Simple and multiple linear models, residual diagnostics, and matrix notation.

For those ready to take the next step, seek out "Statistical Inference" by Casella and Berger for rigor, but complement it with "Naked Statistics" by Charles Wheelan for joy. The PDF you create from synthesizing those two is the true treasure.

This "classical introduction" is far from a dry textbook. It is the product of over two decades of refinement, having been used in draft form for over 20 years in both statistics and mathematics departments. The result is a 478-page work that seeks to bridge the gap between students with strong mathematical backgrounds and those who may be encountering sophisticated statistical concepts for the first time. This article explores what makes this book a unique and valuable contribution to the world of statistical learning.

The infinite joy of mastering these mathematical principles is that they never lose relevance. The same linear regression models, Bayesian inferences, and analysis of variance (ANOVA) techniques developed decades ago remain the bedrock of today's cutting-edge artificial intelligence, machine learning algorithms, and climate models. Understanding mathematical statistics allows you to see past sensational headlines, question flawed methodologies, and interpret the world through a lens of objective truth. Recommended Structure for Self-Study

However, these critiques are often accompanied by a powerful sense of fondness and appreciation. One Hacker News user captures this sentiment perfectly: “That said, I still loved this book in spite of its imperfections. I think it’s important to read it at the correct time in one’s life. When I first read it (at 19 or so), it showed me a lot of things I’d never thought about before”. Another Amazon reviewer was even more direct, calling it the clearest and most concise review of statistics they had encountered in years of study, stating they planned to use it as a reference to "improve my statistical prowess".

Unlike many heavy reference volumes, this text is written to be read linearly. It aims to bridge the gap between a first course in probability and a rigorous theoretical treatment of statistical inference.

Published in September 2022, The Simple and Infinite Joy of Mathematical Statistics is a “classical introduction to mathematical statistics” designed for a varied audience of graduate and undergraduate students with diverse backgrounds and skill sets. The book’s author, J.N. Corcoran (also cited as Jem N. Corcoran), has crafted a text that aims to bridge the gap between groups of students who often find themselves speaking past one another—statistics students who may lack advanced mathematical fluency, and mathematics students who may have little or no statistical background. This bridging is precisely what makes the book so distinctive.