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 I-1(a), I-2 Exercises I-3 - 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 I-3 (All), I-4, I-5 02/17 F Infinity Notes: Well-Ordering Property Exercises I-8, I-9 02/20 M Exercises I-10, I-12 Exercises I-11, I-13 02/22 W Test #2 02/24 F Sequences, arithmetic and geometric progressions Exercises I-14(a), I-15, I-16 Exercises I-14(b), I-17, I-18 02/27 M Definition of convergence of a sequence, Exercises I-19, I-20 Exercises I-21, I-22 03/01 W Definition of divergence of a sequence, Theorems 2.11, 2.14, 2.15, Exercise I-25 Exercises I-23, I-24, I-26 03/03 F Complete the proof of Theorem 2.15 03/06 M Theorems 2.16, 2.17, Exercise I-29 Exercises I-27, I-28 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 05/01-05/05 Final Exam (in the time slot on the final exam schedule)