MATH 462
Introduction to Topology
Syllabus for Fall 2017
Mon, Wed, & Fri, 2:00 – 2:50pm
307 Pasteur Hall
Instructor: Dr. Eric Errthum Winona Email Username: eerrthum Office: 205 Gildemeister Hall Office Hours: See homepage. Or by appointment on any day.
Prerequisite: MATH210/MATH327 or any other proof writing background
Text & Calculator: Topology Now! by Messer and Straffin
Course Website: http://course1.winona.edu/eerrthum/math462
About This Course: Topology is the study of spaces/shapes when size and angle don’t matter/aren’t well-defined. In the attempt to classify and understand these spaces, we will find methods of construction, dissection, and computation of invariants. We will work toward an abstraction of the familiar ideas of measurement, continuity and connectedness.
Expectations: Students who complete this course with a passing grade are expected to be able to demonstrate the following skills: (i) Mastery of prerequisite material, (ii) Computations and classifications of objects and spaces, (iii) Understand and use the algebraic tools required in analyzing topological spaces, and (iv) work with abstract definitions that provide analogies to calculus concepts.
Grading: Homework
(scaled as needed) 90
points---- 13.85%
Video Responses (3 @ 30
points) 90
points---- 13.85%
Quizzes (6 @ 30 points
each, drop lowest) 150 points---- 18.46%
Midterms (2 @ 100
points) 200
points---- 30.77%
Final (In-Class) 100
points---- 15.38%
Final (Take-Home) 50
points------ 7.69%
--------------
680 points total
Grades: A = 90% (612 pts), B = 80% (544 pts), C = 70% (476 pts), D = 60% (408 pts)
Homework: The problem numbers for each section are given below in the rough schedule. Homework should be readable or it will not be graded. (If you have any desire to learn how to type your homework in LaTeX, I will gladly show you.) You are strongly encouraged to work with others (in a mutually educational way) and/or come see me during office hours.
Video Responses: Students will respond to the questions for each of three videos:
· Sphere Inside Out (Part 1) (Part 2) – Questions
· Wind and Mr. Ug – Questions, and Mobius Strip Activities – Treat this video like a science lab and answer the questions in the video at the times it wants you to (i.e. before the cutting). Your response do not have to from a coherent narrative. Just answer the questions in the order they are asked.
· Not Knot (Part 1) (Part 2) – Questions
· Extra Credit Video (worth 15 points): Rubber band into Knot – Questions
The due dates are given in the schedule below. Grades will be determined by the level and depth of your responses as well as on readability/grammar. The reflection is to be written as one coherent piece, not just disjointed answers to questions.
Quizzes: We will have a short quiz after each chapter (or set of chapters), see schedule below. The lowest quiz score will be dropped.
Exams: There will be two in-class midterms and one final exam. The
final exam will be like a third midterm with a comprehensive take-home portion.
Exam dates are tentative until officially announced in class. The final exam is
scheduled for Wednesday, December 6th, 10:30am – 12:30pm. The
take-home portion will be due by noon on Thursday, December 7th.
Extra
Credit: There will be bonus
questions on quizzes and exams. If you’d like to do more extra credit, I might
give a lecture (outside of regular class time, 8am?) on a section of the book
or other topic we didn’t cover and assign work from that section.
Resources: You’re more than welcome to stop by during my office hours and ask questions. Really, please do.
Desire2Learn: Some course materials and approximate grades can be found on D2L.
Late/Missed
Work: Missed quizzes will result in a score of zero.
There are no make-up quizzes. Make-up exams will be given at the discretion of
the instructor. If you miss class, it is your responsibility to obtain notes
and assignments from fellow students. If you have an unavoidable absence,
please inform the instructor beforehand.
Academic Dishonesty: Any type of academic dishonesty (cheating, copying, etc.) will result in failure and will be reported to school authorities. This includes homework. If you are having trouble with an assignment, please see the instructor first.
Note: This syllabus is subject to change if deemed necessary by the instructor.
