Courses Detail Information
MATH1860J – Honors Mathematics II
Instructors:
Credits:
4 (No credits after Vv116 or Vv156.)
Pre-requisites:
Description:
The Honors Mathematics sequence is an introduction to calculus at the honors level. 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 builds a strong mathematical foundation and covers the calculus of functions of a single real variable.
Course Topics:
1. Elements of logic and set theory
2. Properties of rational, real and complex numbers
3. Sequences, convergence, completeness of metric spaces
4. Real functions, convergence and continuity
5. The derivative and applications
6. Normed vector spaces
7. Sequences of functions
8. Series and power series
9. Exponential and trigonometric functions
10. Regulated, Darboux and Riemann integrals
11. Integration in practice
12. Applications, Taylor’s theorem, Stirling’s formula