There is some overlap between M358K and M378K, namely, the basic notions of statistical inference: sampling distributions, hypothesis testing and confidence intervals.

However, there are many differences between the two courses. As the names suggest, M 358K (Applied Statistics) puts more emphasis on applications and M 378K (Introduction to Mathematical Statistics) puts more emphasis on theory.

Topics covered in M 358K that are not usually covered (or only lightly covered) in M 378K:

• Exploratory data analysis
• Data collection
• Deciding which techniques to use when
• Interpretation of results
• Regression
• Use of statistical software

Topics covered in M 378K that are not usually covered (or more lightly covered) in M 358K:

• Probability distributions and their properties
• Derivation of techniques
• Point estimation
• Type I and II errors and statistical power
• Maximum Likelihood methods
• Likelihood ratio tests
  

M 378K also uses calculus more heavily than M 358K.

Textbooks typically used:

• M 358K: Moore, David S., McCabe, George P., Introduction to the Practice of Statistics 5th edition, 2005/6, W.H. Freeman
• M 378K: Wackerly, Mendenhall, Scheaffer, Mathematical Statistics with Applications, sixth ed., 2002, Duxbury.