MATH 462 Introduction to Topology
Syllabus for Spring 2017
Tues & Fri, 9:00 – 9:50am
Gildemeister 326
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
· Introduction to Topology: Pure and Applied by Adams and Franzosa (use supplied pdf)
· Algebraic Topology by Hatcher (maybe)
No calculators will be needed on any quiz or exam, but might be required for some homework problems.
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
Video Responses (2 @ 30
points) 60
points
Quizzes (6 @ 30 points
each, drop lowest) 150 points
Midterms (3 @ 100
points) 300
points
Final (In-Class) 100
points
Final (Take-Home) 50
points
--------------
750 points total
Grades: A = 90%, B = 80%, C = 70%, D = 60%
Homework: You will be responsible for presenting and/or asking questions from the homeworks indicated on the dates below. Your grade will be based on preparedness, not necessarily correctness (though that’d be nice, too!)
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.
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.
Extra
Credit: There will be bonus
questions on quizzes and exams. If you’d like to do more extra credit, I will
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 |
Tuesday |
Friday |
|
1/9 |
1.1
Equivalence 1.2
Bijections |
1.3
Continuous Functions 7.1 General Metric Spaces |
|
1/16 |
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 |
Chapter 7 Activity Basis of a Topology 1.4
Topological Equivalence HW (pg 23): 5, 6, 7, 9, 11, 15 |
|
1/23 |
1.5,
cont. 7.3 General Connectedness HW (pg 226): 1, 2, 3, 6, 7 |
1.6
Isotopy Chapter 1 Activity Isotopic Letters
|
|
1/30 |
Chapter 1 Quiz Midterm I (take-home) |
Go over Midterm Overview of Knot Theory Read Chapter 2, but don’t think too much about it Other readings related to Knot Theory: Origins of Knot Theory (pdf) Relaxing an unknot (video) Application of polynomial algorithm (video) Knot Atlas (wiki) Two Knots, Same Coloribilty: 4_1 and 5_1 Unknotting Unknots (Read pages 1 – 3) Current Simplification Algorithm (Simplify Section) Polynomial Time Unknot Recognition (Read Intro Section) |
|
2/6 |
Video Essay Due: Sphere Inside Out 3.1 Surface Definitions HW (pg 95): 1, 4, 5, 7, 9
|
7.5 General Quotient Spaces 3.2 Cut-and-paste Techniques HW
(pg 230): 2, 4, 5 HW
(pg 101): 2, 3, 7, 8, 9, 11 |
|
2/13 |
3.2, cont 3.3 Euler Characteristic and Orientability HW
(pg 108): 1, 4, 6, 9, 11 |
3.4 Classification of Surfaces HW (pg 117): 2d, 3, 4bef, 6, 7, 9, 10 Chapter 3 Activity |
|
2/20 |
No Class |
Chapter
3 Quiz Midterm II (take-home) |
|
2/27 |
Go over Midterm II |
Video Essay Due: Wind and Mr. Ug and Section 4.1 HW (pg 129): 2, 4, 7, 8 |
|
3/6 |
Spring Break |
|
|
3/13 |
Section 4.2 HW (pg 134): 1, 3, 5, 6, 8 7.4 General Compactness HW (pg 228): 1, 3, 5, 6b, 8 |
Section 4.3 HW (pg 141): 2, 3, 4, 7 Chapter 4 Activity |
|
3/20 |
Chapter
4 Quiz HW (pg 172): 3, 4, 5abc, 6a |
Chapter 7 Quiz (Take-home) Section 6.2 HW (pg 177): 1, 4, 5, 6 Section 6.4 HW (pg 189): 1b, 2, 6, 9, 11, 12ab, 14ac, 15, 16, 17 |
|
3/27 |
Section 6.5 HW (pg 199): 5, 7, 8, 9, 10, 13 Section 6.6 HW (pg 207): 1, 5 |
Chapter 6 Activity Simplicial Complexes: This pdf Document HW (from the pdf): 1, 3, 5, 6, 7 |
|
4/3 |
Quiz Chapter 6 Midterm III (take-home) |
Go over Midterm III TBD |
|
4/10 |
TBD |
No Class |
|
4/17 |
TBD |
TBD |
|
4/24 |
TBD |
TBD |
Final Exam
In Class: TBD
Take-Home: TBD
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, religions, ages, sexual orientations, disabilities,
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 (Short version):
Campus
Resources (Long version):
The Standard Disclaimer
applies.
© Eric Errthum, January 2014, all
rights reserved.
