Assignments
Topology, Math 5520, Winter 2010

Course information.

Homework 1:   Due Friday, January 15.      Solutions
Homework 2: Sect. 2 # 1, 3, 5, 8, 9. Due Mon, Jan 25.      Solutions
Homework 3: Sect. 3 # 3, 4, 7, 8, 10. Due Mon, Feb 1. (Note change.)      Solutions
Homework 4: Sect. 4 # 2, 3, 6, 9 (discrete, indiscrete and finite). Due Mon, Feb 8.      Solutions
   In problem 6, part (a) should read

    "A set A is open iff each point P in A has a neighborhood contained in A."

Also note that the last part of the problem, "Show by an example ..." is not labelled (d), but might as well have been.
In problem 9, work out (a)-(d) for the three topologies 'discrete', 'indiscrete' and 'finite'.

Homework 5: Sect. 5 # 2d,f,g. and Sect. 6 # 2, 4. Due Mon, Feb 15.      Solutions

In section 6, problem 2, give an example of a mapping with no fixed point, to verify that the set you give does not have the fixed point property.

Homework 6: Sect. 7 # 1a,c,e, 5. Sect. 8 # 1,2. Due Mon, Feb 22.      Solutions
In Section 7, problem 1, you may find it easier to use the null-clines and the signs of x' and y' than to use the book's suggestion that you study the differential equation (2) (p. 45).

Midterm: Wednesday, March 3:      Test 1 and its solutions.

Homework 7: Sect. 13 # 1, 3, 4. Due Wed, Mar 10.      Solutions
Homework 8: Sect. 14 # 1, 4. Due Fri, Mar 12.      Solutions

Spring break: Mar 15-19

Homework 9: Sect. 19 # 1, 3, 4, 6. Due Wed, Mar 31.      Solutions

Here is some information of projective space , and
a little paper I wrote about the use of projective space (and other tools) in analyzing differential equations.

Homework 10: Sect. 20 # 5, 6. Due Mon, Apr 5.      Solutions

Homework 11: Sect. 21 # 1, 3, 4, 5. Due Fri, Apr 9.      Solutions
In problem 3(j), the triangle QVW should be added to the list.
In problem 4, do only the surfaces in problems 1 and 3.

Homework 12: Sect. 23 # 1a,b and c. Sect. 24 #12. Also, two not from the book:
Show that in an abelian group, the inverse of an element is unique.
Show that the cyclic group Z/6 is isomorphic to the product Z/2 x Z/3.
Due Mon, Apr 19.      Solutions

Sample final exam. Note that there is a typo in the drawing of the first polyhedron in number 2, namely a two headed arrow for one edge labelled 'a'. You can tell which direction is correct by looking at the other edge labelled 'a', to determine that it is oriented to go from P to Q.
Here are it's solutions.