University of Michigan - Shanghai Jiao Tong University Joint Institute


Vv 186:  Honors Mathematics II

General information

Credits: 4 credits. No credits are counted towards graduation for those who have completed Vv156.
Prerequisites: having passed math placement test
Background and Goals: The sequence Honors Mathematics Vv186-285-286 is an introduction to calculus at the honors level. It differs from the Honors Calculus sequence in that new concepts are often introduced in an abstract context, so that they can be applied in more general settings later. Most theorems are proven and new ideas are shown to evolve from previously established theory. Initially, there are fewer applications, as the emphasis is on first establishing a solid mathematical background before proceeding to the analysis of complex models. The present course covers the calculus of functions of a single real variable.
Content: Elements of logic; set theory; properties of real and complex numbers; sequences, convergence, completeness of metric spaces; functions, convergence and continuity; the derivative and applications; normed vector spaces; series and power series; transcendental functions; the regulated and Riemann integrals and applications; the Lebesgue integral (as time permits).
Alternatives: Vv156 (Honors Calculus II) is an applications-oriented course, which covers much of the samematerial.