| Math 446 Schedule Text: Closer and Closer Introducing Real Analysis, by Carol Schumacher. [ Math 446 Home | Office Hours ] |
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| Note: Each section of the text contains two types of problems for you to work, exercises and problems. The exercises in a given section are sprinkled throughout that section. We will use the notation E2.3.4 to refer to Exercise 2.3.4 from Section 2.3. The problems in a given section are located at the end of each section. We will use the notation P2.3.4 to refer to Problem 4 at the end of Section 2.3. | |||||
| Week | Dates | Reading Assignment | Homework Assignment | Notebook Due Date |
Exam/Quiz Date |
| 1 | Jan 18 - 20 | Syllabus, Note to the Student, Field Axioms, Order Axioms Pgs 3-6, Sections 1.1, 1.2, 1.3 |
Class: E1.2.4, E1.2.7
Notebook(NB): Solutions to all Exercise(E) problems are expected to be in your notebook. E1.2.3, E1.2.6, P1.2.3, P1.2.5 Class: E1.3.1, P1.3.8(part 1) NB: P1.3.5, P1.3.8 |
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| 2 | Jan 25 - 27 | Excursion A, Least Upper Bound Property Excursion A, Section 1.4 |
Class: P1.3.10
NB: P1.3.9bcdf, P1.3.11, P1.3.12 Class: P1.4.2, P1.4.8 NB: P1.4.1 |
Jan 27 | |
| 3 | Feb 1 - 3 | Least Upper Bound Property, Distances Section 2.1, 2.2 |
Lecture/Activity: Theorem 1.4.4
NB: P1.4.4, P1.4.6, Chapter 2 Exercises Class: P2.2.1, P2.2.2, P2.2.3 NB: P2.2.4, P2.2.5 |
Quiz 1 Feb 3 |
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| 4 | Feb 8 - 10 | Open Sets Section 3.1 |
Class: P3.1.1, P3.1.2, 3.1.4
NB: P2.2.9, P3.1.3 Class: P3.1.7bc, P3.1.10, 3.1.11 NB: P3.1.6, 3.1.7d, 3.1.12(abcde) |
Feb 10 | |
| 5 | Feb 15 - 17 | Sequences, Convergence of Sequences Sections 0.4, 3.2, 3.3 |
Class: P0.4.1, P0.4.4 NB: P0.4.5 |
MIDTERM EXAM 1 |
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| 6 | Feb 22 - 24 | Convergence of Sequences, Sequences in R Sections 3.3, 3.4 |
Class: P3.3.1, P3.3.2, P3.3.3, P3.3.4 Class: P3.3.6, P3.3.7, P3.4.1 NB: P3.3.8 |
Feb 24 | |
| 7 | Mar 1 - 3 | Sequences in R, Excursion D Section 3.4 |
Class: P3.4.2, P3.4.4, P3.4.7
NB: P3.4.6, P3.4.9(parts 4&5) Class: Excursion D, Problem 1, 2b, 3 NB: Excursion D, Problem 4 |
Quiz 2 | |
| 8 | Mar 8 - 10 | Limit Points, Closed Sets, Closure of a Set Sections 3.5, 3.6, 3.7 |
Class: P3.5.3, P3.6.2, P3.6.3, P3.6.5
NB: P3.5.1(ab), P3.5.4(a), P3.6.4, P3.6.8 Class: P3.7.4, P3.7.5(ab) NB: P3.7.1, P3.7.5c, P3.7.6 |
Mar 10 | |
| 9 | Mar 15 - 17 | Limit of a Function at a Point Sections 4.1, 4.2 |
Class: P4.2.1
NB: P4.2.2 Class: P4.3.1, P4.3.2, P4.3.4 NB: P4.3.6, P4.3.9a |
Quiz 3 | |
| Spring Break, March 22-26 | |||||
| 10 | Mar 29 - 31 Continuity, Uniform Continuity Sections 4.3, 4.4 |
Class: P4.4.1, P4.4.2 NB: P4.4.3, P4.4.4 |
MIDTERM EXAM 2 |
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| 11 | Apr 5 - 7 | Functions from R to R Cauchy Sequences, Completeness Sections 5.1, 5.2, 5.3, 6.1, 6.2 |
Class: P5.1.1, P5.1.6, P5.2.4, P5.3.1 NB: P5.3.2, P5.3.3 Class: P6.1.1, P6.1.3, P6.2.1 NB: P6.2.3, P6.2.5 |
Apr 7 | |
| 12 | Apr 12 - 14 | Compactness, Continuity and Compactness Sections 7.1, 7.2 |
Class: E.7.1.2, E7.1.5, P7.1.2, P7.1.4, P7.1.5, P7.1.7, P7.1.14 NB: P7.1.11 Class: P7.2.1, P7.2.2, P7.2.5 NB: P7.2.3, P7.2.4 |
Quiz 4 | |
| 13 | Apr 19 SSRD |
Heine-Borel Theorem Section 7.3 |
Lecture: Heine-Borel Theorem NB: P7.3.1, P7.3.2 |
Apr 21 | |
| 14 | Apr 26 - 28 | Connectedness, Intermediate Value Theorem Sections 8.1, 8.2 Sequences of Functions Section 12.1, 12.2 |
Class: P8.1.1, P8.1.3, P8.2.1 NB: P8.1.2 Class: P12.1.1-5 (small groups each present a different prob), P12.2.6 NB: P12.2.10(ab), P12.2.11(bc) |
Quiz 5 | |
| 15 | May 3 | Interchange of Limit Operations Section 12.4 |
Class: P12.4.2, P12.4.4a NB: 12.4.1 |
FINAL EXAM Sat, May 8 2-5PM |
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