Tentative Schedule of Events – Math 462
(subject to change)
|
Week Starting |
Monday |
Wednesday |
Friday |
|
8/21 |
Introductions 1.1
Equivalence |
1.2
Bijections |
1.3
Continuous Functions |
|
8/28 |
HW 1.1, 1.2 & 1.3 Due 7.1 General Metric Spaces |
7.1, cont. HW (pg 215): 1c, 2c, 5, 6b, 7(part 3), 8, 10, 13 |
7.2 General Topological Spaces HW (pg 221): 3b, 4, 5, 9, 10, 12 |
|
9/4 |
No Class |
Chapter 7 Activity Basis of a Topology |
HW 7.1 & 7.2 Due 1.4
Topological Equivalence HW (pg 23): 5, 6, 7, 9, 11, 15 |
|
9/11 |
1.5,
cont. |
7.3 General Connectedness HW (pg 226): 1, 2, 3, 6, 7 |
HW 1.4 & 1.5 Due 1.6
Isotopy |
|
9/18 |
Chapter 1 Activity Isotopic Letters |
HW 7.3, 1.6 Due Chapter 1 Quiz Midterm
Review |
Midterm I |
|
9/25 |
Video Essay Due: Sphere Inside Out 2.1 Knots, Links
|
2.2
Knot Diagrams Application of polynomial algorithm HW (pg 53): 3, 4, 5, 8, read 11, 13, 14(just the middle one). |
2.3,
cont Two Knots, Same Coloribilty: HW (pg 58): 3, 4, 6, 8, 9, 11 HW (pg 64): 2, 6, 7, 8, 10 |
|
10/2 |
HW 2.1 – 2.3 Due 2.5 The Alexander Polynomial Two
Knots, Same Alex. Poly.: HW (pg 75): 1, 3, 5, 7b, 8, 11bef Mathematica Determinant |
Chapter 2 Activity |
Read the following: Unknotting Unknots (Read pages 1 – 3) Current Simplification Algorithm (Simplify Section) Polynomial Time Unknot Recognition (Read Intro Section) HW: Write/Type a 1-page summary/comparison of the three articles 2.6 & 2.7 Skein Relations and Jones Polynomial Extra
Credit: --------------------- HW 2.4 & 2.5 Due |
|
10/9 |
Chapter 2 Quiz |
HW Article Summary Due 3.1 Surface Definitions HW (pg 95): 1, 4, 5, 7, 9
|
Extra Credit 2.6 & 2.7 Due 7.5 General Quotient Spaces 3.2 Cut-and-paste Techniques HW (pg 230): 2, 4, 5 |
|
10/16 |
3.2,
cont. HW (pg 101): 2, 3, 7, 8, 9, 11 |
3.3
Orientability 3.4 Classification of Surfaces HW (pg 108): 1, 4, 6, 9, 11 |
HW 3.1, 7.5, & 3.2 Due 3.4 Classification of Surfaces, cont. HW (pg 117): 2d, 3, 4bef, 6, 7, 9, 10 Extra Lecture: 3.5 Extra Credit: |
|
10/23 |
HW 3.3 & 3.4 Due Chapter 3 Activity |
Chapter
3 Quiz |
Midterm II |
|
10/30 |
Video Essay Due: Wind and Mr. Ug and Section 4.1 HW (pg 129): 2, 4, 7, 8 |
Extra Credit 3.5 Due Section 4.2 HW (pg 134): 1, 3, 5, 6, 8 |
No Class |
|
11/6 |
7.4 General Compactness HW (pg 228): 1, 3, 5, 6b, 8 |
Section 4.3 HW (pg 141): 2, 3, 4, 7 HW 4.1 & 4.2 Due |
No Class |
|
11/13 |
HW 7.4 & 4.3 Due |
Chapter
4 Quiz HW (pg 172): 3, 4, 5abc, 6a |
Video Essay Due: Not Knot Section 6.2 HW (pg 177): 1, 4, 5, 6
|
|
11/20 |
HW 6.1 & 6.2 Due Section 6.4 HW (pg 189): 1b, 2, 6, 9, 11, 12ab, 14ac, 15, 16, 17 |
NO CLASS |
|
|
11/27 |
Section 6.5 HW (pg 199): 5, 7, 8, 9, 10, 13 Section 6.6 HW (pg 207): 1, 5 --------------------- Extra Lecture: This
pdf Document Extra Credit: Extra Credit Video Essay Due: |
HW 6.4
- 6.6 Due Chapter 7 Quiz Final Review (Chaps 1 – 3) |
Chapter 6 Quiz Final Review (Chaps 4 – 6, 7) |
Final Exam
In Class: 10:30 – 12:30pm, December 6th
Take-Home: Noon, December 7th
Welcome to college math!
