Department of Mathematics Statistics MAT 315 Introduction to

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					                     Department of Mathematics & Statistics
                                   MAT 315
                            Introduction to Analysis
                         Spring 2004 (3 Credit Hours)
Instructor:           Kirk E. Jones
Office:               Wallace 414
Phone:                622-6175 (Office), 624-0826 (Home), 622-5942 (Departmental Office)

Prerequisite:         MAT 301 with a minimum grade of "C".

Primary References: Principles of Mathematical Analysis by Walter Rudin
                    Counterexamples in Analysis by Gelbaum & Olmstead

Topics:               Real Number System, Continuity and its consequences, Differentiation and
                      its consequences, Riemann-Stieljes Integration, and Sequences and Series.

Course Objectives:
                      (1)    To advance the proof-writing skills of the students.
                      (2)    To extend the students understanding of the real number system.
                      (3)    To provide a rigorous foundation to the central concepts of calculus
                             by furnishing detailed proofs of the main results concerning limits,
                             continuity, sequences, differentiation, and integration.
                      (4)    To provide an assortment of examples ( and counter-examples ) to
                             primary results of elementary analysis.
                      (5)    Work and learn cooperatively.

Students’ grades will be based on:
       1.     Homework: One or two homework problems will generally be assigned on a daily
              basis and collected the next class period. No late homework will be accepted
              although you may drop the four lowest homework sets. The students are encouraged
              to work in groups when solving homework problems and studying for examinations
              but the final write-up of homework sets must be a representation of your own work.
              Homework will carry a weight of 60% in the final course grade.
       2.     There will comprehensive final exam. Final exam questions will be drawn from
              lecture notes, primary reference material, assigned homework problems, and
              problems from selected texts (see supplemental reading list). The exams are likely
              to contain eight problems from which the students choose five to solve. The final
              exam will be worth 40% of the course grade.
Students are expected to study a minimum of three hours outside class for each hour of class. Hence,
you should average a minimum of 9 hours per week reviewing the lecture notes, solving assigned
homework problems, reading the primary reference material, looking over supplemental materials
and generally synthesizing the course material.

1.     The material in this course appears in such national exams as the PRAXIS Exam and the
       GRE subject exam in mathematics. Therefore, secondary education majors in mathematics
       and students planning to attend graduate school must learn and retain this material beyond
       the time constraints of this class - study accordingly!
2.     March 5, 2004 - Last day to withdraw from full-semester classes.
3.     Missed exams will only be excused if the instructor is notified with a valid excuse such as
       a University excuse, doctor’s excuse, or verifiable catastrophic event. Failure to notify the
       instructor prior to missing an exam will substantially reduce your chances of taking a make-
       up exam.
4.     Cheating on any exam will result in a course grade of “F”.
5.     If you are registered with the Office of Services for Individuals with Disabilities, please
       make an appointment with the course instructor to discuss any academic accommodations
       you need. If you need academic accommodations and are not registered with the Office of
       Services for Individuals with Disabilities, please contact the Office directly either in person
       on the first floor of the Turley House or by telephone at (859) 622-1500 V/TTY. Upon
       individual request, this syllabus can be made available in alternative forms.

Supplemental Reading Material (in no particular order):

       Introductory Analysis                          Analysis with an Introduction to Proof
       by J. A. Friday                                by Steven R. Lay

       Methods of Real Analysis                       Advanced Calculuc
       by Richard Goldberg                            by R. Creighton Buck

       Introduction to Real Analysis                  A First Course in Real Analysis
       by Robert Bartle & Donald Sherbert             by M.H. Protter & C.B. Morrey

       Mathematica Analysis: An Introduction          An Introduction to Analysis
       by Andrew Browder                              by William R. Wade