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I would really appreciate it if I could get book recommendations on the rigorous mathematical theory of x ray crystallography. Which areas of mathematics (pure and applied) would be most useful and applicable?
verty said:Do you not want normal crystallography books? Here are two suggested by MIT to their grad students:
Werner Massa - Crystal Structure Determination
"Everything important is explained and the book starts from scratch."
Carmello Giacarvazzo, et al. - Fundamentals of Crystallography
"The somewhat more advanced student may like [this book]. Even though the word "fundamentals" appears in the title of the book, it is very helpful to have prior knowledge, when attempting to read [it]. This book covers all the basics and should be sufficient for most PhD students.
Macromolecular crystallography is a scientific technique used to study the three-dimensional structure of large molecules, such as proteins and nucleic acids. It involves growing crystals of these molecules and then using X-ray diffraction to determine the arrangement of atoms within the crystal. This information can provide insights into the function and interactions of these molecules.
Mathematics is essential in macromolecular crystallography as it is used to analyze the X-ray diffraction patterns and solve the complex mathematical equations that describe the atomic positions within the crystal. These calculations help determine the structure of the molecule and are crucial in understanding its function.
Some common mathematical techniques used in macromolecular crystallography include Fourier transforms, matrix algebra, and statistical methods. These are used to process and analyze the data collected from X-ray diffraction experiments and to solve the phase problem, which is a key challenge in crystallography.
Mathematics has greatly advanced the field of macromolecular crystallography by providing powerful tools and techniques for analyzing complex crystal structures. The development of new mathematical algorithms and software has also allowed for more accurate and efficient analysis of crystallographic data, leading to significant advancements in our understanding of the structure and function of biological molecules.
Some current challenges in the mathematics of macromolecular crystallography include improving the accuracy and speed of calculations, developing new methods for solving the phase problem, and finding ways to incorporate experimental errors and uncertainties into the mathematical models. Additionally, there is a need for continued collaboration between mathematicians and crystallographers to address these challenges and further advance the field.