# Not Just Calculus: First-Year Introduction to Upper-Level Mathematics

## IndexIndex

$$n$$-th root of unity
addition modulo $$m$$
algebra of sets
argument of a complex number
argument of a vector
arithmetic sequence
Cartesian coordinates
Cartesian Plane
Cartesian product
first entry in an ordered pair
ordered pair
second entry in an ordered pair
characteristic function for a set
column vector
common difference in an arithmetic sequence
common ratio in a geometric sequence
conjugate of a complex number
De Morgan’s laws
determinant
distributive law for complex numbers
distributive law for linear mappings
distributive laws for sets
divides
divisible
Division Algorithm
divisor
dot product
equivalence modulo an integer
equivalence relation
Euler’s formula
exponential growth or decay
extended real numbers
function
bijective function
codomain
composition of functions
domain
graph
identity function
image of a function
image of a point
injective function
inverse function
invertible function
one-to-one correspondence
one-to-one function
onto function
preimage of a point
surjective function
Fundamental Theorem of Arithmetic
geometric sequence
identity matrix
if and only if
image of a set under a function
imaginary part of a complex number
infinite geometric series
initial term of a geometric sequence
initial term of an arithmetic sequence
inverse of a matrix
inverse relation
irrational number
linear fractional transformation
linear growth or decay
linear mapping (or map)
matrix
matrix multiplication
matrix scalar multiplication
modulus of a complex number
modulus of a vector
multiplication modulo $$m$$
multiplicative inverse of a complex number
norm of a complex number
norm of a vector
origin in $$\R^2$$
orthogonal projection of a vector onto another vector
partition
polar coordinates
polar form for a complex number
polar form of a vector
power set
preimage of a set under a function
prime
primitive Pythagorean triple
primitive root of unity
product of two complex numbers
pure imaginary number
Pythagorean triple
quotient
quotient of two complex numbers
rational number
real part of a complex number
rectangular coordinates
rectangular form for a complex number
relation between sets
remainder
scalar multiple
set
difference of sets
element of a set
equal sets
finite set
infinite set
intersection
member of a set
subset
the empty set
union
standard basis vectors in $$\R^2$$
sum in $$\R^2$$
sum of two complex numbers
the set of integers
the set of rational numbers
triangle inequality for complex numbers
unit circle
wrapping function
zero vector