The functions by monomials $x_1^k_1x_2^k_2…x_n^k_n$ for $k_1,k_2,…,k_n<q$ form a basis in the space of all $K$-valued functions on $K^n$How do you count the elements in a finite vector space?Countable/uncountable basis of vector spaceQuestion on quadratic formsAlternative proof that a simple field extension just has a finite number of intermediate fieldsQuery on an example of Morandi's Field and Galois Theory, regarding the degree of a field extension.Any polynomial in $n$ variables over $mathbbR$ is a linear combination of powers of “linear polynomials in $x_i$'s”Problem 2, Chapter 2 from Herstein's bookPreserving transcendence degreeAn efficient way to check the coefficient of $x_1 x_2…x_n$ in the product of $m$ polynomialsProving the universal mapping property for polynomial rings
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