This course, building on the probability theory studied in MTH 246, is intended as an introduction to the mathematical theory of statistical inference with emphasis on statistical concepts and the mathematical foundations from which those concepts are developed. Applications illustrating the statistical concepts are discussed. Main topics include: sampling from the normal distribution; various modes of convergence in large samples; data principles (including sufficiency, completeness, and likelihood principle); point and interval estimations; hypothesis testing (including the Neyman-Pearson lemma, likelihood ratio tests, and power functions). Use of modern methods such as resampling are described as ways to minimize reliance on large sample approximations.