Math 431 Spring 2018

Syllabus

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
Friday January 12 Sets, truth tables 1.1, 1.4 Assignment 1
(due January 24)
Wednesday January 24 Fields; ordered fields; inequalities 1.2
Friday January 26 Archimedean property;the well-ordering and induction principles 1.3 Assignment 2
(due February 2)
Wednesday January 30 Functions; countable sets 2.1 Assignment 3
(February 9)
Friday February 2 Uncountable sets 2.2
Wednesday, February 7 Sequences, convergence, examples 2.2
Friday February 9 Properties of convergent sequences, Cauchy sequences, sup, inf 2.4, 2.5 Assignment 4
(due February 16)
Wednesday February 14 Axiom C is equivalent to l.u.b. axiom 2.4,2.5
Friday February 16 Axiom C is equivalent to convergence of Cauchy sequences plus the Archimedean property; equivalence relations 2.5 Assignment 5
(due February 23)
Wednesday February 21 Bolzano-Weierstrass; the four equivalent properties of the real numbers 2.6 Office Problem
(due March 23)
Friday February 23 Continuous functions 3.1 Assignment 6
(due March 2)
Wednesday February 28 Continuous functions on closed intervals
Friday March 2 Uniform Continuity; upper and lower sums 3.3 Assignment 7
(due March 9)
Wednesday March 7 Riemann Integral 4.1
Friday March 9 Properties of the Riemann integral 4.1 Assignment 8
(due March 23)
Wednesday March 21 Chain rule, mean value theorem 4.2
Friday March 23 FTC 4.2 Assignment 9
(due March 30)
Wednesday March 28 Natural log and exponential, Taylor series 4.3
Friday March 30 Estimates with Taylor series 4.6
Wednesday April 4 Functions of several variables
Friday April 6 The derivative of a function of several variables 5.1 Assignment 10
(due April 13)
Wednesday April 11 Uniform convergence 5.2
Friday April 13 sup norm and completeness 5.3 Assignment 11
(due April 20)
Wednesday April 18 Properties of uniform convergence 5.6
Friday April 20 Construction of exponential function, Picard iteration 5.7 Assignment 12
(due April 25)
Wednesday April 25 Metric spaces;contraction mapping principle 5.7

Final Exam:: Friday May 4, 2-5PM



Last modified: