Prerequisites:  MAT 222 and MAT 301 or graduate standing.

Course Outline:  The typical mathematics student begins their mathematical career by learning about limits, derivative and integrals, and their numerous applications in Calculus.  In developing these concepts, the focus is generally on the outcomes and how the tools will be used.  In this course (often called Advanced Calculus), the student will revisit the topics presented in Calculus but on a deeper level, attempting to gain greater understanding of the underlying principles involved.  Also, many results will be generalized to more abstract situations.

(From the college catalog:  Set Theory, the real number system, metric spaces, continuous functions, differentiation and integration.)

Goals: Investigate the following, time permitting:

• The Field and Order Axioms, The Well-Ordering Principle and The Completeness Axiom
• Functions  and Countability
• Limits of Sequences and the Bolzano-Weierstrass Theorem
• Cauchy Sequences 
• Continuity of Real Functions
• Differentiability of Real Functions
• Integrability of Real Functions using the Riemann Integral
  
• Infinite Series
• Sequences and Series of Functions

Meetings: The format of class meetings will consist of lectures by the instructor and presentations by the students. Student participation will be encouraged via classroom discussions as well as problem sessions where the student will present their work.

This class meets as scheduled. You are expected to be in class on time. University policy states that a student cannot miss more than 25% of the class meetings and receive credit for the course. Further, attendance will be necessary in order to understand the material and make a good grade. The student is responsible for work and material missed when absent. Cheating in any way will be properly rewarded in accordance to University policy.

Grading: There will be several assignments during the semester plus a midterm and a comprehensive final exam. In addition, students will work numerous homework problems in class on the board. Further, some papers may be assigned for the student to review. Graduate students will be assigned some topics to research and to prepare a review of their findings.

For undergraduates, the final average will be determined using equally the two exams with an average of the homework/paper grades .
For graduates, the final average will be determined using equally the exams, an average of the homework grades and an average of the homework and written assignments.
The Grading scale is