Mathematics 5318 - Intermediate Analysis I - Spring 2003
Class Schedule and Homework Assigment

 The problems without * will not be graded, they are meant for practice. You only need to turn in the problems with *.

 Class Date Day Topic Problems 1 Jan 15 Wed 1.1 Sets and Elements 1.1 # 1 -- 4 1.2 Operations on Sets 1.2 # 6, 7*, 8*, 9a)*,b)* 2 Jan 17 Fri 1.3 Functions 1.3 # 2*,13 1.4 Real-valued functions 1.4 # 1*,2*, 5 3 Jan 22 Wed 1.5 Equivalence, countability 10.5 # 3, 4, 5*, 8*, 9* 4 Jan 22 Wed 1.6 Real Numbers 10.6 # 1*, 3*, 5 5 Jan 24 Fri 1.7 Least upper bounds 1.7 # 3*, 4*, 5* 6 Jan 24 Fri 2.1 Sequences 2.1 # 2,3,5*,6* 7 Jan 27 Mon 2.2 Limit of a sequence 2.2 # 7, 11 8 Jan 27 Mon 2.3 Convergent sequences 2.3 # 4, 5* 2.4 divergent sequences 2.4 # 2*, 3* (hint for 3: rationalize) 9 Jan 29 Wed 2.5 Bounded Sequences 2.5 # 2*,3*,5 2.6 Monotone sequences 2.6 # 10* 10 Jan 29 Wed 2.7 Operations on convergents sequences 2.7 # 11* 2.8 Operations on divergent sequences 2.8 # 1, 2, 3 11 Jan 31 Fri 2.9 Limit superior and limit inferior 2.9 # 6* 12 Jan 31 Fri 2.9 Limit superior and limit inferior (continued) 2.9 # 6* 13 Feb 3 Mon 2.10 Cauchy sequences 2.10 # 1, 4*,6 14 Feb 5 Wed 2.11 Summability of sequences 2.11 # 3,5*,6 Feb 7 -- 14 -- No classes, will be visiting the MSRI in Berkeley. Corresponding topics were taught on Jan 22--29 extra sessions. 15 Feb 17 Mon 3.1 Convergence and divergence of series 3.1 # 7* 3.2 Series with nonnegative terms 3.2 # 3* 16 Feb 19 Wed 3.3 Alternating Series 3.3 4* 3.4 Conditional convergence and absolute convergence 3.4 5* 17 Feb 20 Fri 3.5 Rearrangements of series 3.5 4,5 18 Feb 24 Mon 3.6 Tests for absolute convergence 3.6 6*, 12 19 Feb 26 Wed 3.7 Series whose terms form a nonincreasing sequence 3.7 # 4* 3.8 Summation by parts 3.8 # 1*, 2 20 Feb 28 Fri 3.9 (C,1) summability of series 3.9 # 1,5*,6 3.10 The class l^2 3.10 # 2*,3,4*,7 21 Mar 3 Mon 3.11 The real numbers 3.11 # 3* 22 Mar 5 Wed Problem Session I 23 Mar 7 Fri Test I: Chapters 1, 2 & 3 24 Mar 10 Mon 4.1 Limit of a function on the real line 4.1 # 1b), 2a), 12*, 14* 25 Mar 12 Wed 4.2 Metric spaces 4.2 # 3*,7* Mar 14 -- No classes, gone for the Arizona Winter School. Corresponding topics were taught on the Jan 31 extra session. Mar 15 -- 23 -- Spring Break 26 Mar 24 Mon 4.3 Limits in metric spaces 4.3 # 6*,7* 27 Mar 26 Wed 5.1 Functions continuous at a point of the real line 5.1 # 3*,6* 5.2 Reformulation 5.2 # 1,2,3 28 Mar 28 Fri 5.3 Functions continuous on a metric space 5.3 # 5*,7,8*,9 5.4 Open sets 5.4 # 1*,6* 29 Mar 31 Mon 5.4 Open sets (continued) 5.4 # 1*,6* 5.5 Open sets 5.5 # 10*,13* 30 Apr 2 Wed 5.6 Discontinuous functions on R^1 13.4 # 3*,4* 31 Apr 4 Fri 5.7 The distance from a point to a set 13.5 # 1* 32 Apr 7 Mon 6.1 More about open sets 6.1 # 1*, 3* 6.2 Connected sets 6.2# 1*,3*,8 33 Apr 9 Wed 6.3 Bounded sets and totally bounded sets 6.3 # 7* 34 Apr 11 Fri 6.4 Complete metric spaces 6.4 # 4*, 6* 37 Apr 14 Mon 6.5 Compact metric spaces 6.5 # 8*,9*,10*,11 36 Apr 16 Wed Problem Session II 37 Apr 18 Fri Test II: Chapters 4 & 5 Monday, April 21 -- Easter Holiday -- No classes 38 Apr 23 Wed 6.5 Compact metric spaces (continued) 6.5 # 8*,9*,10*,11 39 Apr 25 Fri 6.6 Continuous functions on compact metric spaces 6.6 # 5* 40 Apr 28 Mon 6.7 Continuity of the inverse function 6.7 # 4* 41 Apr 30 Wed 6.8 Uniform continuity 6.8 # 5*,7* 42 May 2 Fri Problem Session III 43 May 5 Mon Problem Session IV May 9 Fri Final Exam, 10:30 a.m. - 1:00 p.m.