Boolean algebra

In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively. Instead of elementary algebra where the values of the variables are numbers, and the main operations are addition and multiplication, the main operations of Boolean algebra are the conjunction and, denoted ∧, the disjunction or, denoted ∨, and the negation not, denoted ¬. It is thus a formalism for describing logical relations in the same way that ordinary algebra describes numeric relations.

Boolean algebra was introduced by George Boole in his first book The Mathematical Analysis of Logic (1847), and set forth more fully in his An Investigation of the Laws of Thought (1854). According to Huntington, the term "Boolean algebra" was first suggested by Sheffer in 1913.

Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages. It is also used in set theory and statistics.

Algebra

Algebra (from Arabic "al-jabr" meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians. Much early work in algebra, as the Arabic origin of its name suggests, was done in the Middle East, by mathematicians such as al-Khwārizmī (780 – 850) and Omar Khayyam (1048–1131).

Digital electronics

Digital electronics or digital (electronic) circuits are electronics that handle digital signals - discrete bands of analog levels - rather than by continuous ranges (as used in analogue electronics). All levels within a band of values represent the same numeric value. Because of this discretization, relatively small changes to the analog signal levels due to manufacturing tolerance, signal attenuation or parasitic noise do not leave the discrete envelope, and as a result are ignored by signal state sensing circuitry.

In most cases, the number of these states is two, and they are represented by two voltage bands: one near a reference value (typically termed as "ground" or zero volts), and the other a value near the supply voltage. These correspond to the "false" ("0") and "true" ("1") values of the Boolean domain respectively, named after its inventor, George Boole, yielding binary code.

Digital techniques are useful because it is easier to get an electronic device to switch into one of a number of known states than to accurately reproduce a continuous range of values.

Crash Course

Crash Course (also known as Driving Academy) is a 1988 made for television teen film directed by Oz Scott.

Plot

Crash Course centers on a group of high schoolers in a driver’s education class; many for the second or third time. The recently divorced teacher, super-passive Larry Pearl, is on thin ice with the football fanatic principal, Principal Paulson, who is being pressured by the district superintendent to raise driver’s education completion rates or lose his coveted football program. With this in mind, Principal Paulson and his assistant, with a secret desire for his job, Abner Frasier, hire an outside driver’s education instructor with a very tough reputation, Edna Savage, aka E.W. Savage, who quickly takes control of the class.

The plot focuses mostly on the students and their interactions with their teachers and each other. In the beginning, Rico is the loner with just a few friends, Chadley is the bookish nerd with few friends who longs to be cool and also longs to be a part of Vanessa’s life who is the young, friendly and attractive girl who had to fake her mother’s signature on her driver’s education permission slip. Kichi is the hip-hop Asian kid who often raps what he has to say and constantly flirts with Maria, the rich foreign girl who thinks that the right-of-way on the roadways always goes to (insert awesomely fake foreign Latino accent) “my father’s limo”. Finally you have stereotypical football meathead J.J., who needs to pass his English exam to keep his eligibility and constantly asks out and gets rejected by Alice, the tomboy whose father owns “Santini & Son” Concrete Company. Alice is portrayed as being the “son” her father wanted.