INTRODUCTION
TO REAL ANALYSIS
William F.Trench
Andrew G. Cowles Distinguished Professor Emeritus
Department of Mathematics
Trinity University
San Antonio, Texas, USA
wtrench@trinity.edu
This book has been judged to meet the evaluation criteria set by
the

Not Always Buried Deep
Selections from Analytic and Combinatorial
Number Theory
c 2003, 2004
Paul Pollack
2003 Summer Course Notes
Ross Summer Mathematics Program
First Draft: June 9, 2003
Second Draft: November 16, 2003
Last updated: May 9, 2004
In memor

Notes on the equivalence of norms
Steven G. Johnson, MIT Course 18.335
September 19, 2012
If we are given two norms k ka and k kb on some finite-dimensional vector space V over C, a very
useful fact is that they are always within a constant factor of one

University of Victoria
Notes for Math 322:
Intermediate Combinatorics
Peter Dukes and Gary MacGillivray
April 5, 2011
Contents
1 Generating Subsets and Permutations
1
2 Systems of Distinct Representatives
11
3 Posets and extremal set theory
19
4 Finite ge

Math 335 Spring 2016
Problem set #1
Due 15 January 2015
(1) Prove that f : I R is differentiable at c I if and only if there exist a number A R
and a function
: I R such that f (x) f (c) = A(x c) + (x) for every x I and
(x)
limxc xc = 0. Show that there