abstract algebra: a study guide for beginners
... What things are the same? You can add or subtract the same integer on both sides of a congruence, and you can multiply both sides of a congruence by the same integer. You can use substitution, and you can use the fact that if a ≡ b (mod n) and b ≡ c (mod n), then a ≡ c (mod n). (Review Proposition 1 ...
... What things are the same? You can add or subtract the same integer on both sides of a congruence, and you can multiply both sides of a congruence by the same integer. You can use substitution, and you can use the fact that if a ≡ b (mod n) and b ≡ c (mod n), then a ≡ c (mod n). (Review Proposition 1 ...
Some Decision Problems of Enormous Complexity - OSU
... function is finite if and only if its domain is finite if and only if its 1-domain is finite. We write dom(f) for the domain of f and 1-dom(f) for the 1-domain of f. Let f be a k-ary function and E ⊆ 1-dom(f). We write k f|E for the restriction of f to E . Thus f|E ⊆ f, dom(f|E) = k E , and 1-dom(f| ...
... function is finite if and only if its domain is finite if and only if its 1-domain is finite. We write dom(f) for the domain of f and 1-dom(f) for the 1-domain of f. Let f be a k-ary function and E ⊆ 1-dom(f). We write k f|E for the restriction of f to E . Thus f|E ⊆ f, dom(f|E) = k E , and 1-dom(f| ...
A note on a one-parameter family of Catalan
... whose k-th column has generating function g(x)f (x)k . We recall that a number sequence an is “Catalan-like” if none of the Hankel determinants |ai+j |ni,j=0 is zero, while a lowertriangular matrix (an,k ) is called an Aigner matrix if there exist two sequences sn and tn such that a0,0 = 1, a0,k = 0 ...
... whose k-th column has generating function g(x)f (x)k . We recall that a number sequence an is “Catalan-like” if none of the Hankel determinants |ai+j |ni,j=0 is zero, while a lowertriangular matrix (an,k ) is called an Aigner matrix if there exist two sequences sn and tn such that a0,0 = 1, a0,k = 0 ...
Introduction to representation theory
... mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics and quantum field theory. Representation theory was born in 1896 in the work of the German mathematician F. G. Frobenius. This work was triggered by a let ...
... mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics and quantum field theory. Representation theory was born in 1896 in the work of the German mathematician F. G. Frobenius. This work was triggered by a let ...
On complete and independent sets of operations in finite algebras
... In [4] Post obtained a variety of results about truth functions in 2-valued sentential calculus. He studied sets of truth functions which could be used as primitive notions for various systems of 2-valued logics. In particular, he was interested in complete sets of truth functions, i.e., sets having ...
... In [4] Post obtained a variety of results about truth functions in 2-valued sentential calculus. He studied sets of truth functions which could be used as primitive notions for various systems of 2-valued logics. In particular, he was interested in complete sets of truth functions, i.e., sets having ...
