Proton-impact-ionization cross sections for argon which are differential in the energy and angle of the ejected electron have been calculated within the framework of the Born approximation using both Hartree-Slater and Hartree-Fock wave functions for the ejected electron. Results of the two types of calculations are compared with each other and with experiment. Differential cross sections for all five sub shells of argon are examined and particular attention is given to some interesting features of the K-shell cross sections. The range of applicability of the theoretical models is discussed.