1}{\delta}\right)\right)\n \]\n using \n \[\n \mathcal{O}\left(\frac{n}{\epsilon}\left(\log \frac{1}{\epsilon}+\log \frac{1}{\delta}\right)\right)\n \]\n labeled examples drawn uniformly from the unit $n$-sphere. This improves upon algorithms given in \cite{DBLP:journals/neco/Baum90}, \cite{DBLP:journals/ipl/Long94} and \cite{DBLP:conf/colt/Servedio99}. The time and sample complexity of our algorithm match the lower bounds given in \cite{DBLP:journals/tnn/Long95} up to logarithmic factors.