| Math 139 | Spring 2008 |
This is a tentative schedule of lecture topics, exams and assignments. You are expected to read and study the text as we go along. Whether you study the text before or after the lecture is up to you; the best approach might be to do both. Assignments are due at the beginning of class on the indicated due date.
The assignments and handouts are PDF files which may be viewed or printed with a recent version of the free Adobe Acrobat Reader.
I stress that the exam times and assignment due dates indicated here are subject to change.
| Date | Topics | Text | Assignments |
| Thursday January 10 | Sets, truth tables; fields | 1.1, 1.4 | Assignment 1 (due 17 January) |
| Tuesday January 15 | Ordered fields and inequalities; Archimedean principle | 1.2, 1.3 | |
| Thursday January 17 | Functions; cardinality; the well-ordering and induction principles | 2.1 | Assignment 2 (due 24 January) |
| Tuesday January 22 | countable sets | 2.2 | |
| Thursday January 24 | Uncountable sets; sequences, convergence | 2.2 | Assignment 3 (due January 31) |
| Tuesday January 29 | Properties of convergent sequences, Axiom C | 2.3 | |
| Thursday January 31 | Completeness, least upper bound, Cauchy sequences | 2.4, 2.5 | Assignment 4 (due February 7) |
| Tuesday February 5 | Cauchy sequences (cont.); equivalence relations;Construction of the real numbers using Cauchy sequences | 2.6 | |
| Thursday February 7 | Bolzano-Weierstrass; continuous functions | 3.1 | Assignment 5 (due February 14) |
| Tuesday, February 12 | Uniform continuity | 3.2 | |
| Thursday, February 14 | Riemann integral | 3.3 | Assignment 6 (due February 21) |
| Tuesday February 19 | Existence of the Riemann integral | ||
| Thursday February 21 | Properties of the Riemann integral; the derivative | 4.1 | Assignment 7 (due February 28) |
| Tuesday February 26 | Chain rule, mean value theorem | 4.2 | |
| Thursday February 28 | Fundamental theorem | Assignment 8 (due March 6) | |
| Tuesday March 4 | Taylor's Theorem | 4.3 | |
| Thursday March 6 | Examples of Taylor's theorem | 4.5, 4.6 | Assignment 9 (due March 20) |
| Tuesday March 18 | Inverse functions | 4.5, 4.6 | |
| Thursday March 20 | Exam | ||
| Tuesday, March 25 | Functions of several variables | 4.6 | |
| Thursday, March 27 | Functions of several variables | 4.6; 5.1 | Assignment 10 (due 3 April) |
| Tuesday April 1 | Pointwise and uniform convergence | 5.1 | |
| Thursday April 3 | Properties of uniform convergence | 5.2 | Assignment 11 (due April 10) |
| Tuesday April 8 | Metric spaces | 5.6 | |
| Thursday April 10 | Examples of metric spaces | 5.6 | Assignment 12 (due 23 April) |
| Tuesday April 15 | Equivalence of metrics, convergence | 6.2 |