SYLLABUS FOR MATHEMATICS CS117: FALL 2016

MWF 1, BLDG 494, Room 164B

Professor: John Douglas Moore, MWF 2 or by appointment, SH6714

Email: moore@math.ucsb.edu

Web page: http://math.ucsb.edu/~moore/CS117Syllabus2016.htm

Text: Edward D. Gaughan, Introduction to real analysis, 5^th edition, Brooks-Cole,Pacific Grove CA, 1998.

Outline of course:

The purpose of this course is to develop techniques for proving theorems about the functions one encounters in calculus. The course will be mostly based upon Chapters 0-4 of the text.

A prerequisite for this course is an understanding of the basic principles of mathematical proof, and the theory of sets and functions. We will give a brief review of set theory and functions during the first week of the course. We will then discuss in succession: sequences, limits, continuity and differentiation.

Homework: Homework will be assigned each Friday and will be due the following Friday.

Quizzes: A few quizzes will be given at various times during the quarter. These will be announced during the lecture just prior to the quiz.

Tentative Schedule:

Monday, January 4: Sets, relations and functions (sections 0.1, 0.2 in text)

Wednesday, January 6: Inductions and cardinality (0.3,0.4)

Friday, January 8: Real numbers (0.5)

Monday, January 11: Convergence of sequences I (1.1,1.3)

Wednesday, January 13: Convergence of sequences II (1.1,1.3)

Friday, January 15: Cauchy sequences (1.2)

Monday, January 18: HOLIDAY

Wednesday, January 20: Subsequences I (1.4)

Friday, January 22: Subsequences II (1.4)

Monday, January 25: Limits of functions I (2.1,2.2)

Wednesday, January 27: Limits of functions II (2.1,2.2)

Friday, January 29: Limits of functions III (2.1,2.2) QUIZ

Monday, February 1: Algebra of limits I (2.3)

Wednesday, February 3: Limits of monotone functions I (2.4)

Friday, February 5: Limits of monotone functions II (2.4)

Monday, February 8: Continuity I (3.1,3.2)

Wednesday, February 10: Continuity II (3.1,3.2)

Friday, February 12: Open, closed and compact sets I (3.3)

Monday, February 15: HOLIDAY

Wednesday, February 17: Open, closed and compact sets II (3.3)

Friday, February 19: Open, closed and compact sets III (3.3) QUIZ

Monday, February 22: Properties of continuous functions I (3.4)

Wednesday, February 24: Properties of continuous functions II (3.4)

Friday, February 26: Derivative of a function I (4.1, 4.2)

Monday, February 29: Derivative of a function II (4.1, 4.2)

Wednesday, March 2: Mean value theorem I (4.3)

Friday, March 4: Mean value theorem II (4.3)

Monday, March 7: Inverse function theorem I (4.4)

Wednesday, March 9: Inverse function theorem II(4.4)

Friday, March 11: QUIZ