COLLEGE
ALGEBRA
ALGEBRA
IN y = mx + b, m IS THIS
What is the slope?
IT HAS A MAGNITUDE AND A DIRECTION
What is a vector?
ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION ARE THE FOUR MOST BASIC EXAMPLES OF THESE
What are operations?
TODAY, WE USE ENGLISH LETTERS TO REPRESENT VARIABLES, BUT DIOPHANTUS USED LETTERS LIKE α AND β FROM THIS ALPHABET INSTEAD
What is the Greek alphabet?
THIS BRANCH OF MATHEMATICS HELPS YOU DETERMINE THE CHANCE OF ROLLING A 1 ON A DICE OR THE CHANCE OF FLIPPING HEADS ON A COIN, FOR EXAMPLE
What is probability?
IF A RELATION PASSES THE VERTICAL LINE TEST, IT IS ALSO THIS
What is a function?
MATRICES WITH DETERMINANT ZERO ARE SINGULAR; OTHERWISE, THEY ARE SAID TO BE THIS
What is invertible?
What is the distributive property?
DAILY DOUBLE!
ALSO KNOWN AS THE "FATHER OF ALGEBRA", THIS MATHEMATICIAN WROTE AL-JABR, THE FIRST BOOK ON ALGEBRA, IN 9TH CENTURY AD
Who is Al-Khwarizmi?
IN GEOMETRY, A = πr2 IS THE FORMULA FOR THE AREA OF THIS GEOMETRICAL SHAPE
What is the circle?
DAILY DOUBLE!
THE DISCRIMINANT b2 - 4ac IS INCLUDED IN THIS FORMULA, WHICH IS USED TO SOLVE QUADRATIC EQUATIONS
What is the quadratic formula?
WHEN TWO VECTORS ARE ORTHOGONAL, THEIR DOT PRODUCT EQUALS THIS
What is 0?
WHEN WRITING AN IDENTITY ELEMENT IN MODERN ALGEBRA, WE DENOTE IT BY THIS SYMBOL, NOT TO BE CONFUSED WITH THE EXPONENTIAL CONSTANT
What is e?
ALSO KNOWN FOR INVENTING CARTESIAN GEOMETRY, THIS MATHEMATICIAN INTRODUCED THE SYMBOL x IN LA GÉOMÉTRIE
Who is Descartes?
IN CALCULUS, DIFFERENTIAL CALCULUS AND INTEGRAL CALCULUS ARE RELATED BY THIS THEOREM
What is the Fundamental Theorem of Calculus?
WHEN TWO LINES CROSS EACH OTHER, THEY ARE SAID TO HAVE THIS MANY SOLUTIONS
What is 1?
IF A MATRIX IS SQUARE, ITS LINEAR TRANSFORMATION CAN BE DESCRIBED BY Av = λv, WHERE λ IS KNOWN AS THIS
What is an eigenvalue?
IF A GROUP IS COMMUTATIVE UNDER AN OPERATION, WE SAY THAT THE GROUP IS THIS
What is abelian?
EUCLID'S ELEMENTS COMBINED ALGEBRA WITH THIS BRANCH OF MATHEMATICS; WE MAY EVEN CALL IT "EUCLIDEAN"!
What is geometry?
IN ANALYSIS, ε-δ AND ε-N DEFINITIONS ARE RELATED TO THIS CONCEPT FROM CALCULUS I
What is the limit?
ONE OF THE SOLUTIONS TO x2 + 1 = 0 IS i = √-1, WHICH CAN BE USED TO EXTEND THE REAL NUMBERS TO THESE TYPES OF NUMBERS
What are complex numbers?
THE UNIT VECTORS i, j, and k FORM THIS ON ℝ3
What is the standard basis?
{1, 2}, {A, B}, AND {〇, △} ALL HAVE SOMETHING IN COMMON! THEY ALL FORM THIS WITH ℤ MOD 2
What is an isomorphism?
About 263 AD, LIU HUI COMMENTED ON THIS MATHEMATICAL TEXT, WHICH INCLUDED TECHNIQUES FOR SOLVING SYSTEMS OF LINEAR EQUATIONS
What is The Nine Chapters on the Mathematical Art?
NOT TO BE CONFUSED WITH GRAPHS IN ALGEBRA, THESE GRAPHS HAVE NODES AND EDGES, AND THEY ARE THE CENTERPIECE OF THIS BRANCH OF MATHEMATICS
What is graph theory?