Advanced Analysis I

General Info:

Prerequisites: MAT 211 and MAT 271 with grade C or better.

Textbook: Introduction to Analysis by Maxwell Rosenlicht ISBN-13: 9780486650388 Dover Publications

References


There are also a few classic analysis books listed in "Suggestions for Further Reading" of our textbook. If you want to go further, read Rudin and Royden's books. (both have newer editions).

Syllabus: The system of real numbers, metric spaces, continuous functions and differential functions. This roughly corresponds to Chapter 2, 3 and 4 of the textbook.

Course Management: BlackBoard

LaTeX: is a modern typesetting system for mathematics and more. Visit The LaTeX Project for more information.

Overleaf is a web-base service (has free option) that allows you to use LaTeX without installing it on your machine. ShareLaTeX is another one. And these services are going to merge.

Homework: can earn you up to 5 extra-credit points. To earn them you need to present homework problems in class and typeset them in LaTeX.

Test:

  1. Test 1 (25 pts), on Chapter 2, (9/20)
  2. Test 2 (25 pts), on Chapter 3, (11/01)
  3. Test 3 (25 pts), on Chapter 4, (12/04)
  4. Final Exam (25 pts+5 extra credits), accumulative, (Dec 13) 5:30pm--7:30pm.

Grading Scheme:

A A- B+ B B-
100--93  92--89  88--84  83--79  78--74 
C+ C C- D+ D
73--69 68--64 63--59 58--54 53--50


Schedule Outline: Chapter 2,3 and 4. There are roughly 85 pages of materials.

Tentative Schedule
08-21 The field properties 08-23 Order
08-28 The least upper bound property 08-30 The least upper bound property
09-04 Labor Day 09-06 Existence of square roots
09-11 discussion 09-13 discussion
09-18 discussion 09-20 Test 1
09-25 Metric Spaces 09-27 Open and Closed sets
10-02 Open and Closed Sets 10-04 Convergent sequences
10-09 Completeness 10-11 Completeness
10-16 Compactness 10-18 Compactness
10-23 Connectedness 10-25 discussion
10-30 discussion 11-01 Test 2
11-06 Definition of continuity 11-08 Continuity and Limits
11-13 Continuity of Rational operations 11-15 Continuous functions on a compact space
11-20 Continuous functions on a compact space 11-22 Continuous functions on a connected space
11-27 discussion 11-29 discussion
12-04 Test 3

Learning Outcomes: Please refer to this Expected Outcomes section.

Other Policies: For policies on academic integrity, accommodation for students with disabilities, due dates and make-up work and various other topics, please consult this page .