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Instructor
Dr. William J. Thistleton, Associate Professor of Mathematics
Donovan 2269
315-792-7508
thistlet@sunyit.edu

Find us on the Web
http://math.sunyit.edu/math/mat425

Class Meetings
Classes meet on Monday and Wednesday evenings from 4:00 - 5:50 PM in Donovan G244.

Office Hours
Formal office hours will be on Tuesdays and Thursdays from 2:00 till 4:00 PM in my office.

Prerequisites
Calculus III, MAT323 or equivalent.

Course Description
This course introduces the student to a rigorous development of the real number system and the theory of Calculus on the real number line. Topics include: basic set theory, the real number system, sequences and series, limits and continuity, the derivative, the Riemann Integral, the Fundamental Theorem of Calculus, and sequences and series of functions.

Required Text
Elementary Analysis, The Theory of Calculus, by Kenneth A. Ross, Springer UTM (1980), ISBN 978-0387904597.

Attendance
Your presence in class is needed on a daily basis. The material presented in this course continually builds upon past lectures. Please don't fall behind!

Course Outline

• Preliminaries: Proofs, Naturals, Rationals, Reals, Completeness, Infinity
• Basic Set Theory
• Fields
• Intervals, Neighborhoods, Upper and Lower Bounds, liminf, limsup
• Decimal Expansions
• Basic Topology and the Real Numbers
• Sequences and Series of Numbers
• Continuity and Uniform Continuity
• Limits of Functions
• Sequences and Series of Functions
• Differentiation (MVT, L'Hopital, Taylor)
• Integration (Riemann, FTC, Riemann Stieltjes, etc.)

Texts for further reading

• Real Analysis, by H. L. Royden, MacMillan (1976).
• Principles of Mathematical Analysis, by W. Rudin, McGraw Hill (1976).
• Real Analysis, A First Course with Foundations, by M.N. Pownall, Wm. C. Brown (1994)
• The Elements of Real Analysis, by R. G. Bartle, John Wiley and Sons (1975).
• Undergraduate Analysis, by S. Lang, Springer-Verlag (1983).
• Advanced Calculus, An Introduction to Analysis, by W. Fulks, John Wiley and Sons (1969).
• Probability and Measure by Patrick Billingsley, John Wiley and Sons (1995).

Methods of Evaluation
There will be two ``in class'' exams and a final. There will also be weekly homework assignments and class presentations. The breakdown for these is as follows:

• 25% for each exam
• 25% for final
• 25% for homework, attendance, and presentations.