| Symbol |
Description |
Location |
| \(x\in A\) |
\(x\) is an element of \(A\)
|
Paragraph |
| \(\not\in\) |
\(x\) is not an element of \(A\)
|
Paragraph |
| \(\{\ldots\}\) |
curly brackets |
Paragraph |
| \(\emptyset\) |
the empty set |
Paragraph |
| \(A
\subseteq B\) |
\(A\) is a subset of \(B\)
|
Paragraph |
| \(A \not\subseteq B\) |
\(A\) is not a subset of \(B\)
|
Paragraph |
| \(A \cap B\) |
intersection of sets \(A,B\)
|
Paragraph |
| \(A \cup B\) |
union of sets \(A,B\)
|
Paragraph |
| \(A \setminus B\) |
difference of sets \(A,B\)
|
Paragraph |
| \({\mathcal P}(A)\) |
power set of a set \(A\)
|
Exercise 1.1.2 |
| \((x,y)\) |
ordered pair |
Paragraph |
| \(A\times
B\) |
the (Cartesian) product of sets \(A,B\)
|
Paragraph |
| \(f\colon S\to T\) |
a function \(f\) with domain \(S\) and codomain \(T\)
|
Paragraph |
| \(f(s)=t\) |
\((s,t)\) is an element of \(f\)
|
Paragraph |
| \(g\of f\) |
composition of functions \(g,f\)
|
Paragraph |
| \(I_S\) |
identity function on a set \(S\)
|
Paragraph |
| \(\Id_S\) |
identity function on a set \(S\)
|
Paragraph |
| \(\One_S\) |
identity function on a set \(S\)
|
Paragraph |
| \(f(U)\) |
the image of the set \(U\) under the function \(f\)
|
Paragraph |
| \(f^{-1}(V)\) |
the preimage of the set \(V\) under the function \(f\)
|
Paragraph |
| \(|S|\) |
size of a finite set \(S\)
|
Paragraph |
| \(\Z\) |
the set of integers |
Paragraph |
| \(a|b\) |
\(a\) divides \(b\)
|
Paragraph |
| \(a\nmid b\) |
\(a\) does not divide \(b\)
|
Paragraph |
| \(a\equiv b \pmod{m}\) |
\(a\) is equivalent to \(b\) modulo \(m\)
|
Paragraph |
| \(\Z_m\) |
the set \(\{0,1,\ldots,m-1\}\)
|
Paragraph |
| \(n \MOD m\) |
\(n\) modulo \(m\)
|
Paragraph |
| \(\Q\) |
the set of rational numbers |
Paragraph |
| \(\chi_A\) |
characteristic function for the set \(A\)
|
Exercise 1.8.3.1 |
| \({\mathbf e}_1,{\mathbf e}_2\) |
standard basis vectors in \(\R^2\)
|
Paragraph |
| \(\left\Vert(a,b)\right\Vert\) |
norm of the ordered pair \((a,b)\)
|
Paragraph |
| \(S^1\) |
unit circle |
Paragraph |
| \([L]\) |
matrix for a linear map \(L\)
|
Paragraph |
| \(\det\) |
determinant of a matrix |
Paragraph |
| \(\re(z)\) |
real part of the complex number \(z\)
|
Paragraph |
| \(\im(z)\) |
imaginary part of the complex number \(z\)
|
Paragraph |
| \(|z|\) |
norm of the complex number \(z\)
|
Paragraph |
| \(\arg(z)\) |
argument of the complex number \(z\)
|
Paragraph |
| \(i\) |
the complex number \(i\)
|
Paragraph |
| \(\expi(\theta)\) |
complex number corresponding to \((\cos\theta,\sin\theta)\)
|
Paragraph |
| \(\overline{z}\) |
conjugate of the complex number \(z\)
|
Paragraph |
| \({z}^\ast\) |
conjugate of the complex number \(z\)
|
Paragraph |
| \(\proj_{\mathbf{u}}\mathbf{v}\) |
orthogonal projection of vector \(\mathbf{v}\) onto vector \(\mathbf{u}\)
|
Exercise 2.4.1.3 |
