# Analytical Theory

#### Group Theory and Symmetry, Part IV: Great or Grand, We've Got GOT

September 01, 2010

Here, we continue our treatment of symmetry and group theory by introducing a very useful mathematical tool in group theory. It has two names in common use, but thankfully they both have the same acronym: GOT.

#### Classical Least Squares, Part II: Mathematical Theory Continued

June 01, 2010

The authors continue their discussion of the classical least squares approach to calibration.

#### Classical Least Squares, Part I: Mathematical Theory

May 01, 2010

In this month's installment of "Chemometrics in Spectroscopy," the authors begin a new subseries with the goal of explaining the classical least squares algorithm.

#### Group Theory and Symmetry, Part III: Representations and Character Tables

April 01, 2010

In the third part of this series, David Ball starts getting into the mathematical aspects of group theory, aspects that ultimately become useful in spectroscopy.

#### Group Theory and Symmetry, Part II: Groups

January 01, 2010

In the previous installment of this column, David Ball introduced the five types of symmetry elements that are important in physical science. Here, he discuss why it’s called "group" theory in the first place.

#### Group Theory and Symmetry, Part I: Symmetry Elements

December 01, 2009

Group theory is the field of mathematics that includes, among other things, the treatment of symmetry. Well, it turns out that molecules have symmetry, so group theoretical principles can be applied to molecules. Because spectroscopy uses light to probe the properties of molecules, it might not be surprising that group theory has some application to spectroscopy. Here, we start a multipart discussion of symmetry and group theory.

#### The Role of Naturally Occurring Stable Isotopes in Mass Spectrometry, Part I: The Theory

October 01, 2008

In this tutorial, the authors explain how naturally occurring stable isotopes contribute to experimentally determined mass spectra and how this information can be exploited in quantitative experiments, structural elucidation studies, and tracer methodologies. The first installment of this series focuses on the theoretical aspects of stable isotopes and the calculation of their distribution patterns.