If this is your first math class taken in college, there are some important things you need to know. College math classes are run very differently from high school math classes. On the surface it may seem they are similar as you listen to the lecture and take notes, but there are significant underlying differences. Knowing these ahead of time can help you make the most of this coming semester.
#1: College math classes generally stay on the schedule in the syllabus. If there is one day allotted to the topic that is probably all of the class time that will be spent on it, even if “most” of the students “don’t get it.”
#2: It is expected that you will read the text and do the problems in order to learn the material, even if no one checks up on you. The instructor might never collect the homework, but that doesn’t mean it doesn’t affect your grade.
#3: You will sometimes be responsible for material in the textbook that is not covered in class. If there is a text reading and/or homework problems covering a concept that was not discussed in class, you are still expected to learn it. If you don’t understand it, make an appointment with your instructor for help.
#4: Some material is covered only in class, is not in the textbook, and may not have any homework problems on it. If you miss class, you may miss content that you are responsible to know. If you have an unavoidable absence, be sure to get the notes and any announcements from a classmate.
#5: There will be test questions that don’t look “just like the homework.” In college, you are expected to focus on learning the concepts, not just memorizing how to do certain types of problems. These concepts can – and will – appear in very different forms on tests and quizzes.
#6: At times you will be expected to be able to explain why a problem is done a certain way in addition to being expected to do the problem. As you work on problems in class and on homework, don’t be satisfied with getting the correct answer; ask yourself why that method is logical, and how you could explain that logic to someone else.
#7: Most importantly, you are responsible for your own learning. If you attend class faithfully, get the notes and announcements if you have an unavoidable absence, read the text, do the homework and question yourself (as in #6), and still don’t understand something, it is up to you to get the extra help you need. Visit the instructor during office hours or make a special appointment to ask questions, form a study group, etc. There are many resources and people willing and happy to help, but you need to take the initiative and seek out the help you need.
Good luck on a happy and successful semester!
Commitment to
Inclusive Excellence
WSU
recognizes that our individual differences can deepen our understanding of one
another and the world around us, rather than divide us. In this class, people
of all ethnicities, genders and gender identities, religions, ages, sexual
orientations, dis/abilities, socioeconomic backgrounds, regions, and
nationalities are strongly encouraged to share their rich array of perspectives
and experiences. If you feel your differences may in some way isolate you
from WSU’s community or if you have a need of any specific accommodations,
please speak with the instructor early in the semester about your concerns and
what we can do together to help you become an active and engaged member of our
class and community.
Campus
Resources
Details about
Campus Resources
·
Two good places to help you find resources of all kinds on
campus are Student Support/Campus Services and the Inclusion
and Diversity Office. Both offices are dedicated to helping students of all
racial, ethnic, economic, national, sexual, and gender identities. They can
facilitate tutoring and point you to a wide range of resources.
·
If you have a mental, physical, or learning disability,
the Access Services office can document it for your professors
and facilitate accommodations. If you have a documented disability that
requires accommodation, please contact Access Services as soon as possible.
·
College can be very stressful. Counseling offices
on both campuses are here to help you with a wide range of difficulties, ranging
from sexual assault, depression, and grief after the loss of a loved one to
stress management, anxiety, general adjustment to college, and many
others.
·
The KEAP-Diversity-Resource-Center Faculty Liaison can direct
people to multicultural resources on and off campus.
·
To find out about web registration, placement tests, program
requirements and support tools to help students succeed, visit the Advising
Services office and website for answers to all your questions!
·
For help with understanding the concepts of a particular class
or understanding the requirements of an assignment, Tutoring Services offers
three types of tutoring: drop-in appointments, 1-on-1 tutoring, and group
sessions. You can visit them in Krueger Library 220 or go on-line and use TutorTrac
to schedule a session, https://tutortrac.winona.edu/TracWeb40/Default.html.
·
For help specifically with writing and the development of
papers, the English department has a Writing Center that is
staffed by trained graduate students pursuing their Master’s degree in
English. The Writing Center is located in Minné Hall 348. You can
make an appointment on the sign-up sheet on the door or call 457-5505.
The Standard Disclaimer
applies.
© Eric Errthum, December 2017, all rights reserved.
