New Syllabus Algebra

Algebra Oral Qualifying Exam Syllabus

algebra is the study of fundamental algebraic structures that occur throughout mathematics: groups, rings, modules, categories, and fields—as well as maps between them. A solid grasp of algebra can be useful to students of all mathematical stripes, and accordingly the suggested syllabus is a “strong core plus more” model: a student preparing for an oral qualifying exam in algebra should (1) fee...

Algebra Qualifying Exam Syllabus and Suggested References

A new branch of the logical algebra: UP-algebras

In this paper, we introduce a new algebraic structure, called a UP-algebra (UP means the University of Phayao) and a concept of UP-ideals, UP-subalgebras, congruences and UP-homomorphisms in UP-algebras, and investigated some related properties of them. We also describe connections between UP-ideals, UP-subalgebras, congruences and UP-homomorphisms, and show that the notion of UP-algebras is a ...

Setting a New Syllabus: Environmental Health Science in the Classroom

Environmental health is a subject that has only relatively recently become prominent in the social consciousness. Even as its significance becomes known, finding ways to integrate the subject into education for primary and secondary students is difficult because of federal testing requirements under the No Child Left Behind Act of 2001 and other demands placed on teachers. A number of efforts a...

Syllabus: Bifurcations

Recall that a homeomorphism is a continuous bijection with a continuous inverse. Definition 1.1. Let U be a domain in R. Consider vector fields X,Y ∈ X(U) with flows F , F : I × U → U , where I is an open interval in R such that 0 ∈ I. The dynamics of X and Y is said to be C-equivalent if there exists a homeomorphism φ : U → U with the following property: for all t ∈ I there exists a t′ ∈ I suc...