Algebra, from the Arabic word al-jabr, meaning "reunion of broken parts," is the study of variables and the rules for manipulating these variables in formulas; it is the unifying thread of almost all of mathematics. Elementary algebra deals with the manioulation of variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in education, to the study of algebraic structures such as groups, rings, and fields. Linear algebra, which deals with linear equations and linear mappings, is used for modern presentations of geometry, and has many practical applications (in weather forecasting, for example). There are many areas of nathematics that belong to algebra, some having "algebra" in their name, such as communitative algebra, and some have not, such as Galois theory. The word algebra is not only used for naming an area of mathematics and some subareas...

Food microbiology is the study of the microorganisms that inhabit, create or contaminate food. This includes the study of microorganisms causing spoilage; pathogens that may cause disease (especially if the food is improperly cooked or stored); microbes used to produce fermented foods such as cheese, yogurt, bread, beer, and wine; and microbes with other useful roles, such as producing probiotics. In the study of bacteria in food, important groups have been subdivided based on certain characteristics. These groupings are not of taxonomic significance: Lactic acid bacteria are bacteria that use carbohydrates to produce lactic acid. The main genera are Lactococcus, Leoconostoc, Pediococcus, Lactobacillus, and Streptococcus thermophilus. Acetic acid bacteria like Acetobacter aceti produce acetic acid. Bacteria such as Propionibacterium freudenrencii that produce propionic acid are used to ferment dairy products. Some Clostridium spp. Clostridium butyricum produce butyric acid. Proteolytic...