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Math 551 (Fall 2017)

Announcements
  • HW#6 was post and is due Friday, Oct. 20.
  • HW#5 is due Monday, Oct. 16.
  • Office Hours of the week of Oct. 9: Monday, 11am-Noon and 4:30pm-6:30pm, in 809 Van Vleck. 
  • Welcome to the class! The first lecture is at 12:05pm on Wednesday, Sep. 6, in B135 Van Vleck.

Lectures

Time: 12:05pm-12:55pm, on Mondays, Wednesdays, and Fridays
Location: B135 Van Vleck Hall


Instructor

Lu Wang 
Office: 809 Van Vleck Hall


Office Hours

Time: 11am-Noon, on Mondays and Wednesdays
Location: 809 Van Vleck Hall


Textbook

Title: Topology (2nd Edition)
Author: James Munkres
Publisher: PEARSON 
ISBN 13: 9780131816299


Syllabus
  • Elementary Set Theory: sets, Cartesian products, equivalence relations, countability, the real line
  • Basic Topology: metric spaces, topological spaces, basis, continuity, connectedness, compactness

Homework

There will be weekly homework assignments mostly selected from the textbook. Assignments are usually posted here on Fridays and due in the beginning of the lecture on the following Friday. No late homework will be accepted, but the lowest two scores will be dropped when calculating the course grade.
  • HW#1 (due Sep. 15): Section 1: #1, 2, 8, 10
  • HW#2 (due Sep. 22): Section 2: #1, 4, 5; Section 3: #4, 9; Section 5: #1
  • HW#3 (due Sep. 29): Section 6: #2, 3, 5, 6; Section 7: #1, 2, 3. For Honor Students: Section 6: #7
  • HW#4 (due Oct. 6): Section 13: #1, 3, 4, 5. For Honor Students: Section 13: #7
  • HW#5 (due Oct. 16): Section 16: #1, 3, 4, 6; Section 17: #6, 8(a)(b). For Honor Students: Section 16: #9, 10; Section 17: #8(c)
  • HW#6 (due Oct. 20): Section 17: #9, 11, 12, 13. For Honor Students: Section 17: #19
  • HW#7 (due Oct. 27): Section 18: #3, 4, 5, 6, 10, 11, 12

Exams

There will be two close-book (i.e., no textbook, notes, homework, etc. are allowed), in-class midterm exams and one take-home final. Make-up exams will be provided only with the instructor's consent, and only in case of illness, academic conflicts, or family emergency. The tentative exam times are listed here.
  • Midterm I: Oct. 11, in class (Chapter 1: Sections 1--7; Chapter 2: Sections 12--15)
  • Midterm II: Nov. 15, in class
  • Final: due Dec. 19, take-home

Grading
  • Homework: 20% 
  • Midterm I: 25%
  • Midterm II: 25%
  • Final: 30% 

Letter grades for the course will be roughly assigned according to the following standard:

  • A: 90+
  • AB: 86+
  • B: 77+
  • BC: 72+
  • C: 60+
  • D: 48+
  • F: 0+

Lecture Schedule

The following lecture schedule will be updated during the semester.
  • Week of Sep. 6
    • Introduction
    • Logic and elementary set theory: Munkres 1-1
  • Week of Sep. 11 
    • Functions, domain and range: 1-2
    • Injective, surjective, bijective functions: 1-2
    • Inverse image of sets in range of functions: 1-2
    • Relations and equivalence relations: 1-3
    • Order relations and dictionary relations: 1-3
  • Week of Sep. 18
    • Supremum and infimum: 1-3
    • Real numbers, well-ordering property and induction: 1-4
    • Finite and countable Cartesian product: 1-5
    • Finite sets: 1-6
    • Proof that cardinality of a finite set is well-defined: 1-6
    • Finite unions and finite cartesian products of finite sets are finite: 1-6
  • Week of Sep. 25 
    • Infinite sets, countably infinite: 1-7
    • Countable union of countable sets is countable
    • Finite Cartesian product of countable sets is countable
    • {0,1}^\omega is uncountable
    • The set of real numbers is uncountable
    • The power set of X cannot be in bijection with X
    • Definition of a topology: 2-12
    • Discrete and trivial topologies
  • Week of Oct. 2 
    • Basis for a topology: 2-13
    • Subbasis for a topology
    • The Order Topology: 2-14
    • The Product Topology: 2-15
  • Week of Oct. 9 
    • The Subspace Topology: 2-16
    • Midterm I on Oct. 11
    • Closed sets: 2-17
    • Closure and interior of a set
  • Week of Oct. 16 
    • Limit points: 2-17
    • Hausdorff spaces
    • Continuous functions: 2-18
    • Homeomorphisms and embeddings
  • Week of Oct. 23 
    • Rules for continuous functions: 2-18
    • Pasting together continuous functions
    • Continuous maps into product spaces
    • Arbitrary Cartesian products: 2-19
    • Comparison of Box and Product Topologies
  • Week of Oct. 30 
    • TBA
  • Week of Nov. 6 
    • TBA
  • Week of Nov. 13 
    • Midterm II on Nov. 15
  • Week of Nov. 20 
    • No class on Nov. 24 due to thanksgiving recess
  • Week of Nov. 27 
    • TBA
  • Week of Dec. 4 
    • TBA
  • Week of Dec. 11 
    • TBA
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