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References Notation

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
\((x,y)\) 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
\({\mathcal P}(A)\) power set of a set \(A\) Exercise 1.5.3.1
\(\chi_A\) characteristic function for the set \(A\) Exercise 1.5.3.3
\({\mathbf e}_1,{\mathbf e}_2\) 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
\(\overline{z}\) 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 2.4.3