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. |
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01/16 M |
Definitions 1 to 4 |
Exercise 1 |
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01/18 W |
Definitions 5 to 9 |
Exercise 2 |
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01/20 F |
Theorem 1, Definition 10 |
Exercises 3, 4,
5, 6 |
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01/23 M |
Theorem 2 |
Exercises 7,
8, 9, 10 |
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01/25 W |
Definitions 11 to 13,
Example 1 |
Exercises 11,
12, 16 |
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01/27 F |
Definitions 14 to 17,
Examples 2 to 4 |
Exercises 13,
14, 17 |
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01/30 M |
Theorems 3 and 4, Examples
5 and 6 |
Exercises 15, 18, 19, 20 |
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02/01 W |
Test #1 |
Three proofs selected from Exercises
12, 13, 14, 15 |
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02/03 F |
Definition 18, Symbolic
Representation of Large Integers |
Exercises 22, 23, 34, 35 |
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02/06 M |
Decimal Representation of
Rational Numbers, Example 7 |
Exercises 21,
24, 25, 26, 27, 28, 29 |
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02/08 W |
Definition 19, Theorems 5
and 6, Examples 8, 9, 10, 11, 12 |
Exercises 30, 31, 32, 33, 37 |
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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 |
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02/17 F |
Infinity Notes: Well-Ordering Property |
Exercises I-8,
I-9 |
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02/20 M |
Exercises I-10, I-12 |
Exercises I-11,
I-13 |
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02/22 W |
Test #2 |
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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 |
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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 |
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03/10 F |
More Interval Arithmetic |
Exercises 47, 48,
49 |
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03/13 to 03/17 |
***** Spring Break: NO CLASSES ***** |
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03/20 M |
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03/22 W |
Polynumbers and their properties |
Exercises 50, 51,
56, 57 |
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Fundamental Theorem of
Arithmetic (Theorem 8) |
Exercises 52, 53,
58 |
|
|
03/24 F |
Evaluation of polynumbers |
Exercises 54, 55,
59 |
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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 |
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04/03 M |
Test #3 |
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04/07 F |
***** NO CLASSES ***** |
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04/10 M |
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04/12 W |
Summations and series,
Theorem 12 (Binomial Expansion) |
Exercises 68, 69, 70, 71 |
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04/14 F |
Sums of Powers of the First
n Positive Integers |
Exercises 72, 73, 74 |
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04/17 M |
Bernoulli numbers and the
“derivative” and “integral” operators, Theorem 13 |
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04/19 W |
Test #4 |
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04/21 F |
Affine points and lines |
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04/24 M |
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04/26 W |
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04/28 F |
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05/01-05/05 |
Final Exam (in the time slot
on the final exam schedule) |
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