Schedule for Math 432
(Real Analysis)
Dates 
Class Notes and Reading
Assignments 
Exercises for Class and
Homework Exercises in red are due next class. Exercises in
green should already have been submitted. 
01/16 M 
Definitions 1 to 4 
Exercise 1 
01/18 W 
Definitions 5 to 9 
Exercise 2 
01/20 F 
Theorem 1, Definition 10 
Exercises 3, 4,
5, 6 
01/23 M 
Theorem 2 
Exercises 7,
8, 9, 10 
01/25 W 
Definitions 11 to 13,
Example 1 
Exercises 11,
12, 16 
01/27 F 
Definitions 14 to 17,
Examples 2 to 4 
Exercises 13,
14, 17 
01/30 M 
Theorems 3 and 4, Examples
5 and 6 
Exercises 15, 18, 19, 20 
02/01 W 
Test #1 
Three proofs selected from Exercises
12, 13, 14, 15 
02/03 F 
Definition 18, Symbolic
Representation of Large Integers 
Exercises 22, 23, 34, 35 
02/06 M 
Decimal Representation of
Rational Numbers, Example 7 
Exercises 21,
24, 25, 26, 27, 28, 29 
02/08 W 
Definition 19, Theorems 5
and 6, Examples 8, 9, 10, 11, 12 
Exercises 30, 31, 32, 33, 37 
02/10 F 
Definition 20, Theorem 7,
Example 13 
Exercises 36, 38,
39, 40, 41, 42, 43 
02/13 M 
Infinity Notes: Definitions 1.1, 1.2, 1.3, 1.4, Exercises I1(a),
I2 
Exercises I3
 ONLY the upper and lower bounds & the max and min 
02/15 W 
Infinity Notes: Definitions 1.9, 1.10, Completeness Axiom,
Archimedean Property 
Exercises I3 (All), I4, I5 
02/17 F 
Infinity Notes: WellOrdering Property 
Exercises I8,
I9 
02/20 M 
Exercises I10, I12 
Exercises I11,
I13 
02/22 W 
Test #2 

02/24 F 
Sequences, arithmetic and
geometric progressions Exercises I14(a), I15,
I16 
Exercises
I14(b), I17, I18 
02/27 M 
Definition of convergence
of a sequence, Exercises I19, I20 
Exercises I21,
I22 
03/01 W 
Definition of divergence of
a sequence, Theorems 2.11, 2.14, 2.15, Exercise I25 
Exercises I23,
I24, I26 
03/03 F 

Complete the
proof of Theorem 2.15 
03/06 M 
Theorems 2.16, 2.17,
Exercise I29 
Exercises I27,
I28 
03/08 W 
Interval Arithmetic 
Exercises 44, 45,
46 
03/10 F 
More Interval Arithmetic 
Exercises 47, 48,
49 
03/13 to 03/17 
***** Spring Break: NO CLASSES ***** 

03/20 M 


03/22 W 
Polynumbers and their properties 
Exercises 50, 51,
56, 57 
Fundamental Theorem of
Arithmetic (Theorem 8) 
Exercises 52, 53,
58 

03/24 F 
Evaluation of polynumbers 
Exercises 54, 55,
59 
03/27 M 
Descartes Factor Theorem
(Theorem 9) 
Exercises 61, 62,
63 
03/29 W 
Evaluation of rational polynumbers 
Exercises 60 
03/31 F 
Field extension and
extended rational numbers 
Exercises 64 
04/03 M 
Test #3 

04/07 F 
***** NO CLASSES ***** 

04/10 M 


04/12 W 
Summations and series,
Theorem 12 (Binomial Expansion) 
Exercises 68, 69, 70, 71 
04/14 F 
Sums of Powers of the First
n Positive Integers 
Exercises 72, 73, 74 
04/17 M 
Bernoulli numbers and the
“derivative” and “integral” operators, Theorem 13 

04/19 W 
Test #4 

04/21 F 
Affine points and lines 

04/24 M 


04/26 W 


04/28 F 


05/0105/05 
Final Exam (in the time slot
on the final exam schedule) 